From 574e5d54263ed607c02433be196858eb9f390e95 Mon Sep 17 00:00:00 2001 From: Copilot <198982749+Copilot@users.noreply.github.com> Date: Mon, 26 Oct 2026 18:20:57 +0000 Subject: [PATCH 01/30] python/ intersphinx cache should not store other files MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * python/pyproject.toml (docs): require sphinx>=9 for on-disk intersphinx inventory cache. * ‎.github/workflows/python.yml (build-doc): Cache only python/doc/_build/doctrees/__intersphinx_cache__/ Co-authored-by: MLopez-Ibanez <2620021+MLopez-Ibanez@users.noreply.github.com> --- .github/workflows/python.yml | 2 +- python/pyproject.toml | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/.github/workflows/python.yml b/.github/workflows/python.yml index 7ee6898a5..77d4e406f 100644 --- a/.github/workflows/python.yml +++ b/.github/workflows/python.yml @@ -144,7 +144,7 @@ jobs: - name: Cache intersphinx inventories uses: actions/cache@v5 with: - path: python/doc/_build/doctrees/ + path: python/doc/_build/doctrees/__intersphinx_cache__/ key: intersphinx-${{ hashFiles('python/doc/source/conf.py') }} restore-keys: intersphinx- diff --git a/python/pyproject.toml b/python/pyproject.toml index e3672ff31..f36004a7d 100644 --- a/python/pyproject.toml +++ b/python/pyproject.toml @@ -70,7 +70,7 @@ docs = [ "plotly", "pydata-sphinx-theme>=0.16", "seaborn", - "sphinx>=6", + "sphinx>=9", "sphinx-autodoc-typehints", "sphinx-copybutton", "sphinx-design", From 94d54082492ad9acdfc0599f92d258d02ac6882f Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 17:34:39 +0300 Subject: [PATCH 02/30] c/ Implement crossover operators * c/crossover.c, c/crossover.h: New. * c/rng.h (rng_integer): New. * c/Makefile: Add crossover.c and crossover.h. * c/NEWS.md: Document. --- c/Makefile | 3 + c/NEWS.md | 3 + c/crossover.c | 409 ++++++++++++++++++++++++++++++++++++++++++++++++++ c/crossover.h | 92 ++++++++++++ c/rng.h | 8 + 5 files changed, 515 insertions(+) create mode 100644 c/crossover.c create mode 100644 c/crossover.h diff --git a/c/Makefile b/c/Makefile index 81922b8d6..919cc075b 100644 --- a/c/Makefile +++ b/c/Makefile @@ -56,6 +56,7 @@ BINDIR:=$(abspath $(BINDIR)) ## Define source files SRCS = avl.c \ cmdline.c \ + crossover.c \ dominatedsets.c \ eaf3d.c \ eaf.c \ @@ -90,6 +91,7 @@ HDRS = avl.h \ cmdline.h \ common.h \ config.h \ + crossover.h \ cvector.h \ eaf.h \ epsilon.h \ @@ -208,6 +210,7 @@ $(EXE_FILES): cmdline.o io.o avl.o: avl.h cmdline.o: cmdline.h io.h +crossover.o: crossover.h rng.h mt19937/mt19937.h dominatedsets.o: cmdline.h io.h nondominated.h epsilon.h eaf.o: eaf.h io.h bit_array.h cvector.h eaf3d.o: eaf.h io.h bit_array.h cvector.h avl.h diff --git a/c/NEWS.md b/c/NEWS.md index 317b10c1d..ebcb229c8 100644 --- a/c/NEWS.md +++ b/c/NEWS.md @@ -3,6 +3,9 @@ ## 0.20 * radixsort.h, insort.h: New. + * crossover.c, crossover.h: New crossover operators (uniform, single-point, + blend-alpha, single arithmetic, local, bounded exponential, differential + evolution and parent-centric). * main-nondominated.c: Renamed from nondominated.c. * hv and hvapprox executables now use -U instead of -u for --union to be consistent with nondominated. diff --git a/c/crossover.c b/c/crossover.c new file mode 100644 index 000000000..061e71c0b --- /dev/null +++ b/c/crossover.c @@ -0,0 +1,409 @@ +/************************************************************************* + + crossover.c + + Crossover operators for real-valued (and, for uniform and single-point + crossover, any numerical) decision vectors. See crossover.h for the + conventions shared by all functions. + + --------------------------------------------------------------------- + + Copyright (C) 2026 + Bhupinder Saini + + This Source Code Form is subject to the terms of the Mozilla Public + License, v. 2.0. If a copy of the MPL was not distributed with this + file, You can obtain one at https://mozilla.org/MPL/2.0/. + + ---------------------------------------------------------------------- + + +*************************************************************************/ +#include +#include // memcpy(), memmove() +#include +#include "common.h" +#include "crossover.h" +#include "rng.h" + +// parent_centric_crossover() treats an index parent this close to the +// centroid of its three parents as degenerate. +#define PCX_DEGENERATE 1e-12 + +static inline double +clamp_to_bounds(double x, double lower, double upper) +{ + return fmin(fmax(x, lower), upper); +} + +/* Rows I and I + 1 of PARENTS mate and their children go to rows I and I + 1 + of OFFSPRING. If I + 1 == N, row I mates with row 0 and its second child + goes to SCRATCH, so it is discarded. */ +static inline void +get_pair(const double * parents, double * offspring, double * scratch, + size_t i, size_t n, size_t nvar, + const double ** p1, const double ** p2, double ** c1, double ** c2) +{ + const bool last = (i + 1 == n); + *p1 = parents + i * nvar; + *p2 = parents + (last ? 0 : i + 1) * nvar; + *c1 = offspring + i * nvar; + *c2 = last ? scratch : offspring + (i + 1) * nvar; +} + +static inline double * +scratch_new(size_t n, size_t nvar) +{ + return (n % 2 == 1) ? MOOCORE_MALLOC(nvar, double) : NULL; +} + +/* Draw K distinct indices in [0, N) that also differ from the NEXCLUDED + indices in EXCLUDED. EXCLUDED must be sorted in ascending order and have + room for K more values. Each draw picks among the indices not yet excluded + and shifts the result past the excluded ones, so there is no rejection + loop. */ +static void +sample_distinct(rng_state * rng, size_t n, size_t * excluded, size_t nexcluded, + size_t k, size_t * chosen) +{ + for (size_t c = 0; c < k; c++, nexcluded++) { + ASSUME(n > nexcluded); + size_t d = rng_integer(rng, n - nexcluded); + size_t pos = 0; + while (pos < nexcluded && excluded[pos] <= d) { + d++; + pos++; + } + // Insert D at POS to keep EXCLUDED sorted. + memmove(excluded + pos + 1, excluded + pos, + (nexcluded - pos) * sizeof(*excluded)); + excluded[pos] = d; + chosen[c] = d; + } +} + +void +uniform_crossover(double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, double swap_prob, double pair_prob, + uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 1); + rng_state * rng = rng_new(seed); + double * scratch = scratch_new(n, nvar); + for (size_t i = 0; i < n; i += 2) { + const double *p1, *p2; + double *c1, *c2; + get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + const bool recombine = rng_random(rng) < pair_prob; + for (size_t j = 0; j < nvar; j++) { + const bool swap = recombine && rng_random(rng) < swap_prob; + c1[j] = swap ? p2[j] : p1[j]; + c2[j] = swap ? p1[j] : p2[j]; + } + } + free(scratch); + rng_free(rng); +} + +void +single_point_crossover(double * restrict offspring, + const double * restrict parents, + size_t n, size_t nvar, uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 2); + rng_state * rng = rng_new(seed); + double * scratch = scratch_new(n, nvar); + for (size_t i = 0; i < n; i += 2) { + const double *p1, *p2; + double *c1, *c2; + get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + // Cut point in [1, nvar - 1], so each child takes at least one + // variable from each parent. + const size_t cut = 1 + rng_integer(rng, nvar - 1); + memcpy(c1, p1, cut * sizeof(*c1)); + memcpy(c1 + cut, p2 + cut, (nvar - cut) * sizeof(*c1)); + memcpy(c2, p2, cut * sizeof(*c2)); + memcpy(c2 + cut, p1 + cut, (nvar - cut) * sizeof(*c2)); + } + free(scratch); + rng_free(rng); +} + +void +blend_alpha_crossover(double * restrict offspring, + const double * restrict parents, + size_t n, size_t nvar, const double * restrict lower, + const double * restrict upper, double alpha, + uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 1); + ASSUME(alpha >= 0); + rng_state * rng = rng_new(seed); + for (size_t i = 0; i < n; i += 2) { + const double * p1 = parents + i * nvar; + const double * p2 = parents + ((i + 1 < n) ? i + 1 : 0) * nvar; + double * child = offspring + (i / 2) * nvar; + for (size_t j = 0; j < nvar; j++) { + const double lo = fmin(p1[j], p2[j]); + const double hi = fmax(p1[j], p2[j]); + const double span = hi - lo; + // Widen [lo, hi] by ALPHA * SPAN on each side, clip it to the + // bounds and sample uniformly from it. + const double a = fmax(lo - alpha * span, lower[j]); + const double b = fmin(hi + alpha * span, upper[j]); + child[j] = a + rng_random(rng) * (b - a); + } + } + rng_free(rng); +} + +void +single_arithmetic_crossover(double * restrict offspring, + const double * restrict parents, + size_t n, size_t nvar, double pair_prob, + uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 1); + rng_state * rng = rng_new(seed); + double * scratch = scratch_new(n, nvar); + for (size_t i = 0; i < n; i += 2) { + const double *p1, *p2; + double *c1, *c2; + get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + const bool recombine = rng_random(rng) < pair_prob; + const size_t k = rng_integer(rng, nvar); + memcpy(c1, p1, nvar * sizeof(*c1)); + memcpy(c2, p2, nvar * sizeof(*c2)); + if (recombine) + c1[k] = c2[k] = 0.5 * (p1[k] + p2[k]); + } + free(scratch); + rng_free(rng); +} + +void +local_crossover(double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 1); + rng_state * rng = rng_new(seed); + double * scratch = scratch_new(n, nvar); + for (size_t i = 0; i < n; i += 2) { + const double *p1, *p2; + double *c1, *c2; + get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + for (size_t j = 0; j < nvar; j++) { + const double a = rng_random(rng); + c1[j] = a * p1[j] + (1 - a) * p2[j]; + c2[j] = (1 - a) * p1[j] + a * p2[j]; + } + } + free(scratch); + rng_free(rng); +} + +/* Child of parent value X. It moves X by BETA * SPAN, where BETA follows a + two-sided exponential distribution with scale SCALE, truncated so that the + child stays within [LOWER, UPPER]. U and R are uniform in [0, 1). */ +static inline double +bex_child(double x, double span, double lower, double upper, double scale, + double u, double r) +{ + double beta; + if (r < 0.5) { + const double e = exp((lower - x) / (scale * span)); + // 1 - U is in (0, 1], which avoids log(0) when LOWER is -INFINITY. + beta = scale * log(e + (1 - u) * (1 - e)); + } else { + const double e = exp((x - upper) / (scale * span)); + beta = -scale * log(1 - u * (1 - e)); + } + // Rounding may step just outside the bounds. + return clamp_to_bounds(x + beta * span, lower, upper); +} + +void +bounded_exponential_crossover(double * restrict offspring, + const double * restrict parents, + size_t n, size_t nvar, + const double * restrict lower, + const double * restrict upper, double scale, + double pair_prob, double swap_prob, + uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 1); + ASSUME(scale > 0); + rng_state * rng = rng_new(seed); + double * scratch = scratch_new(n, nvar); + for (size_t i = 0; i < n; i += 2) { + const double *p1, *p2; + double *c1, *c2; + get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + if (!(rng_random(rng) < pair_prob)) { + memcpy(c1, p1, nvar * sizeof(*c1)); + memcpy(c2, p2, nvar * sizeof(*c2)); + continue; + } + for (size_t j = 0; j < nvar; j++) { + // The distance between the parents scales the move of both + // children, whichever parent is smaller. + const double span = fabs(p2[j] - p1[j]); + if (span == 0) { + c1[j] = p1[j]; + c2[j] = p2[j]; + continue; + } + // Both children use the same random numbers. + const double u = rng_random(rng); + const double r = rng_random(rng); + c1[j] = bex_child(p1[j], span, lower[j], upper[j], scale, u, r); + c2[j] = bex_child(p2[j], span, lower[j], upper[j], scale, u, r); + if (swap_prob > 0 && rng_random(rng) < swap_prob) { + const double tmp = c1[j]; + c1[j] = c2[j]; + c2[j] = tmp; + } + } + } + free(scratch); + rng_free(rng); +} + +void +de_rand_1_bin_crossover(double * restrict offspring, + const double * restrict population, + size_t n, size_t nvar, const size_t * restrict targets, + size_t ntargets, const double * restrict lower, + const double * restrict upper, double scaling_factor, + double crossover_rate, uint32_t seed) +{ + ASSUME(n >= 4 && nvar >= 1); + rng_state * rng = rng_new(seed); + for (size_t t = 0; t < ntargets; t++) { + ASSUME(targets[t] < n); + const double * x = population + targets[t] * nvar; + size_t excluded[4] = { targets[t] }; + size_t r[3]; + sample_distinct(rng, n, excluded, 1, 3, r); + const double * x1 = population + r[0] * nvar; + const double * x2 = population + r[1] * nvar; + const double * x3 = population + r[2] * nvar; + // The child takes at least the variable JRAND from the mutant. + const size_t jrand = rng_integer(rng, nvar); + double * child = offspring + t * nvar; + for (size_t j = 0; j < nvar; j++) { + const double v = (j == jrand || rng_random(rng) < crossover_rate) + ? x1[j] + scaling_factor * (x2[j] - x3[j]) + : x[j]; + child[j] = clamp_to_bounds(v, lower[j], upper[j]); + } + } + rng_free(rng); +} + +void +de_current_1_crossover(double * restrict offspring, + const double * restrict population, + size_t n, size_t nvar, const size_t * restrict targets, + size_t ntargets, const double * restrict lower, + const double * restrict upper, double scaling_factor, + double crossover_rate, uint32_t seed) +{ + ASSUME(n >= 2 && nvar >= 1); + rng_state * rng = rng_new(seed); + for (size_t t = 0; t < ntargets; t++) { + ASSUME(targets[t] < n); + const double * x = population + targets[t] * nvar; + // The two donors differ from each other, but either may be the target. + size_t excluded[2]; + size_t r[2]; + sample_distinct(rng, n, excluded, 0, 2, r); + const double * x1 = population + r[0] * nvar; + const double * x2 = population + r[1] * nvar; + double * child = offspring + t * nvar; + for (size_t j = 0; j < nvar; j++) { + const double v = (rng_random(rng) < crossover_rate) + ? x[j] + scaling_factor * (x1[j] - x2[j]) + : x[j]; + child[j] = clamp_to_bounds(v, lower[j], upper[j]); + } + } + rng_free(rng); +} + +void +parent_centric_crossover(double * restrict offspring, + const double * restrict population, + size_t n, size_t nvar, + const size_t * restrict targets, size_t ntargets, + const double * restrict lower, + const double * restrict upper, + double sigma_zeta, double sigma_eta, uint32_t seed) +{ + ASSUME(n >= 3 && nvar >= 1); + rng_state * rng = rng_new(seed); + double * direction = MOOCORE_MALLOC(3 * nvar, double); + double * unit = direction + nvar; + double * orthogonal = unit + nvar; + for (size_t t = 0; t < ntargets; t++) { + ASSUME(targets[t] < n); + const double * x = population + targets[t] * nvar; + size_t excluded[3] = { targets[t] }; + size_t r[2]; + sample_distinct(rng, n, excluded, 1, 2, r); + const double * others[2] = { population + r[0] * nvar, + population + r[1] * nvar }; + + // Direction from the centroid of the three parents to the index + // parent X. + double norm = 0; + for (size_t j = 0; j < nvar; j++) { + direction[j] = x[j] - (x[j] + others[0][j] + others[1][j]) / 3; + norm += direction[j] * direction[j]; + } + norm = sqrt(norm); + const bool degenerate = norm < PCX_DEGENERATE; + const double divisor = degenerate ? 1 : norm; + for (size_t j = 0; j < nvar; j++) + unit[j] = direction[j] / divisor; + + // Mean distance from the other two parents to the line through X + // along DIRECTION. + double spread = 0; + for (int k = 0; k < 2; k++) { + const double * o = others[k]; + double along = 0; + for (size_t j = 0; j < nvar; j++) + along += (o[j] - x[j]) * unit[j]; + double dist = 0; + for (size_t j = 0; j < nvar; j++) { + const double perp = (o[j] - x[j]) - along * unit[j]; + dist += perp * perp; + } + spread += sqrt(dist); + } + spread /= 2; + + // Gaussian noise with its component along DIRECTION removed. This + // has the same distribution as summing independent normal steps + // along an orthonormal basis of the subspace orthogonal to DIRECTION. + double proj = 0; + for (size_t j = 0; j < nvar; j++) { + orthogonal[j] = sigma_eta * rng_standard_normal(rng); + proj += orthogonal[j] * unit[j]; + } + if (!degenerate) { + for (size_t j = 0; j < nvar; j++) + orthogonal[j] -= proj * unit[j]; + } + const double zeta = sigma_zeta * rng_standard_normal(rng); + + double * child = offspring + t * nvar; + for (size_t j = 0; j < nvar; j++) + child[j] = clamp_to_bounds( + x[j] + zeta * direction[j] + spread * orthogonal[j], + lower[j], upper[j]); + } + free(direction); + rng_free(rng); +} diff --git a/c/crossover.h b/c/crossover.h new file mode 100644 index 000000000..30118d9c6 --- /dev/null +++ b/c/crossover.h @@ -0,0 +1,92 @@ +/************************************************************************* + + crossover.h + + --------------------------------------------------------------------- + + Copyright (C) 2026 + Bhupinder Saini + + This Source Code Form is subject to the terms of the Mozilla Public + License, v. 2.0. If a copy of the MPL was not distributed with this + file, You can obtain one at https://mozilla.org/MPL/2.0/. + + ---------------------------------------------------------------------- + + +*************************************************************************/ +#ifndef CROSSOVER_H_ +#define CROSSOVER_H_ + +#include +#include // uint32_t +#include "libmoocore-config.h" + +// C++ needs to know that types and declarations are C, not C++. +BEGIN_C_DECLS + +/* + All matrices are stored by rows, one decision vector per row, with NVAR + variables each. OFFSPRING must be allocated by the caller. + + Two-parent operators mate rows 2i and 2i+1 of PARENTS (N rows). If N is + odd, the last row mates with row 0. Operators that produce two children per + pair write them to rows 2i and 2i+1 of OFFSPRING (N rows), dropping the + second child of the last pair when N is odd. blend_alpha_crossover() + produces one child per pair, so OFFSPRING has (N + 1) / 2 rows. + + Population-based operators produce one child per row index in TARGETS + (NTARGETS values in [0, N)), so OFFSPRING has NTARGETS rows. + + LOWER and UPPER give the bounds of each variable. Use -INFINITY and + INFINITY for unbounded variables. +*/ + +MOOCORE_API void uniform_crossover( + double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, double swap_prob, double pair_prob, uint32_t seed); + +MOOCORE_API void single_point_crossover( + double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, uint32_t seed); + +MOOCORE_API void blend_alpha_crossover( + double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, const double * restrict lower, + const double * restrict upper, double alpha, uint32_t seed); + +MOOCORE_API void single_arithmetic_crossover( + double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, double pair_prob, uint32_t seed); + +MOOCORE_API void local_crossover( + double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, uint32_t seed); + +MOOCORE_API void bounded_exponential_crossover( + double * restrict offspring, const double * restrict parents, + size_t n, size_t nvar, const double * restrict lower, + const double * restrict upper, double scale, double pair_prob, + double swap_prob, uint32_t seed); + +MOOCORE_API void de_rand_1_bin_crossover( + double * restrict offspring, const double * restrict population, + size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, + const double * restrict lower, const double * restrict upper, + double scaling_factor, double crossover_rate, uint32_t seed); + +MOOCORE_API void de_current_1_crossover( + double * restrict offspring, const double * restrict population, + size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, + const double * restrict lower, const double * restrict upper, + double scaling_factor, double crossover_rate, uint32_t seed); + +MOOCORE_API void parent_centric_crossover( + double * restrict offspring, const double * restrict population, + size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, + const double * restrict lower, const double * restrict upper, + double sigma_zeta, double sigma_eta, uint32_t seed); + +END_C_DECLS + +#endif // CROSSOVER_H_ diff --git a/c/rng.h b/c/rng.h index 3b5a65cc7..892140218 100644 --- a/c/rng.h +++ b/c/rng.h @@ -37,6 +37,14 @@ rng_uniform(rng_state * rng, double low, double high) return low + (high - low) * rng_random(rng); } +/* Returns an integer between [0, n) */ +static inline size_t +rng_integer(rng_state * rng, size_t n) +{ + assert(n > 0); + return STATIC_CAST(size_t, rng_random(rng) * STATIC_CAST(double, n)); +} + double rng_standard_normal(rng_state *rng); void rng_bivariate_normal_fill(rng_state * rng, From 03537c3a9e1a75b2189ada27389831a4554c922d Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 17:34:40 +0300 Subject: [PATCH 03/30] python/ Add crossover operators * python/src/moocore/_crossover.py: New. * python/src/moocore/__init__.py: Export the crossover functions. * python/src/moocore/_docsubstitute.py (COMMON_PARAMS): Add parents, pair_offspring, population, targets, lower_bound and upper_bound. * python/src/moocore/_ffi_build.py: Compile crossover.c. * python/src/moocore/libmoocore.h: Declare the crossover functions. * python/tests/test_crossover.py: New. --- python/src/moocore/__init__.py | 21 + python/src/moocore/_crossover.py | 830 +++++++++++++++++++++++++++ python/src/moocore/_docsubstitute.py | 16 + python/src/moocore/_ffi_build.py | 2 + python/src/moocore/libmoocore.h | 11 + python/tests/test_crossover.py | 392 +++++++++++++ 6 files changed, 1272 insertions(+) create mode 100644 python/src/moocore/_crossover.py create mode 100644 python/tests/test_crossover.py diff --git a/python/src/moocore/__init__.py b/python/src/moocore/__init__.py index d07f559f0..1e7aaa5ba 100644 --- a/python/src/moocore/__init__.py +++ b/python/src/moocore/__init__.py @@ -38,6 +38,18 @@ from ._generate import generate_ndset, generate_sequence +from ._crossover import ( + blend_alpha_crossover, + bounded_exponential_crossover, + de_current_1_crossover, + de_rand_1_bin_crossover, + local_crossover, + parent_centric_crossover, + single_arithmetic_crossover, + single_point_crossover, + uniform_crossover, +) + from importlib.metadata import version as _metadata_version __version__ = _metadata_version("moocore") @@ -52,6 +64,10 @@ "any_dominated", "apply_within_sets", "avg_hausdorff_dist", + "blend_alpha_crossover", + "bounded_exponential_crossover", + "de_current_1_crossover", + "de_rand_1_bin_crossover", "eaf", "eafdiff", "epsilon_additive", @@ -70,11 +86,16 @@ "is_nondominated", "is_nondominated_within_sets", "largest_eafdiff", + "local_crossover", "normalise", + "parent_centric_crossover", "pareto_rank", "r2_exact", "read_datasets", + "single_arithmetic_crossover", + "single_point_crossover", "total_whv_rect", + "uniform_crossover", "vorob_dev", "vorob_t", "whv_hype", diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py new file mode 100644 index 000000000..ef9a6f162 --- /dev/null +++ b/python/src/moocore/_crossover.py @@ -0,0 +1,830 @@ +from collections.abc import Callable +from typing import Any + +import numpy as np +from numpy.typing import ArrayLike + +from ._docsubstitute import DocSubstitute +from ._libmoocore import ffi, lib +from ._utils import _get_seed_for_c, array_1d_of_length_n, np2d_to_double_array + + +def _as_matrix(x: ArrayLike, name: str, min_rows: int) -> np.ndarray: + x = np.asarray(x, dtype=float) + if x.ndim != 2 or x.shape[1] == 0: + raise ValueError(f"{name!r} must be a 2D array with at least 1 column") + if x.shape[0] < min_rows: + raise ValueError(f"{name!r} must have at least {min_rows} rows") + return x + + +def _check_probability(value: float, name: str) -> float: + if not 0 <= value <= 1: + raise ValueError(f"{name!r} must be within [0, 1]") + return float(value) + + +def _check_positive(value: float, name: str) -> float: + if not value > 0: + raise ValueError(f"{name!r} must be larger than 0") + return float(value) + + +def _bounds( + lower: ArrayLike | None, upper: ArrayLike | None, nvar: int +) -> tuple[np.ndarray, np.ndarray]: + if lower is None: + lower = np.full(nvar, -np.inf) + else: + lower = array_1d_of_length_n( + np.asarray(lower, dtype=float), nvar, name="lower" + ) + if upper is None: + upper = np.full(nvar, np.inf) + else: + upper = array_1d_of_length_n( + np.asarray(upper, dtype=float), nvar, name="upper" + ) + if np.any(lower > upper): + raise ValueError("'lower' must not be larger than 'upper'") + return np.ascontiguousarray(lower), np.ascontiguousarray(upper) + + +def _targets(targets: ArrayLike | None, n: int) -> np.ndarray: + if targets is None: + return np.arange(n, dtype=np.uintp) + targets = np.atleast_1d(targets) + if targets.ndim != 1 or ( + targets.size > 0 and not np.issubdtype(targets.dtype, np.integer) + ): + raise ValueError("'targets' must be a 1D vector of row indices") + if np.any((targets < 0) | (targets >= n)): + raise ValueError(f"'targets' must be row indices within [0, {n - 1}]") + return np.ascontiguousarray(targets, dtype=np.uintp) + + +def _call( + fun: Callable[..., None], x: np.ndarray, nrows: int, *args: Any +) -> np.ndarray: + """Call the C function ``fun`` and return the offspring it writes.""" + out = np.empty((nrows, x.shape[1]), dtype=float) + x_p, n, nvar = np2d_to_double_array(x, ctype_shape=("size_t", "size_t")) + fun(ffi.from_buffer("double []", out), x_p, n, nvar, *args) + return out + + +def _keep_dtype(out: np.ndarray, dtype: np.dtype) -> np.ndarray: + if np.issubdtype(dtype, np.integer) or np.issubdtype(dtype, np.bool_): + return out.astype(dtype) + return out + + +def _call_with_targets( + fun: Callable[..., None], + population: np.ndarray, + targets: np.ndarray, + lower: np.ndarray, + upper: np.ndarray, + *args: Any, +) -> np.ndarray: + return _call( + fun, + population, + len(targets), + ffi.from_buffer("size_t []", targets), + len(targets), + ffi.from_buffer("double []", lower), + ffi.from_buffer("double []", upper), + *args, + ) + + +@DocSubstitute() +def uniform_crossover( + parents: ArrayLike, + /, + *, + swap_prob: float = 0.5, + pair_prob: float = 1.0, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Uniform crossover. + + Each pair of parents produces two children. With probability + ``pair_prob``, each variable is swapped between the two children with + probability ``swap_prob``. Otherwise, the children are copies of their + parents. + + The children only take values from their parents, so this operator works + for binary, integer and real-valued variables alike. Integer and Boolean + inputs keep their dtype. + + Parameters + ---------- + parents : + ${parents} + swap_prob : + Probability of swapping each variable between the two children. + pair_prob : + Probability of recombining each pair of parents. + seed : + ${random_seed} + + Returns + ------- + ${pair_offspring} + + See Also + -------- + single_point_crossover : Exchange the tails of two parents. + + Notes + ----- + Uniform crossover was proposed by :footcite:t:`Syswerda89`. See also + :footcite:t:`EibSmi2003`. + + References + ---------- + .. footbibliography:: + + Examples + -------- + >>> parents = np.array([[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1]]) + >>> moocore.uniform_crossover(parents, seed=5) + array([[0, 1, 0, 1, 0, 0], + [1, 0, 1, 0, 1, 1]]) + + """ + dtype = np.asarray(parents).dtype + parents = _as_matrix(parents, "parents", min_rows=2) + swap_prob = _check_probability(swap_prob, "swap_prob") + pair_prob = _check_probability(pair_prob, "pair_prob") + out = _call( + lib.uniform_crossover, + parents, + len(parents), + swap_prob, + pair_prob, + _get_seed_for_c(seed), + ) + return _keep_dtype(out, dtype) + + +@DocSubstitute() +def single_point_crossover( + parents: ArrayLike, + /, + *, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Single-point crossover. + + Each pair of parents produces two children. A cut point :math:`k` is drawn + uniformly from :math:`\{1, \dots, n_\text{var} - 1\}`. The first child + takes the first :math:`k` variables from the first parent and the rest from + the second parent, and the second child takes the complement. + + The children only take values from their parents, so this operator works + for binary, integer and real-valued variables alike. Integer and Boolean + inputs keep their dtype. + + Parameters + ---------- + parents : + ${parents} It must have at least 2 columns. + seed : + ${random_seed} + + Returns + ------- + ${pair_offspring} + + See Also + -------- + uniform_crossover : Swap each variable independently. + + Notes + ----- + Single-point crossover is the classical crossover of genetic algorithms + :footcite:p:`Hol75,Goldberg89`. + + References + ---------- + .. footbibliography:: + + Examples + -------- + >>> parents = np.array([[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1]]) + >>> moocore.single_point_crossover(parents, seed=42) + array([[0, 0, 1, 1, 1, 1], + [1, 1, 0, 0, 0, 0]]) + + """ + dtype = np.asarray(parents).dtype + parents = _as_matrix(parents, "parents", min_rows=2) + if parents.shape[1] < 2: + raise ValueError("'parents' must have at least 2 columns") + out = _call( + lib.single_point_crossover, + parents, + len(parents), + _get_seed_for_c(seed), + ) + return _keep_dtype(out, dtype) + + +@DocSubstitute() +def blend_alpha_crossover( + parents: ArrayLike, + /, + *, + lower: ArrayLike | None = None, + upper: ArrayLike | None = None, + alpha: float = 0.5, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Blend crossover (BLX-:math:`\alpha`). + + Each pair of parents :math:`x, y` produces **one** child :math:`z`. For + each variable :math:`j`, let :math:`m_j = \min(x_j, y_j)`, :math:`M_j = + \max(x_j, y_j)` and :math:`d_j = M_j - m_j`. Then :math:`z_j` is sampled + uniformly from :math:`[m_j - \alpha d_j, M_j + \alpha d_j]`, clipped to + the bounds of the variable. + + Parameters + ---------- + parents : + ${parents} + lower : + ${lower_bound} + upper : + ${upper_bound} + alpha : + Fraction of the distance between the parents by which the sampling + interval extends beyond them on each side. With ``alpha=0``, children + lie between their parents. + seed : + ${random_seed} + + Returns + ------- + Array with :math:`\lceil n/2 \rceil` rows, where :math:`n` is the + number of rows of ``parents``. Row ``i`` is the child of rows ``2i`` + and ``2i + 1`` of ``parents``. + + See Also + -------- + local_crossover : Children inside the box spanned by the parents. + + Notes + ----- + BLX-:math:`\alpha` was proposed by :footcite:t:`EshSch1992`. Each variable + is sampled independently, so the children fill the whole (clipped) box + around the parents. + + To produce more than one child per pair, call the function again. If + ``seed`` is an integer, every call returns the same children. Pass the + same :class:`numpy.random.Generator` to every call to get different + children each time, as in the example below. + + References + ---------- + .. footbibliography:: + + Examples + -------- + >>> parents = np.array([[0.2, 0.2], [0.6, 0.8]]) + >>> rng = np.random.default_rng(42) + >>> moocore.blend_alpha_crossover(parents, lower=0, upper=1, seed=rng) + array([[0.63478113, 0.52182563]]) + >>> moocore.blend_alpha_crossover(parents, lower=0, upper=1, seed=rng) + array([[0.21852882, 0.04409984]]) + + """ + parents = _as_matrix(parents, "parents", min_rows=2) + lower, upper = _bounds(lower, upper, parents.shape[1]) + if not alpha >= 0: + raise ValueError("'alpha' must be non-negative") + return _call( + lib.blend_alpha_crossover, + parents, + (len(parents) + 1) // 2, + ffi.from_buffer("double []", lower), + ffi.from_buffer("double []", upper), + float(alpha), + _get_seed_for_c(seed), + ) + + +@DocSubstitute() +def single_arithmetic_crossover( + parents: ArrayLike, + /, + *, + pair_prob: float = 1.0, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Single arithmetic crossover. + + Each pair of parents :math:`x, y` produces two children. With probability + ``pair_prob``, one variable :math:`k` is chosen uniformly at random and + both children get :math:`(x_k + y_k) / 2` in that variable. All other + variables are copied from the parents. Otherwise, the children are copies + of their parents. + + Parameters + ---------- + parents : + ${parents} + pair_prob : + Probability of recombining each pair of parents. + seed : + ${random_seed} + + Returns + ------- + ${pair_offspring} + + See Also + -------- + local_crossover : Recombine every variable with a random weight. + + Notes + ----- + This operator is described by :footcite:t:`EibSmi2003` and compared with + other real-coded crossover operators by Picek, Jakobovic and Golub (2013). + + References + ---------- + .. footbibliography:: + + S. Picek, D. Jakobovic and M. Golub (2013). On the recombination operator + in the real-coded genetic algorithms. *2013 IEEE Congress on Evolutionary + Computation*, pages 3103--3110. https://doi.org/10.1109/CEC.2013.6557948 + + Examples + -------- + >>> parents = np.array([[0.0, 0.0, 0.0, 0.0], [1.0, 1.0, 1.0, 1.0]]) + >>> moocore.single_arithmetic_crossover(parents, seed=42) + array([[0. , 0. , 0. , 0.5], + [1. , 1. , 1. , 0.5]]) + + """ + parents = _as_matrix(parents, "parents", min_rows=2) + pair_prob = _check_probability(pair_prob, "pair_prob") + return _call( + lib.single_arithmetic_crossover, + parents, + len(parents), + pair_prob, + _get_seed_for_c(seed), + ) + + +@DocSubstitute() +def local_crossover( + parents: ArrayLike, + /, + *, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Local crossover. + + Each pair of parents :math:`x, y` produces two children + + .. math:: + u_j = a_j x_j + (1 - a_j) y_j, \qquad v_j = (1 - a_j) x_j + a_j y_j, + + where each weight :math:`a_j` is drawn uniformly from :math:`[0, 1)`. The + children lie in the box spanned by their parents, and :math:`u + v = x + + y`. + + Parameters + ---------- + parents : + ${parents} + seed : + ${random_seed} + + Returns + ------- + ${pair_offspring} + + See Also + -------- + single_arithmetic_crossover : Average a single variable. + blend_alpha_crossover : Sample around the parents. + + Notes + ----- + This operator is described by Dumitrescu et al. (2000) and compared with + other real-coded crossover operators by Picek, Jakobovic and Golub (2013). + + References + ---------- + D. Dumitrescu, B. Lazzerini, L. C. Jain and A. Dumitrescu (2000). + *Evolutionary Computation*. CRC Press. https://doi.org/10.1201/9781482273960 + + S. Picek, D. Jakobovic and M. Golub (2013). On the recombination operator + in the real-coded genetic algorithms. *2013 IEEE Congress on Evolutionary + Computation*, pages 3103--3110. https://doi.org/10.1109/CEC.2013.6557948 + + Examples + -------- + >>> parents = np.array([[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]]) + >>> moocore.local_crossover(parents, seed=42) + array([[0.62545988, 0.04928569, 0.26800606], + [0.37454012, 0.95071431, 0.73199394]]) + + """ + parents = _as_matrix(parents, "parents", min_rows=2) + return _call( + lib.local_crossover, + parents, + len(parents), + _get_seed_for_c(seed), + ) + + +@DocSubstitute() +def bounded_exponential_crossover( + parents: ArrayLike, + /, + *, + lower: ArrayLike | None = None, + upper: ArrayLike | None = None, + scale: float = 0.1, + pair_prob: float = 1.0, + swap_prob: float = 0.0, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Bounded exponential crossover (BEX). + + Each pair of parents :math:`x, y` produces two children :math:`u, v` with + probability ``pair_prob``; otherwise, the children are copies of their + parents. For each variable :math:`j` with :math:`d_j = |x_j - y_j| > 0`, + + .. math:: + u_j = x_j + \beta_j^x d_j, \qquad v_j = y_j + \beta_j^y d_j, + + where :math:`\beta_j^x` follows an exponential distribution with scale + :math:`\lambda` (``scale``), truncated so that :math:`u_j` stays within + the bounds of the variable. With probability 1/2, a child moves towards + the lower bound :math:`l_j`, with :math:`\beta = \lambda \ln(e_l + r(1 - + e_l))` and :math:`e_l = \exp((l_j - x_j) / (\lambda d_j))`. Otherwise, it + moves towards the upper bound :math:`h_j`, with :math:`\beta = -\lambda + \ln(1 - r(1 - e_h))` and :math:`e_h = \exp((x_j - h_j) / (\lambda d_j))`. + The uniform random number :math:`r` and the direction are shared by both + children. Variables where the parents are equal are copied. + + After that, each variable is swapped between the two children with + probability ``swap_prob``, as in :func:`uniform_crossover`. + + Parameters + ---------- + parents : + ${parents} Every value must be within the bounds. + lower : + ${lower_bound} + upper : + ${upper_bound} + scale : + Scale :math:`\lambda > 0` of the exponential distribution. Smaller + values keep the children closer to their parents. + pair_prob : + Probability of recombining each pair of parents. + swap_prob : + Probability of swapping each variable between the two children. + seed : + ${random_seed} + + Returns + ------- + ${pair_offspring} + + Notes + ----- + BEX was proposed by Thakur, Meghwani and Jalota (2014) as a bounded + version of the Laplace crossover of Deep and Thakur (2007). Without + bounds, :math:`\beta` follows a Laplace distribution. + + References + ---------- + M. Thakur, S. S. Meghwani and H. Jalota (2014). A modified real coded + genetic algorithm for constrained optimization. *Applied Mathematics and + Computation*, 235:292--317. https://doi.org/10.1016/j.amc.2014.02.093 + + K. Deep and M. Thakur (2007). A new crossover operator for real coded + genetic algorithms. *Applied Mathematics and Computation*, + 188(1):895--911. https://doi.org/10.1016/j.amc.2006.10.047 + + Examples + -------- + >>> parents = np.array([[0.2, 0.2], [0.6, 0.8]]) + >>> moocore.bounded_exponential_crossover(parents, lower=0, upper=1, seed=42) + array([[0.32040486, 0.14833417], + [0.72036984, 0.74522359]]) + + """ + parents = _as_matrix(parents, "parents", min_rows=2) + lower, upper = _bounds(lower, upper, parents.shape[1]) + if np.any(parents < lower) or np.any(parents > upper): + raise ValueError("'parents' must be within 'lower' and 'upper'") + scale = _check_positive(scale, "scale") + pair_prob = _check_probability(pair_prob, "pair_prob") + swap_prob = _check_probability(swap_prob, "swap_prob") + return _call( + lib.bounded_exponential_crossover, + parents, + len(parents), + ffi.from_buffer("double []", lower), + ffi.from_buffer("double []", upper), + scale, + pair_prob, + swap_prob, + _get_seed_for_c(seed), + ) + + +@DocSubstitute() +def de_rand_1_bin_crossover( + population: ArrayLike, + /, + *, + targets: ArrayLike | None = None, + lower: ArrayLike | None = None, + upper: ArrayLike | None = None, + scaling_factor: float = 0.5, + crossover_rate: float = 0.9, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Differential evolution crossover (DE/rand/1/bin). + + For each target :math:`x_i`, three rows :math:`x_{r_1}, x_{r_2}, x_{r_3}` + are drawn from ``population``, distinct from each other and from the + target. The child takes each variable :math:`j` from the mutant + :math:`x_{r_1} + F (x_{r_2} - x_{r_3})` with probability :math:`CR`, and + from the target otherwise. One variable chosen at random always comes + from the mutant. Finally, the child is clipped to the bounds. + + Parameters + ---------- + population : + ${population} It must have at least 4 rows. + targets : + ${targets} + lower : + ${lower_bound} + upper : + ${upper_bound} + scaling_factor : + Scaling factor :math:`F > 0` of the difference vector. + crossover_rate : + Crossover rate :math:`CR`, the probability of taking each variable + from the mutant. + seed : + ${random_seed} + + Returns + ------- + Array with one row per target, where row ``i`` is the child of target + ``targets[i]``. + + See Also + -------- + de_current_1_crossover : The variant used by MOEA/D-DE. + + Notes + ----- + This is the DE/rand/1/bin scheme of :footcite:t:`StoPri1997:de`, who + recommend :math:`F = 0.5` and suggest trying :math:`CR = 0.9` first. + Multi-objective DE algorithms such as GDE3 :footcite:p:`KukLam2005:gde3` + and DEMO :footcite:p:`RobFil05demo` use this variant + :footcite:p:`BezLopStu2015emode`. + + Storn and Price do not specify how to handle values outside the bounds. + Clipping them, as done here, is a common choice. + + References + ---------- + .. footbibliography:: + + Examples + -------- + >>> population = np.array( + ... [[0.1, 0.1], [0.4, 0.9], [0.8, 0.3], [0.5, 0.5], [0.9, 0.9]] + ... ) + >>> moocore.de_rand_1_bin_crossover( + ... population, targets=[0, 3], lower=0, upper=1, seed=42 + ... ) + array([[1. , 0.5], + [0. , 0.1]]) + + """ + population = _as_matrix(population, "population", min_rows=4) + targets = _targets(targets, len(population)) + lower, upper = _bounds(lower, upper, population.shape[1]) + scaling_factor = _check_positive(scaling_factor, "scaling_factor") + crossover_rate = _check_probability(crossover_rate, "crossover_rate") + return _call_with_targets( + lib.de_rand_1_bin_crossover, + population, + targets, + lower, + upper, + scaling_factor, + crossover_rate, + _get_seed_for_c(seed), + ) + + +@DocSubstitute() +def de_current_1_crossover( + population: ArrayLike, + /, + *, + targets: ArrayLike | None = None, + lower: ArrayLike | None = None, + upper: ArrayLike | None = None, + scaling_factor: float = 0.5, + crossover_rate: float = 1.0, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Differential evolution crossover used by MOEA/D-DE (DE/current/1). + + For each target :math:`x_i`, two distinct rows :math:`x_{r_1}, x_{r_2}` + are drawn from ``population``. Either of them may be the target itself. + The child takes each variable :math:`j` from :math:`x_i + F (x_{r_1} - + x_{r_2})` with probability :math:`CR`, and from the target otherwise. + Finally, the child is clipped to the bounds. + + Unlike :func:`de_rand_1_bin_crossover`, the base vector is the target and + no variable is forced to come from the mutant, so with :math:`CR = 0` the + child is a copy of the target. + + Parameters + ---------- + population : + ${population} In MOEA/D, this is the neighbourhood of the subproblem, + and ``targets`` gives the row of the subproblem's current solution. + targets : + ${targets} + lower : + ${lower_bound} + upper : + ${upper_bound} + scaling_factor : + Scaling factor :math:`F > 0` of the difference vector. + crossover_rate : + Crossover rate :math:`CR`, the probability of changing each variable. + seed : + ${random_seed} + + Returns + ------- + Array with one row per target, where row ``i`` is the child of target + ``targets[i]``. + + See Also + -------- + de_rand_1_bin_crossover : The classical DE/rand/1/bin scheme. + + Notes + ----- + This is the DE operator of MOEA/D-DE :footcite:p:`LiZha2009:moead-de`, + which uses :math:`CR = 1` and :math:`F = 0.5`. With :math:`CR = 1`, the + operator is invariant to rotations of the decision space. MOEA/D-DE then + applies polynomial mutation, which is not part of this function. + + Li and Zhang reset values outside the bounds to a random value within + them. Their own implementation clips them instead, which is what this + function does, and which Tanabe and Ishibuchi (2019) found to work best + with this operator. Tanabe and Ishibuchi also explain why some + implementations of MOEA/D-DE use DE/rand/1 instead. + + References + ---------- + .. footbibliography:: + + R. Tanabe and H. Ishibuchi (2019). Review and analysis of three components + of the differential evolution mutation operator in MOEA/D-DE. *Soft + Computing*, 23(23):12843--12857. + https://doi.org/10.1007/s00500-019-03842-6 + + Examples + -------- + >>> neighbourhood = np.array([[0.5, 0.5], [0.4, 0.9], [0.8, 0.3]]) + >>> moocore.de_current_1_crossover( + ... neighbourhood, targets=[0], lower=0, upper=1, seed=42 + ... ) + array([[0.3, 0.8]]) + + """ + population = _as_matrix(population, "population", min_rows=2) + targets = _targets(targets, len(population)) + lower, upper = _bounds(lower, upper, population.shape[1]) + scaling_factor = _check_positive(scaling_factor, "scaling_factor") + crossover_rate = _check_probability(crossover_rate, "crossover_rate") + return _call_with_targets( + lib.de_current_1_crossover, + population, + targets, + lower, + upper, + scaling_factor, + crossover_rate, + _get_seed_for_c(seed), + ) + + +@DocSubstitute() +def parent_centric_crossover( + population: ArrayLike, + /, + *, + targets: ArrayLike | None = None, + lower: ArrayLike | None = None, + upper: ArrayLike | None = None, + sigma_zeta: float = 0.1, + sigma_eta: float = 0.1, + seed: int | np.random.Generator | None = None, +) -> np.ndarray: + r"""Parent-centric crossover (PCX). + + Each target :math:`x` is an index parent. Two more parents :math:`a, b` + are drawn from ``population``, distinct from each other and from the + target. Let :math:`d = x - g`, where :math:`g` is the centroid of the + three parents, and let :math:`\bar{D}` be the mean distance from :math:`a` + and :math:`b` to the line through :math:`x` along :math:`d`. The child is + + .. math:: + x + \zeta d + \bar{D} \eta, + + where :math:`\zeta \sim N(0, \sigma_\zeta^2)` and :math:`\eta` is a + vector of independent :math:`N(0, \sigma_\eta^2)` values projected onto + the subspace orthogonal to :math:`d`. Finally, the child is clipped to the + bounds. + + Parameters + ---------- + population : + ${population} It must have at least 3 rows. + targets : + ${targets} + lower : + ${lower_bound} + upper : + ${upper_bound} + sigma_zeta : + Standard deviation :math:`\sigma_\zeta > 0` of the step along + :math:`d`. + sigma_eta : + Standard deviation :math:`\sigma_\eta > 0` of the steps orthogonal to + :math:`d`. + seed : + ${random_seed} + + Returns + ------- + Array with one row per target, where row ``i`` is the child of index + parent ``targets[i]``. + + Notes + ----- + PCX was proposed by Deb, Anand and Joshi (2002), who sum one normal step + along each vector of an orthonormal basis of the subspace orthogonal to + :math:`d`. Projecting an isotropic normal vector onto that subspace gives + the same distribution. If :math:`x` is (almost) the centroid, the + projection is skipped. + + References + ---------- + K. Deb, A. Anand and D. Joshi (2002). A computationally efficient + evolutionary algorithm for real-parameter optimization. *Evolutionary + Computation*, 10(4):371--395. https://doi.org/10.1162/106365602760972767 + + Examples + -------- + >>> population = np.array([[0.2, 0.2], [0.4, 0.9], [0.8, 0.3], [0.5, 0.5]]) + >>> moocore.parent_centric_crossover( + ... population, targets=[0, 3], lower=0, upper=1, seed=42 + ... ) + array([[0.18832072, 0.19642879], + [0.50136187, 0.44711562]]) + + """ + population = _as_matrix(population, "population", min_rows=3) + targets = _targets(targets, len(population)) + lower, upper = _bounds(lower, upper, population.shape[1]) + sigma_zeta = _check_positive(sigma_zeta, "sigma_zeta") + sigma_eta = _check_positive(sigma_eta, "sigma_eta") + return _call_with_targets( + lib.parent_centric_crossover, + population, + targets, + lower, + upper, + sigma_zeta, + sigma_eta, + _get_seed_for_c(seed), + ) diff --git a/python/src/moocore/_docsubstitute.py b/python/src/moocore/_docsubstitute.py index 4e1f142d6..6e39e605d 100644 --- a/python/src/moocore/_docsubstitute.py +++ b/python/src/moocore/_docsubstitute.py @@ -27,6 +27,22 @@ # ------------------------------------------------------------------------- "whv_rectangles": """Weighted rectangles that will bias the computation of the hypervolume. Maybe generated by :func:`eafdiff()` with ``rectangles=True`` or by :func:`choose_eafdiff()`.""", + # ------------------------------------------------------------------------- + "parents": """2D array of numerical values, where each row is a decision vector. + Rows ``2i`` and ``2i + 1`` are mated. If the number of rows is odd, the last row is mated with the first one.""", + # ------------------------------------------------------------------------- + "pair_offspring": """Array with the same shape as ``parents``, where rows ``2i`` and ``2i + 1`` are the two children of rows ``2i`` and ``2i + 1`` of ``parents``. + If the number of rows is odd, the second child of the last pair is dropped, so the number of rows does not change.""", + # ------------------------------------------------------------------------- + "population": """2D array of numerical values, where each row is a decision vector.""", + # ------------------------------------------------------------------------- + "targets": """1D vector of row indices of ``population``. Each index produces one child. ``None`` uses every row.""", + # ------------------------------------------------------------------------- + "lower_bound": """Lower bounds of the decision variables. Either a single value, which will be used for all variables, + or one value per column. ``None`` means no lower bound.""", + # ------------------------------------------------------------------------- + "upper_bound": """Upper bounds of the decision variables. Either a single value, which will be used for all variables, + or one value per column. ``None`` means no upper bound.""", } diff --git a/python/src/moocore/_ffi_build.py b/python/src/moocore/_ffi_build.py index 87e32fff0..1803bbeec 100644 --- a/python/src/moocore/_ffi_build.py +++ b/python/src/moocore/_ffi_build.py @@ -30,9 +30,11 @@ #include "whv.h" #include "whv_hype.h" #include "hvapprox.h" +#include "crossover.h" """ sources = [ "avl.c", + "crossover.c", "eaf.c", "eaf3d.c", "eafdiff.c", diff --git a/python/src/moocore/libmoocore.h b/python/src/moocore/libmoocore.h index 5f0c0a45e..feae11273 100644 --- a/python/src/moocore/libmoocore.h +++ b/python/src/moocore/libmoocore.h @@ -85,3 +85,14 @@ hype_sample_dist * hype_dist_gaussian_new(const double *mu, unsigned long int se void hype_dist_free(hype_sample_dist * d); double whv_hype_estimate(const double *points, size_t n, const double *ideal, const double *ref, hype_sample_dist * dist, size_t nsamples); */ + +// crossover.h +void uniform_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, double swap_prob, double pair_prob, uint32_t seed); +void single_point_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, uint32_t seed); +void blend_alpha_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double alpha, uint32_t seed); +void single_arithmetic_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, double pair_prob, uint32_t seed); +void local_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, uint32_t seed); +void bounded_exponential_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double scale, double pair_prob, double swap_prob, uint32_t seed); +void de_rand_1_bin_crossover(double * restrict offspring, const double * restrict population, size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, const double * restrict lower, const double * restrict upper, double scaling_factor, double crossover_rate, uint32_t seed); +void de_current_1_crossover(double * restrict offspring, const double * restrict population, size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, const double * restrict lower, const double * restrict upper, double scaling_factor, double crossover_rate, uint32_t seed); +void parent_centric_crossover(double * restrict offspring, const double * restrict population, size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, const double * restrict lower, const double * restrict upper, double sigma_zeta, double sigma_eta, uint32_t seed); diff --git a/python/tests/test_crossover.py b/python/tests/test_crossover.py new file mode 100644 index 000000000..6ef6610cf --- /dev/null +++ b/python/tests/test_crossover.py @@ -0,0 +1,392 @@ +# ruff: noqa: D100, D103 +import math + +import numpy as np +import pytest +from numpy.testing import assert_allclose, assert_array_equal + +import moocore + +LOWER, UPPER = 0.0, 10.0 + +TWO_CHILDREN = { + "uniform": moocore.uniform_crossover, + "single_point": moocore.single_point_crossover, + "single_arithmetic": moocore.single_arithmetic_crossover, + "local": moocore.local_crossover, + "bounded_exponential": moocore.bounded_exponential_crossover, +} +PAIR_OPERATORS = {**TWO_CHILDREN, "blend_alpha": moocore.blend_alpha_crossover} +POPULATION_OPERATORS = { + "de_rand_1_bin": moocore.de_rand_1_bin_crossover, + "de_current_1": moocore.de_current_1_crossover, + "parent_centric": moocore.parent_centric_crossover, +} +ALL_OPERATORS = {**PAIR_OPERATORS, **POPULATION_OPERATORS} +BOUNDED = { + "blend_alpha", + "bounded_exponential", + *POPULATION_OPERATORS, +} + + +def random_matrix(n, nvar=4, seed=0): + return np.random.default_rng(seed).uniform(LOWER, UPPER, size=(n, nvar)) + + +def pairs(x): + return x[0::2], x[1::2] + + +@pytest.mark.parametrize("name", TWO_CHILDREN) +@pytest.mark.parametrize("n", [2, 3, 4, 5, 10]) +def test_two_children_per_pair_keep_row_count(name, n): + x = random_matrix(n) + assert TWO_CHILDREN[name](x, seed=1).shape == x.shape + + +@pytest.mark.parametrize("n", [2, 3, 4, 5, 10]) +def test_blend_alpha_crossover_one_child_per_pair(n): + x = random_matrix(n) + out = moocore.blend_alpha_crossover(x, seed=1) + assert out.shape == (math.ceil(n / 2), x.shape[1]) + + +@pytest.mark.parametrize("name", POPULATION_OPERATORS) +def test_population_operators_one_child_per_target(name): + fun = POPULATION_OPERATORS[name] + x = random_matrix(6) + assert fun(x, seed=1).shape == x.shape + assert fun(x, targets=[4, 0, 4], seed=1).shape == (3, x.shape[1]) + assert fun(x, targets=2, seed=1).shape == (1, x.shape[1]) + assert fun(x, targets=[], seed=1).shape == (0, x.shape[1]) + + +@pytest.mark.parametrize("n", [3, 5, 7]) +def test_odd_number_of_parents_pairs_last_with_first(n): + x = random_matrix(n) + assert_array_equal(moocore.uniform_crossover(x, swap_prob=0, seed=1), x) + # Swapping every variable gives each child the other parent. + out = moocore.uniform_crossover(x, swap_prob=1, seed=1) + assert_array_equal(out[0], x[1]) + assert_array_equal(out[-1], x[0]) + + out = moocore.blend_alpha_crossover(x, alpha=0, seed=1) + assert np.all(out[-1] >= np.minimum(x[-1], x[0])) + assert np.all(out[-1] <= np.maximum(x[-1], x[0])) + + +@pytest.mark.parametrize("name", PAIR_OPERATORS) +@pytest.mark.parametrize("n", [3, 4, 5]) +def test_identical_parents_reproduce_themselves(name, n): + # The row has distinct values, so a transposed output would not match. + row = np.arange(1.0, 6.0) + x = np.tile(row, (n, 1)) + out = PAIR_OPERATORS[name](x, seed=1) + assert_allclose(out, np.tile(row, (len(out), 1))) + + +@pytest.mark.parametrize("name", ALL_OPERATORS) +def test_seed(name): + fun = ALL_OPERATORS[name] + x = random_matrix(8) + assert_array_equal(fun(x, seed=42), fun(x, seed=42)) + assert_array_equal( + fun(x, seed=np.random.default_rng(42)), + fun(x, seed=np.random.default_rng(42)), + ) + assert not np.array_equal(fun(x, seed=1), fun(x, seed=2)) + # The same Generator gives new children on each call. + rng = np.random.default_rng(42) + assert not np.array_equal(fun(x, seed=rng), fun(x, seed=rng)) + # seed=None still works. + assert fun(x).shape[1] == x.shape[1] + + +@pytest.mark.parametrize("name", ALL_OPERATORS) +def test_inputs_are_not_modified(name, immutable_call): + x = random_matrix(6) + kwargs = {} + if name in BOUNDED: + kwargs = {"lower": np.full(4, LOWER), "upper": np.full(4, UPPER)} + if name in POPULATION_OPERATORS: + kwargs["targets"] = np.array([0, 2]) + immutable_call(ALL_OPERATORS[name], x, seed=3, **kwargs) + + +def test_uniform_crossover_only_copies_parent_values(): + x = random_matrix(200, nvar=6) + p1, p2 = pairs(x) + c1, c2 = pairs(moocore.uniform_crossover(x, seed=1)) + from_first = c1 == p1 + assert np.all(from_first | (c1 == p2)) + assert_array_equal(c2, np.where(from_first, p2, p1)) + assert_array_equal(moocore.uniform_crossover(x, pair_prob=0, seed=1), x) + + +@pytest.mark.parametrize("swap_prob", [0.0, 0.25, 0.5, 0.75, 1.0]) +def test_uniform_crossover_swap_rate(swap_prob): + x = np.tile([np.zeros(10), np.ones(10)], (2000, 1)) + out = moocore.uniform_crossover(x, swap_prob=swap_prob, seed=1) + # The first child gets a 1 only where it was swapped. + assert abs(out[0::2].mean() - swap_prob) < 0.02 + + +@pytest.mark.parametrize( + "fun", [moocore.uniform_crossover, moocore.single_point_crossover] +) +@pytest.mark.parametrize("dtype", [int, bool, np.int8, np.float32]) +def test_value_copying_operators_keep_dtype(fun, dtype): + x = np.array([[0, 0, 0, 0], [1, 1, 1, 1], [0, 1, 0, 1]], dtype=dtype) + out = fun(x, seed=1) + if np.issubdtype(dtype, np.floating): + assert out.dtype == np.float64 + else: + assert out.dtype == x.dtype + assert np.all((out == 0) | (out == 1)) + + +def test_single_point_crossover_exchanges_tails(): + nvar = 5 + x = np.tile([np.zeros(nvar), np.ones(nvar)], (2000, 1)) + c1, c2 = pairs(moocore.single_point_crossover(x, seed=1)) + cuts = (c1 == 0).sum(axis=1) + assert_array_equal(c1, (np.arange(nvar) >= cuts[:, None]).astype(float)) + assert_array_equal(c2, 1 - c1) + assert set(cuts) == set(range(1, nvar)) + + +@pytest.mark.parametrize("alpha", [0.0, 0.5, 1.0]) +def test_blend_alpha_crossover_interval(alpha): + x = random_matrix(400, nvar=3) + p1, p2 = pairs(x) + out = moocore.blend_alpha_crossover( + x, lower=LOWER, upper=UPPER, alpha=alpha, seed=1 + ) + lo, hi = np.minimum(p1, p2), np.maximum(p1, p2) + span = hi - lo + assert np.all(out >= np.maximum(lo - alpha * span, LOWER) - 1e-12) + assert np.all(out <= np.minimum(hi + alpha * span, UPPER) + 1e-12) + + +def test_blend_alpha_crossover_samples_variables_independently(): + x = np.tile([[2.0, 8.0], [8.0, 2.0]], (5000, 1)) + out = moocore.blend_alpha_crossover(x, alpha=0, seed=1) + corr = np.corrcoef(out[:, 0], out[:, 1])[0, 1] + assert abs(corr) < 0.05 + + +def test_single_arithmetic_crossover_changes_one_variable(): + x = random_matrix(100, nvar=5) + p1, p2 = pairs(x) + c1, c2 = pairs(moocore.single_arithmetic_crossover(x, seed=1)) + changed = c1 != p1 + assert np.all(changed.sum(axis=1) == 1) + assert_array_equal(changed, c2 != p2) + mean = 0.5 * (p1 + p2) + assert_array_equal(c1[changed], mean[changed]) + assert_array_equal(c2[changed], mean[changed]) + assert_array_equal( + moocore.single_arithmetic_crossover(x, pair_prob=0, seed=1), x + ) + + +def test_local_crossover_children_lie_between_parents(): + x = random_matrix(100, nvar=5) + p1, p2 = pairs(x) + c1, c2 = pairs(moocore.local_crossover(x, seed=1)) + assert_allclose(c1 + c2, p1 + p2) + lo, hi = np.minimum(p1, p2) - 1e-12, np.maximum(p1, p2) + 1e-12 + for c in (c1, c2): + assert np.all((c >= lo) & (c <= hi)) + + +def test_bounded_exponential_crossover_shared_values(): + x = np.tile([[0.0, 5.0, 10.0, 3.0], [0.0, 5.0, 10.0, 7.0]], (50, 1)) + out = moocore.bounded_exponential_crossover(x, lower=0, upper=10, seed=1) + assert np.all(np.isfinite(out)) + assert_array_equal(out[:, :3], x[:, :3]) + assert np.all((out >= 0) & (out <= 10)) + + +def test_bounded_exponential_crossover_bounds(): + x = random_matrix(1000) + out = moocore.bounded_exponential_crossover( + x, lower=LOWER, upper=UPPER, scale=1.0, seed=1 + ) + assert np.all((out >= LOWER) & (out <= UPPER)) + out = moocore.bounded_exponential_crossover(x, scale=1.0, seed=1) + assert np.all(np.isfinite(out)) + assert np.any((out < LOWER) | (out > UPPER)) + assert_array_equal( + moocore.bounded_exponential_crossover(x, pair_prob=0, seed=1), x + ) + + +@pytest.mark.parametrize( + ("swap_prob", "expected"), [(0.0, 1.0), (0.5, 0.5), (1.0, 0.0)] +) +def test_bounded_exponential_crossover_swap_prob(swap_prob, expected): + x = np.tile([np.full(10, 2.0), np.full(10, 8.0)], (1000, 1)) + out = moocore.bounded_exponential_crossover( + x, lower=0, upper=10, swap_prob=swap_prob, seed=1 + ) + # Fraction of the variables of the first child that stay near its parent. + c1 = out[0::2] + kept = (np.abs(c1 - 2) < np.abs(c1 - 8)).mean() + assert abs(kept - expected) < 0.02 + + +@pytest.mark.parametrize("order", [1, -1]) +def test_bounded_exponential_crossover_children_near_their_parent(order): + pair = np.array([[3.0, 3.0], [7.0, 7.0]])[::order] + x = np.tile(pair, (2000, 1)) + out = moocore.bounded_exponential_crossover(x, lower=0, upper=10, seed=1) + assert_allclose(np.median(out[0::2], axis=0), pair[0], atol=0.1) + assert_allclose(np.median(out[1::2], axis=0), pair[1], atol=0.1) + + +def test_de_rand_1_bin_crossover_forces_one_mutant_variable(): + x = random_matrix(20, nvar=6) + out = moocore.de_rand_1_bin_crossover(x, crossover_rate=0, seed=1) + assert np.all((out != x).sum(axis=1) == 1) + + +def test_de_rand_1_bin_crossover_base_is_another_row(): + x = random_matrix(10, nvar=3) + out = moocore.de_rand_1_bin_crossover( + x, scaling_factor=1e-12, crossover_rate=1, seed=1 + ) + for i, child in enumerate(out): + dist = np.abs(x - child).max(axis=1) + nearest = np.argmin(dist) + assert nearest != i + assert dist[nearest] < 1e-9 + + +def test_de_current_1_crossover_base_is_the_target(): + x = random_matrix(10) + assert_array_equal( + moocore.de_current_1_crossover(x, crossover_rate=0, seed=1), x + ) + out = moocore.de_current_1_crossover(x, scaling_factor=1e-12, seed=1) + assert_allclose(out, x, atol=1e-9) + + +def test_de_current_1_crossover_two_rows(): + # The donors are the two rows, in either order. + x = random_matrix(2) + step = 0.5 * (x[0] - x[1]) + out = moocore.de_current_1_crossover(x, seed=1) + for i in range(2): + assert np.allclose(out[i], x[i] + step) or np.allclose( + out[i], x[i] - step + ) + + +def test_parent_centric_crossover_tiny_sigmas_return_index_parent(): + x = random_matrix(10) + out = moocore.parent_centric_crossover( + x, sigma_zeta=1e-12, sigma_eta=1e-12, seed=1 + ) + assert_allclose(out, x, atol=1e-9) + + +def test_parent_centric_crossover_sigma_zeta_scales_step_along_direction(): + x = random_matrix(10) + step1 = ( + moocore.parent_centric_crossover( + x, sigma_zeta=0.1, sigma_eta=1e-12, seed=1 + ) + - x + ) + step2 = ( + moocore.parent_centric_crossover( + x, sigma_zeta=0.2, sigma_eta=1e-12, seed=1 + ) + - x + ) + assert_allclose(step2, 2 * step1, atol=1e-9) + + +@pytest.mark.parametrize("name", POPULATION_OPERATORS) +def test_population_operators_clip_to_bounds(name): + x = random_matrix(30) + if name == "parent_centric": + kwargs = {"sigma_zeta": 5.0, "sigma_eta": 5.0} + else: + kwargs = {"scaling_factor": 5.0} + out = POPULATION_OPERATORS[name]( + x, lower=LOWER, upper=UPPER, seed=1, **kwargs + ) + assert np.all((out >= LOWER) & (out <= UPPER)) + assert np.any((out == LOWER) | (out == UPPER)) + + +@pytest.mark.parametrize("name", ALL_OPERATORS) +def test_errors_shape(name): + fun = ALL_OPERATORS[name] + with pytest.raises(ValueError, match=r"must be a 2D array"): + fun([1.0, 2.0, 3.0]) + with pytest.raises(ValueError, match=r"must have at least \d rows"): + fun([[1.0, 2.0]]) + + +@pytest.mark.parametrize("name", sorted(BOUNDED)) +def test_errors_bounds(name): + fun = ALL_OPERATORS[name] + x = random_matrix(6) + with pytest.raises(ValueError, match=r"'lower' must not be larger"): + fun(x, lower=1, upper=0) + with pytest.raises(ValueError, match=r"'upper' must have length 4"): + fun(x, upper=[1, 2]) + + +@pytest.mark.parametrize( + ("fun", "kwargs", "match"), + [ + (moocore.uniform_crossover, {"swap_prob": 1.5}, "'swap_prob'"), + (moocore.uniform_crossover, {"pair_prob": -0.1}, "'pair_prob'"), + (moocore.single_arithmetic_crossover, {"pair_prob": 2}, "'pair_prob'"), + (moocore.blend_alpha_crossover, {"alpha": -1}, "'alpha'"), + (moocore.bounded_exponential_crossover, {"scale": 0}, "'scale'"), + (moocore.bounded_exponential_crossover, {"swap_prob": 2}, "swap_prob"), + (moocore.de_rand_1_bin_crossover, {"scaling_factor": 0}, "scaling"), + (moocore.de_rand_1_bin_crossover, {"crossover_rate": 2}, "crossover"), + (moocore.de_current_1_crossover, {"scaling_factor": -1}, "scaling"), + (moocore.de_current_1_crossover, {"crossover_rate": -1}, "crossover"), + (moocore.parent_centric_crossover, {"sigma_zeta": 0}, "'sigma_zeta'"), + (moocore.parent_centric_crossover, {"sigma_eta": 0}, "'sigma_eta'"), + ], +) +def test_errors_parameters(fun, kwargs, match): + with pytest.raises(ValueError, match=match): + fun(random_matrix(6), **kwargs) + + +def test_errors_operator_specific(): + with pytest.raises(ValueError, match=r"at least 2 columns"): + moocore.single_point_crossover([[0], [1]]) + with pytest.raises(ValueError, match=r"at least 4 rows"): + moocore.de_rand_1_bin_crossover(random_matrix(3)) + with pytest.raises(ValueError, match=r"at least 3 rows"): + moocore.parent_centric_crossover(random_matrix(2)) + with pytest.raises(ValueError, match=r"within 'lower' and 'upper'"): + moocore.bounded_exponential_crossover( + [[0.5, 2.0], [0.2, 0.3]], lower=0, upper=1 + ) + + +@pytest.mark.parametrize("name", POPULATION_OPERATORS) +@pytest.mark.parametrize( + ("targets", "match"), + [ + ([6], r"within \[0, 5\]"), + ([-1], r"within \[0, 5\]"), + ([[0, 1]], "1D vector"), + ([0.5], "1D vector"), + ], +) +def test_errors_targets(name, targets, match): + with pytest.raises(ValueError, match=match): + POPULATION_OPERATORS[name](random_matrix(6), targets=targets) From 292c72792b0374dad37d406d03e8ac003162ea95 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 17:40:31 +0300 Subject: [PATCH 04/30] python/doc/ Document crossover operators * bibkeys.txt (BezLopStu2015emode, EibSmi2003, EshSch1992, Goldberg89, Hol75, KukLam2005:gde3, LiZha2009:moead-de, RobFil05demo, StoPri1997:de, Syswerda89): New. * python/doc/source/reference/functions.variation.rst: New. * python/doc/source/reference/index.rst: Add it. * python/doc/source/index.rst: Mention crossover operators. * python/doc/source/whatsnew/index.rst: Document. * python/examples/plot_crossover.py: New. * python/doc/source/REFERENCES.bib: Regenerate. * r/inst/REFERENCES.bib: Regenerate. --- bibkeys.txt | 10 + python/doc/source/REFERENCES.bib | 119 +++++++++ python/doc/source/index.rst | 1 + .../source/reference/functions.variation.rst | 58 +++++ python/doc/source/reference/index.rst | 1 + python/doc/source/whatsnew/index.rst | 1 + python/examples/plot_crossover.py | 235 ++++++++++++++++++ r/inst/REFERENCES.bib | 119 +++++++++ 8 files changed, 544 insertions(+) create mode 100644 python/doc/source/reference/functions.variation.rst create mode 100644 python/examples/plot_crossover.py diff --git a/bibkeys.txt b/bibkeys.txt index 0a0ff5285..74fa1abbc 100644 --- a/bibkeys.txt +++ b/bibkeys.txt @@ -1,5 +1,6 @@ AugBadBroZit2009gecco BeuFonLopPaqVah09:tec +BezLopStu2015emode BezLopStu2017assessment BezLopStu2017emo BinGinRou2015gaupar @@ -14,24 +15,30 @@ Deb02nsga2 DenZha2019approxhv DiaLop2020ejor DubLopStu2011amai +EibSmi2003 EmmFon2011emo +EshSch1992 FanWan1994numtheory FonGueLopPaq2011emo FonPaqLop06:hypervolume Gla2017fast +Goldberg89 GruFon2009:emaa Grunert01 GueFon2017hv4d GueFonPaq2021hv HanJas1998 HerWer1987tabucol +Hol75 IshHeSha2019regular IshMasTanNoj2015igd Jen03 JohAraMcGSch1991 KnoCor2002cec +KukLam2005:gde3 KunLucPre1975jacm LacKlaFon2017box +LiZha2009:moead-de Lop2026hvapprox LopPaqStu09emaa LopVerDreDoe2025 @@ -39,9 +46,12 @@ LopezIbanezPhD Molchanov2005theory Muller1959sphere Rob2018unreasonable +RobFil05demo RubMel1998simulation SchEsqLarCoe2012tec SchKer2025r2v2 +StoPri1997:de +Syswerda89 VelLam1998gp WuAza2001metrics ZhoZhaJin2009igdx diff --git a/python/doc/source/REFERENCES.bib b/python/doc/source/REFERENCES.bib index b752aab29..1e533f89b 100644 --- a/python/doc/source/REFERENCES.bib +++ b/python/doc/source/REFERENCES.bib @@ -343,6 +343,17 @@ @article{LacKlaFon2017box doi = {10.1016/j.cor.2016.06.021} } +@article{LiZha2009:moead-de, + title = {Multiobjective Optimization Problems with Complicated + {Pareto} sets, {MOEA/D} and {NSGA-II}}, + author = {Li, Hui and Zhang, Qingfu }, + journal = {IEEE Transactions on Evolutionary Computation}, + volume = 13, + number = 2, + pages = {284--302}, + year = 2009 +} + @article{LopVerDreDoe2025, author = { Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Diederick Vermetten and Johann Dreo and Carola Doerr }, title = {Using the Empirical Attainment Function for Analyzing @@ -412,6 +423,19 @@ @article{SchKer2025r2v2 doi = {10.1162/evco.a.366} } +@article{StoPri1997:de, + author = {Storn, Rainer and Price, Kenneth}, + title = {Differential Evolution -- A Simple and Efficient Heuristic + for Global Optimization over Continuous Spaces}, + journal = {Journal of Global Optimization}, + year = 1997, + volume = 11, + number = 4, + pages = {341--359}, + annote = {Proposed differential evolution}, + doi = {10.1023/A:1008202821328} +} + @article{WuAza2001metrics, author = {J. Wu and S. Azam}, title = {Metrics for Quality Assessment of a Multiobjective Design @@ -480,6 +504,29 @@ @incollection{AugBadBroZit2009gecco2 pages = {563--570} } +@misc{BezLopStu2015emoDEsupp, + author = { Leonardo C. T. Bezerra and Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Thomas St{\"u}tzle }, + title = {To {DE} or Not to {DE}? {Multi}-objective Differential + Evolution Revisited from a Component-Wise Perspective: {Supplementary} material}, + howpublished = {\url{https://iridia.ulb.ac.be/supp/IridiaSupp2015-001/}}, + year = 2015 +} + +@incollection{BezLopStu2015emode, + booktitle = { Evolutionary Multi-criterion Optimization, EMO 2015 Part {I}}, + address = { Heidelberg, Germany}, + series = {Lecture Notes in Computer Science}, + volume = 9018, + year = 2015, + publisher = {Springer}, + editor = { Ant{\'o}nio Gaspar{-}Cunha and Carlos Henggeler Antunes and Carlos A. {Coello Coello} }, + author = { Leonardo C. T. Bezerra and Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Thomas St{\"u}tzle }, + title = {To {DE} or Not to {DE}? {Multi}-objective Differential + Evolution Revisited from a Component-Wise Perspective}, + pages = {48--63}, + doi = {10.1007/978-3-319-15934-8_4} +} + @incollection{BezLopStu2017emo, address = { Cham, Switzerland}, series = {Lecture Notes in Computer Science}, @@ -550,6 +597,14 @@ @incollection{CoeSie2004igd keywords = {IGD} } +@book{EibSmi2003, + title = {Introduction to Evolutionary Computing}, + author = { Agoston E. Eiben and Smith, James E. }, + publisher = {Springer}, + year = 2003, + isbn = 3540401849 +} + @incollection{EmmFon2011emo, booktitle = { Evolutionary Multi-criterion Optimization, EMO 2011}, address = {Berlin~/ Heidelberg}, @@ -590,6 +645,17 @@ @incollection{EmmFon2011emo pages = {121--135} } +@incollection{EshSch1992, + isbn = {1-55860-263-1}, + year = 1993, + publisher = {Morgan Kaufmann Publishers}, + booktitle = {Foundations of Genetic Algorithms (FOGA)}, + editor = { Darrell Whitley }, + author = { Larry J. Eshelman and J. David Schaffer }, + title = {Real-Coded Genetic Algorithms and Interval-Schemata}, + pages = {187--202} +} + @book{FanWan1994numtheory, author = {Fang, K. T. and Wang, Y.}, title = {Number-Theoretic Methods in Statistics}, @@ -681,6 +747,15 @@ @incollection{Gla2017fast keywords = {archiving} } +@book{Goldberg89, + author = { David E. Goldberg }, + title = {Genetic Algorithms in Search, Optimization and + Machine Learning}, + publisher = {Addison-Wesley}, + address = { Boston, MA}, + year = 1989 +} + @incollection{GruFon2009:emaa, editor = { Thomas Bartz-Beielstein and Marco Chiarandini and Lu{\'i}s Paquete and Mike Preuss }, year = 2010, @@ -744,6 +819,13 @@ @techreport{HanJas1998 annote = {Proposed R2 indicator} } +@book{Hol75, + author = { J. Holland }, + title = {Adaptation in Natural and Artificial Systems}, + publisher = {University of Michigan Press}, + year = 1975 +} + @inproceedings{IshHeSha2019regular, month = jun, year = 2019, @@ -786,6 +868,19 @@ @inproceedings{KnoCor2002cec pages = {711--716} } +@inproceedings{KukLam2005:gde3, + address = {Piscataway, NJ}, + publisher = {IEEE Press}, + month = sep, + year = 2005, + booktitle = {Proceedings of the 2005 Congress on Evolutionary Computation (CEC 2005)}, + key = {IEEE CEC}, + author = {Kukkonen, S. and Lampinen, J.}, + title = {{GDE3}: the third evolution step of generalized differential + evolution}, + pages = {443--450} +} + @incollection{Lop2026hvapprox, location = {San Jos{\'e}, Costa Rica}, address = { New York, NY}, @@ -881,6 +976,19 @@ @misc{Rob2018unreasonable annote = {Proposed the Rphi low-discrepancy sequence} } +@incollection{RobFil05demo, + address = {Berlin~/ Heidelberg}, + publisher = {Springer}, + volume = 3410, + series = {Lecture Notes in Computer Science}, + editor = { Carlos A. {Coello Coello} and Hern{\'a}ndez Aguirre, Arturo and Eckart Zitzler }, + year = 2005, + booktitle = { Evolutionary Multi-criterion Optimization, EMO 2005}, + author = {Tea Robi{\v c} and Bogdan Filipi{\v c}}, + title = {{DEMO}: Differential Evolution for Multiobjective Optimization}, + pages = {520--533} +} + @book{RubMel1998simulation, author = {R. Y. Rubinstein and B. Melamed}, title = {Modern simulation and modeling}, @@ -890,6 +998,17 @@ @book{RubMel1998simulation notes = {Uniform sampling from the simplex.} } +@inproceedings{Syswerda89, + publisher = {Morgan Kaufmann Publishers, San Mateo, CA}, + editor = { J. David Schaffer }, + year = 1989, + booktitle = {Proceedings of the Third International Conference on Genetic Algorithms (ICGA'89)}, + author = { Gilbert Syswerda }, + title = {Uniform Crossover in Genetic Algorithms}, + pages = {2--9}, + keywords = {uniform crossover} +} + @inproceedings{VelLam1998gp, year = 1998, publisher = {Stanford University Bookstore}, diff --git a/python/doc/source/index.rst b/python/doc/source/index.rst index 9e5c57014..f7e3cfaeb 100644 --- a/python/doc/source/index.rst +++ b/python/doc/source/index.rst @@ -30,6 +30,7 @@ The goal of the **moocore** project (https://github.com/multi-objective/moocore/ * :ref:`Identify and filter dominated vectors `. * :ref:`Quality metrics ` such as (weighted) hypervolume, epsilon, IGD+, (exact) R2, etc. * :ref:`Computation of the Empirical Attainment Function `. The empirical attainment function (EAF) describes the probabilistic distribution of the outcomes obtained by a stochastic algorithm in the objective space. +* :ref:`Crossover operators ` for evolutionary algorithms, such as uniform, blend-alpha, bounded exponential, differential evolution and parent-centric crossover. Most critical functionality is implemented in C, with the R and Python packages providing convenient interfaces to the C code. diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst new file mode 100644 index 000000000..f4e8fec1e --- /dev/null +++ b/python/doc/source/reference/functions.variation.rst @@ -0,0 +1,58 @@ +.. _variation_operators: + +=================== +Variation operators +=================== + +.. currentmodule:: moocore + +Crossover operators combine decision vectors, called parents, to produce new +decision vectors, called children. Every function takes a 2D array with one +decision vector per row and accepts a ``seed`` for reproducible results. The +:ref:`crossover example ` shows where +each operator places its children. + +Two-parent crossover +==================== +.. autosummary:: + :toctree: generated/ + + uniform_crossover + single_point_crossover + blend_alpha_crossover + single_arithmetic_crossover + local_crossover + bounded_exponential_crossover + +These functions mate rows ``2i`` and ``2i + 1`` of ``parents``, so the order of +the rows decides which parents mate, for example after a selection step. If +the number of rows is odd, the last row mates with the first one. Most of +these operators produce two children per pair and return as many rows as +``parents``, dropping one child when the number of rows is odd. +:func:`blend_alpha_crossover` produces one child per pair. + +Population-based crossover +========================== +.. autosummary:: + :toctree: generated/ + + de_rand_1_bin_crossover + de_current_1_crossover + parent_centric_crossover + +These functions produce one child for each target row of ``population`` and +draw the other parents at random from ``population``. + +Differential evolution (DE) comes in two variants that are common in +multi-objective optimization. :func:`de_rand_1_bin_crossover` is the +DE/rand/1/bin scheme of :footcite:t:`StoPri1997:de`, which most Pareto-based +multi-objective DE algorithms use :footcite:p:`BezLopStu2015emode`. +:func:`de_current_1_crossover` is the operator of MOEA/D-DE +:footcite:p:`LiZha2009:moead-de`. It starts from the target instead of a +random row and does not force any variable to change. + + +Bibliography +============ + +.. footbibliography:: diff --git a/python/doc/source/reference/index.rst b/python/doc/source/reference/index.rst index c28449611..f2123fd85 100644 --- a/python/doc/source/reference/index.rst +++ b/python/doc/source/reference/index.rst @@ -29,3 +29,4 @@ indentation. functions.dominance functions.metrics functions.eaf + functions.variation diff --git a/python/doc/source/whatsnew/index.rst b/python/doc/source/whatsnew/index.rst index ea58ce81e..de39f4e4a 100644 --- a/python/doc/source/whatsnew/index.rst +++ b/python/doc/source/whatsnew/index.rst @@ -12,6 +12,7 @@ Version 0.4.0 - :func:`~moocore.is_nondominated` is up to 10x faster in some inputs thanks to a customized radixsort implementation. - New shapes ``"concave-cliff"`` and ``"convex-cliff"`` added to :func:`~moocore.generate_ndset`. - New function :func:`~moocore.generate_sequence` to generate sequences of dominated and nondominated points. +- New :ref:`crossover operators `: :func:`~moocore.uniform_crossover`, :func:`~moocore.single_point_crossover`, :func:`~moocore.blend_alpha_crossover`, :func:`~moocore.single_arithmetic_crossover`, :func:`~moocore.local_crossover`, :func:`~moocore.bounded_exponential_crossover`, :func:`~moocore.de_rand_1_bin_crossover`, :func:`~moocore.de_current_1_crossover` and :func:`~moocore.parent_centric_crossover`. Version 0.3.2 (11/07/2026) diff --git a/python/examples/plot_crossover.py b/python/examples/plot_crossover.py new file mode 100644 index 000000000..4f0a54c78 --- /dev/null +++ b/python/examples/plot_crossover.py @@ -0,0 +1,235 @@ +r""" +Crossover Operators +=================== + +This example shows where each crossover operator places the children of +fixed parents. Each figure mates the same parents many times and plots all +the children. Two-parent operators mate rows ``2i`` and ``2i + 1``, so +stacking copies of one pair of parents gives many independent draws in a +single call. + +First we define a few functions useful for plotting. +""" + +import matplotlib.pyplot as plt +import numpy as np +import moocore + +LOWER, UPPER = 0.0, 10.0 +BOUNDS = dict(lower=LOWER, upper=UPPER) + + +def mate(fun, a, b, n_pairs=50_000, **kwargs): + """Mate parents ``a`` and ``b`` ``n_pairs`` times.""" + parents = np.tile(np.array([a, b], dtype=float), (n_pairs, 1)) + return fun(parents, seed=42, **kwargs) + + +def plot_density(ax, values, **kwargs): + """Plot the distribution of ``values`` within the bounds.""" + ax.hist( + values, + bins=200, + range=(LOWER, UPPER), + density=True, + histtype="step", + **kwargs, + ) + + +def mark_parents(ax, positions): + """Show the parents as dotted vertical lines.""" + for x in positions: + ax.axvline(x, color="gray", linestyle=":", linewidth=1) + + +# %% +# +# Where two-parent operators put their children +# --------------------------------------------- +# +# The parents are :math:`(3, 3)` and :math:`(7, 7)` within :math:`[0, 10]^2`. +# Each panel shows the distribution of the first variable of the children for +# the default parameters of each operator. Uniform and single arithmetic +# crossover only produce a few distinct values, which appear as spikes. + +a, b = [3.0, 3.0], [7.0, 7.0] +operators = { + "Bounded exponential": (moocore.bounded_exponential_crossover, BOUNDS), + "Blend alpha": (moocore.blend_alpha_crossover, BOUNDS), + "Local": (moocore.local_crossover, {}), + "Uniform": (moocore.uniform_crossover, {}), + "Single arithmetic": (moocore.single_arithmetic_crossover, {}), +} +fig, axes = plt.subplots(len(operators), 1, figsize=(6, 8), sharex=True) +for i, (ax, (name, (fun, kwargs))) in enumerate(zip(axes, operators.items())): + plot_density(ax, mate(fun, a, b, **kwargs)[:, 0], color=f"C{i}") + mark_parents(ax, [a[0], b[0]]) + ax.set_title(name, loc="left", fontsize="medium") + ax.set_yticks([]) +axes[-1].set_xlabel("$x_1$") +fig.tight_layout() +plt.show() + +# %% +# +# Bounded exponential crossover: the scale parameter +# -------------------------------------------------- +# +# The parameter ``scale`` (:math:`\lambda`) controls how far the children move +# from their parents. Each child stays close to one parent, and the bounds +# truncate the distribution. On a logarithmic scale, the exponential tails +# become straight lines. + +fig, ax = plt.subplots(figsize=(6, 3.5)) +for i, scale in enumerate([0.01, 0.05, 0.1, 0.5]): + children = mate( + moocore.bounded_exponential_crossover, a, b, scale=scale, **BOUNDS + ) + plot_density( + ax, + children[:, 0], + color=plt.cm.viridis(i / 4), + label=rf"$\lambda = {scale}$", + ) +mark_parents(ax, [a[0], b[0]]) +ax.set_yscale("log") +ax.set_ylim(1e-3, None) +ax.set_xlabel("$x_1$") +ax.set_ylabel("Density") +ax.legend() +fig.tight_layout() +plt.show() + +# %% +# +# Blend crossover: the alpha parameter +# ------------------------------------ +# +# BLX-:math:`\alpha` samples uniformly from the interval between the parents, +# widened by ``alpha`` times their distance on each side. + +fig, ax = plt.subplots(figsize=(6, 3.5)) +for i, alpha in enumerate([0.0, 0.25, 0.5, 1.0]): + children = mate(moocore.blend_alpha_crossover, a, b, alpha=alpha, **BOUNDS) + plot_density( + ax, + children[:, 0], + color=plt.cm.viridis(i / 4), + label=rf"$\alpha = {alpha}$", + ) +mark_parents(ax, [a[0], b[0]]) +ax.set_xlabel("$x_1$") +ax.set_ylabel("Density") +ax.legend() +fig.tight_layout() +plt.show() + +# %% +# +# Offspring geometry +# ------------------ +# +# With the parents at opposite corners, :math:`(2, 8)` and :math:`(8, 2)`, the +# operators differ in which regions of the decision space their children +# reach. Uniform and single-point crossover recombine whole variables, so +# their children land on the corners of the box spanned by the parents. + +a, b = [2.0, 8.0], [8.0, 2.0] +operators = { + "Bounded exponential": (moocore.bounded_exponential_crossover, BOUNDS), + "Blend alpha": (moocore.blend_alpha_crossover, BOUNDS), + "Local": (moocore.local_crossover, {}), + "Uniform": (moocore.uniform_crossover, {}), + "Single arithmetic": (moocore.single_arithmetic_crossover, {}), + "Single point": (moocore.single_point_crossover, {}), +} +fig, axes = plt.subplots(2, 3, figsize=(9, 6), sharex=True, sharey=True) +for i, (ax, (name, (fun, kwargs))) in enumerate( + zip(axes.flat, operators.items()) +): + children = mate(fun, a, b, n_pairs=1000, **kwargs) + ax.scatter(children[:, 0], children[:, 1], s=4, alpha=0.3, color=f"C{i}") + ax.scatter(*np.array([a, b]).T, marker="D", s=40, color="black") + ax.set_title(name, fontsize="medium") + ax.set_xlim(LOWER, UPPER) + ax.set_ylim(LOWER, UPPER) + ax.set_aspect("equal") +for ax in axes[1]: + ax.set_xlabel("$x_1$") +for ax in axes[:, 0]: + ax.set_ylabel("$x_2$") +fig.tight_layout() +plt.show() + +# %% +# +# Which parent each variable comes from +# ------------------------------------- +# +# Uniform and single-point crossover only copy values, so they also work for +# binary and integer variables. With one parent of all zeros and one of all +# ones, the share of ones in the first child shows how likely each variable is +# to come from the second parent. Uniform crossover treats all variables +# alike, whereas single-point crossover keeps neighbouring variables together. + +nvar = 10 +zeros, ones = np.zeros(nvar, dtype=int), np.ones(nvar, dtype=int) +fig, ax = plt.subplots(figsize=(6, 3.5)) +for fun, name in [ + (moocore.uniform_crossover, "Uniform"), + (moocore.single_point_crossover, "Single point"), +]: + first_children = mate(fun, zeros, ones, n_pairs=4000)[0::2] + ax.plot( + np.arange(1, nvar + 1), first_children.mean(axis=0), "o-", label=name + ) +ax.axhline(0.5, color="gray", linestyle=":", linewidth=1) +ax.set_xticks(np.arange(1, nvar + 1)) +ax.set_ylim(-0.05, 1.05) +ax.set_xlabel("Variable") +ax.set_ylabel("Share taken from the second parent") +ax.legend() +fig.tight_layout() +plt.show() + +# %% +# +# Population-based operators +# -------------------------- +# +# Differential evolution and parent-centric crossover draw their other parents +# from the whole population. Here, every member of a population of 60 points +# (circles) is a target, and each operator is called 40 times. Passing the +# same :class:`numpy.random.Generator` as ``seed`` gives new children on each +# call. Both DE variants spread their children over the region covered by +# the population, whereas PCX keeps them close to their index parents. + +rng = np.random.default_rng(42) +population = np.clip(rng.normal([4.0, 6.0], 1.2, size=(60, 2)), 0.2, 9.8) +operators = { + "DE/rand/1/bin": moocore.de_rand_1_bin_crossover, + "DE/current/1": moocore.de_current_1_crossover, + "Parent-centric": moocore.parent_centric_crossover, +} +fig, axes = plt.subplots(1, 3, figsize=(10, 3.8), sharex=True, sharey=True) +for i, (ax, (name, fun)) in enumerate(zip(axes, operators.items())): + children = np.vstack( + [fun(population, seed=rng, **BOUNDS) for _ in range(40)] + ) + ax.scatter(children[:, 0], children[:, 1], s=3, alpha=0.3, color=f"C{i}") + ax.scatter( + population[:, 0], + population[:, 1], + s=20, + facecolors="none", + edgecolors="black", + ) + ax.set_title(name, fontsize="medium") + ax.set_xlim(LOWER, UPPER) + ax.set_ylim(LOWER, UPPER) + ax.set_aspect("equal") + ax.set_xlabel("$x_1$") +axes[0].set_ylabel("$x_2$") +fig.tight_layout() +plt.show() diff --git a/r/inst/REFERENCES.bib b/r/inst/REFERENCES.bib index b752aab29..1e533f89b 100644 --- a/r/inst/REFERENCES.bib +++ b/r/inst/REFERENCES.bib @@ -343,6 +343,17 @@ @article{LacKlaFon2017box doi = {10.1016/j.cor.2016.06.021} } +@article{LiZha2009:moead-de, + title = {Multiobjective Optimization Problems with Complicated + {Pareto} sets, {MOEA/D} and {NSGA-II}}, + author = {Li, Hui and Zhang, Qingfu }, + journal = {IEEE Transactions on Evolutionary Computation}, + volume = 13, + number = 2, + pages = {284--302}, + year = 2009 +} + @article{LopVerDreDoe2025, author = { Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Diederick Vermetten and Johann Dreo and Carola Doerr }, title = {Using the Empirical Attainment Function for Analyzing @@ -412,6 +423,19 @@ @article{SchKer2025r2v2 doi = {10.1162/evco.a.366} } +@article{StoPri1997:de, + author = {Storn, Rainer and Price, Kenneth}, + title = {Differential Evolution -- A Simple and Efficient Heuristic + for Global Optimization over Continuous Spaces}, + journal = {Journal of Global Optimization}, + year = 1997, + volume = 11, + number = 4, + pages = {341--359}, + annote = {Proposed differential evolution}, + doi = {10.1023/A:1008202821328} +} + @article{WuAza2001metrics, author = {J. Wu and S. Azam}, title = {Metrics for Quality Assessment of a Multiobjective Design @@ -480,6 +504,29 @@ @incollection{AugBadBroZit2009gecco2 pages = {563--570} } +@misc{BezLopStu2015emoDEsupp, + author = { Leonardo C. T. Bezerra and Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Thomas St{\"u}tzle }, + title = {To {DE} or Not to {DE}? {Multi}-objective Differential + Evolution Revisited from a Component-Wise Perspective: {Supplementary} material}, + howpublished = {\url{https://iridia.ulb.ac.be/supp/IridiaSupp2015-001/}}, + year = 2015 +} + +@incollection{BezLopStu2015emode, + booktitle = { Evolutionary Multi-criterion Optimization, EMO 2015 Part {I}}, + address = { Heidelberg, Germany}, + series = {Lecture Notes in Computer Science}, + volume = 9018, + year = 2015, + publisher = {Springer}, + editor = { Ant{\'o}nio Gaspar{-}Cunha and Carlos Henggeler Antunes and Carlos A. {Coello Coello} }, + author = { Leonardo C. T. Bezerra and Manuel L{\'o}pez-Ib{\'a}{\~n}ez and Thomas St{\"u}tzle }, + title = {To {DE} or Not to {DE}? {Multi}-objective Differential + Evolution Revisited from a Component-Wise Perspective}, + pages = {48--63}, + doi = {10.1007/978-3-319-15934-8_4} +} + @incollection{BezLopStu2017emo, address = { Cham, Switzerland}, series = {Lecture Notes in Computer Science}, @@ -550,6 +597,14 @@ @incollection{CoeSie2004igd keywords = {IGD} } +@book{EibSmi2003, + title = {Introduction to Evolutionary Computing}, + author = { Agoston E. Eiben and Smith, James E. }, + publisher = {Springer}, + year = 2003, + isbn = 3540401849 +} + @incollection{EmmFon2011emo, booktitle = { Evolutionary Multi-criterion Optimization, EMO 2011}, address = {Berlin~/ Heidelberg}, @@ -590,6 +645,17 @@ @incollection{EmmFon2011emo pages = {121--135} } +@incollection{EshSch1992, + isbn = {1-55860-263-1}, + year = 1993, + publisher = {Morgan Kaufmann Publishers}, + booktitle = {Foundations of Genetic Algorithms (FOGA)}, + editor = { Darrell Whitley }, + author = { Larry J. Eshelman and J. David Schaffer }, + title = {Real-Coded Genetic Algorithms and Interval-Schemata}, + pages = {187--202} +} + @book{FanWan1994numtheory, author = {Fang, K. T. and Wang, Y.}, title = {Number-Theoretic Methods in Statistics}, @@ -681,6 +747,15 @@ @incollection{Gla2017fast keywords = {archiving} } +@book{Goldberg89, + author = { David E. Goldberg }, + title = {Genetic Algorithms in Search, Optimization and + Machine Learning}, + publisher = {Addison-Wesley}, + address = { Boston, MA}, + year = 1989 +} + @incollection{GruFon2009:emaa, editor = { Thomas Bartz-Beielstein and Marco Chiarandini and Lu{\'i}s Paquete and Mike Preuss }, year = 2010, @@ -744,6 +819,13 @@ @techreport{HanJas1998 annote = {Proposed R2 indicator} } +@book{Hol75, + author = { J. Holland }, + title = {Adaptation in Natural and Artificial Systems}, + publisher = {University of Michigan Press}, + year = 1975 +} + @inproceedings{IshHeSha2019regular, month = jun, year = 2019, @@ -786,6 +868,19 @@ @inproceedings{KnoCor2002cec pages = {711--716} } +@inproceedings{KukLam2005:gde3, + address = {Piscataway, NJ}, + publisher = {IEEE Press}, + month = sep, + year = 2005, + booktitle = {Proceedings of the 2005 Congress on Evolutionary Computation (CEC 2005)}, + key = {IEEE CEC}, + author = {Kukkonen, S. and Lampinen, J.}, + title = {{GDE3}: the third evolution step of generalized differential + evolution}, + pages = {443--450} +} + @incollection{Lop2026hvapprox, location = {San Jos{\'e}, Costa Rica}, address = { New York, NY}, @@ -881,6 +976,19 @@ @misc{Rob2018unreasonable annote = {Proposed the Rphi low-discrepancy sequence} } +@incollection{RobFil05demo, + address = {Berlin~/ Heidelberg}, + publisher = {Springer}, + volume = 3410, + series = {Lecture Notes in Computer Science}, + editor = { Carlos A. {Coello Coello} and Hern{\'a}ndez Aguirre, Arturo and Eckart Zitzler }, + year = 2005, + booktitle = { Evolutionary Multi-criterion Optimization, EMO 2005}, + author = {Tea Robi{\v c} and Bogdan Filipi{\v c}}, + title = {{DEMO}: Differential Evolution for Multiobjective Optimization}, + pages = {520--533} +} + @book{RubMel1998simulation, author = {R. Y. Rubinstein and B. Melamed}, title = {Modern simulation and modeling}, @@ -890,6 +998,17 @@ @book{RubMel1998simulation notes = {Uniform sampling from the simplex.} } +@inproceedings{Syswerda89, + publisher = {Morgan Kaufmann Publishers, San Mateo, CA}, + editor = { J. David Schaffer }, + year = 1989, + booktitle = {Proceedings of the Third International Conference on Genetic Algorithms (ICGA'89)}, + author = { Gilbert Syswerda }, + title = {Uniform Crossover in Genetic Algorithms}, + pages = {2--9}, + keywords = {uniform crossover} +} + @inproceedings{VelLam1998gp, year = 1998, publisher = {Stanford University Bookstore}, From db40998e6122efc1c54c1cc263fadf3eabb54033 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 19:19:35 +0300 Subject: [PATCH 05/30] c/crossover.h: Describe the functions by their arguments, not by operator groups. --- c/crossover.h | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/c/crossover.h b/c/crossover.h index 30118d9c6..cc643e81d 100644 --- a/c/crossover.h +++ b/c/crossover.h @@ -29,14 +29,15 @@ BEGIN_C_DECLS All matrices are stored by rows, one decision vector per row, with NVAR variables each. OFFSPRING must be allocated by the caller. - Two-parent operators mate rows 2i and 2i+1 of PARENTS (N rows). If N is - odd, the last row mates with row 0. Operators that produce two children per + Functions that take PARENTS (N rows) mate rows 2i and 2i+1. If N is odd, + the last row mates with row 0. Operators that produce two children per pair write them to rows 2i and 2i+1 of OFFSPRING (N rows), dropping the second child of the last pair when N is odd. blend_alpha_crossover() produces one child per pair, so OFFSPRING has (N + 1) / 2 rows. - Population-based operators produce one child per row index in TARGETS - (NTARGETS values in [0, N)), so OFFSPRING has NTARGETS rows. + Functions that take POPULATION (N rows) produce one child per row index in + TARGETS (NTARGETS values in [0, N)), so OFFSPRING has NTARGETS rows. They + choose the other parents at random from POPULATION. LOWER and UPPER give the bounds of each variable. Use -INFINITY and INFINITY for unbounded variables. From 6d33da0dea2c71534b4b2aeffae21cc003e0c221 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 19:19:35 +0300 Subject: [PATCH 06/30] python/doc/ Replace crossover groups with a table of parents and children * python/doc/source/reference/functions.variation.rst: List all crossover functions together and add a table of children and parents per operation. * python/examples/plot_crossover.py: Do not use the group names. --- .../source/reference/functions.variation.rst | 69 ++++++++++++++----- python/examples/plot_crossover.py | 18 ++--- 2 files changed, 60 insertions(+), 27 deletions(-) diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst index f4e8fec1e..7ce091ca8 100644 --- a/python/doc/source/reference/functions.variation.rst +++ b/python/doc/source/reference/functions.variation.rst @@ -12,8 +12,8 @@ decision vector per row and accepts a ``seed`` for reproducible results. The :ref:`crossover example ` shows where each operator places its children. -Two-parent crossover -==================== +Crossover +========= .. autosummary:: :toctree: generated/ @@ -23,25 +23,57 @@ Two-parent crossover single_arithmetic_crossover local_crossover bounded_exponential_crossover - -These functions mate rows ``2i`` and ``2i + 1`` of ``parents``, so the order of -the rows decides which parents mate, for example after a selection step. If -the number of rows is odd, the last row mates with the first one. Most of -these operators produce two children per pair and return as many rows as -``parents``, dropping one child when the number of rows is odd. -:func:`blend_alpha_crossover` produces one child per pair. - -Population-based crossover -========================== -.. autosummary:: - :toctree: generated/ - de_rand_1_bin_crossover de_current_1_crossover parent_centric_crossover -These functions produce one child for each target row of ``population`` and -draw the other parents at random from ``population``. +The operators differ in how many parents one crossover operation uses and how +many children it produces: + +.. list-table:: + :header-rows: 1 + + * - Function + - Children per operation + - Parents per operation + * - :func:`uniform_crossover` + - 2 + - 2 + * - :func:`single_point_crossover` + - 2 + - 2 + * - :func:`blend_alpha_crossover` + - 1 + - 2 + * - :func:`single_arithmetic_crossover` + - 2 + - 2 + * - :func:`local_crossover` + - 2 + - 2 + * - :func:`bounded_exponential_crossover` + - 2 + - 2 + * - :func:`de_rand_1_bin_crossover` + - 1 + - 1, plus 3 other parents chosen at random + * - :func:`de_current_1_crossover` + - 1 + - 1, plus 2 other parents chosen at random + * - :func:`parent_centric_crossover` + - 1 + - 1, plus 2 other parents chosen at random + +The functions that use 2 parents per operation take a matrix ``parents`` and +mate rows ``2i`` and ``2i + 1``, so the order of the rows decides which parents +mate, for example after a selection step. If the number of rows is odd, the +last row mates with the first one. When an operation produces 2 children, the +output has as many rows as ``parents``, and one child is dropped when the +number of rows is odd. :func:`blend_alpha_crossover` returns one row per pair. + +The functions that use 1 parent per operation take a matrix ``population`` and +the row indices ``targets`` of the parents, and return one child per target. +They choose the other parents at random from ``population``. Differential evolution (DE) comes in two variants that are common in multi-objective optimization. :func:`de_rand_1_bin_crossover` is the @@ -49,7 +81,8 @@ DE/rand/1/bin scheme of :footcite:t:`StoPri1997:de`, which most Pareto-based multi-objective DE algorithms use :footcite:p:`BezLopStu2015emode`. :func:`de_current_1_crossover` is the operator of MOEA/D-DE :footcite:p:`LiZha2009:moead-de`. It starts from the target instead of a -random row and does not force any variable to change. +random row and does not force any variable to change. Its 2 other parents may +include the target itself. Bibliography diff --git a/python/examples/plot_crossover.py b/python/examples/plot_crossover.py index 4f0a54c78..4cef3a46c 100644 --- a/python/examples/plot_crossover.py +++ b/python/examples/plot_crossover.py @@ -4,9 +4,9 @@ This example shows where each crossover operator places the children of fixed parents. Each figure mates the same parents many times and plots all -the children. Two-parent operators mate rows ``2i`` and ``2i + 1``, so -stacking copies of one pair of parents gives many independent draws in a -single call. +the children. Operators that use 2 parents per operation mate rows ``2i`` +and ``2i + 1``, so stacking copies of one pair of parents gives many +independent draws in a single call. First we define a few functions useful for plotting. """ @@ -45,8 +45,8 @@ def mark_parents(ax, positions): # %% # -# Where two-parent operators put their children -# --------------------------------------------- +# Where the children of two parents end up +# ---------------------------------------- # # The parents are :math:`(3, 3)` and :math:`(7, 7)` within :math:`[0, 10]^2`. # Each panel shows the distribution of the first variable of the children for @@ -195,11 +195,11 @@ def mark_parents(ax, positions): # %% # -# Population-based operators -# -------------------------- +# Differential evolution and parent-centric crossover +# --------------------------------------------------- # -# Differential evolution and parent-centric crossover draw their other parents -# from the whole population. Here, every member of a population of 60 points +# These operators produce one child per parent and choose the other parents at +# random from the population. Here, every member of a population of 60 points # (circles) is a target, and each operator is called 40 times. Passing the # same :class:`numpy.random.Generator` as ``seed`` gives new children on each # call. Both DE variants spread their children over the region covered by From 3475a1d400d2b625fca7ed465f9ec55f98629af0 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 19:29:51 +0300 Subject: [PATCH 07/30] c/ Say offspring and crossed over instead of children and mate * c/crossover.c (bex_child): Rename to bex_offspring. (get_pair): Rename c1 and c2 to off1 and off2. Update comments. * c/crossover.h: Update comment. --- c/crossover.c | 112 +++++++++++++++++++++++++++----------------------- c/crossover.h | 15 +++---- 2 files changed, 68 insertions(+), 59 deletions(-) diff --git a/c/crossover.c b/c/crossover.c index 061e71c0b..f02071a2a 100644 --- a/c/crossover.c +++ b/c/crossover.c @@ -36,19 +36,19 @@ clamp_to_bounds(double x, double lower, double upper) return fmin(fmax(x, lower), upper); } -/* Rows I and I + 1 of PARENTS mate and their children go to rows I and I + 1 - of OFFSPRING. If I + 1 == N, row I mates with row 0 and its second child - goes to SCRATCH, so it is discarded. */ +/* Rows I and I + 1 of PARENTS are crossed over and their offspring go to rows + I and I + 1 of OFFSPRING. If I + 1 == N, row I is crossed over with row 0 + and its second offspring goes to SCRATCH, so it is discarded. */ static inline void get_pair(const double * parents, double * offspring, double * scratch, size_t i, size_t n, size_t nvar, - const double ** p1, const double ** p2, double ** c1, double ** c2) + const double ** p1, const double ** p2, double ** off1, double ** off2) { const bool last = (i + 1 == n); *p1 = parents + i * nvar; *p2 = parents + (last ? 0 : i + 1) * nvar; - *c1 = offspring + i * nvar; - *c2 = last ? scratch : offspring + (i + 1) * nvar; + *off1 = offspring + i * nvar; + *off2 = last ? scratch : offspring + (i + 1) * nvar; } static inline double * @@ -92,13 +92,14 @@ uniform_crossover(double * restrict offspring, const double * restrict parents, double * scratch = scratch_new(n, nvar); for (size_t i = 0; i < n; i += 2) { const double *p1, *p2; - double *c1, *c2; - get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + double *off1, *off2; + get_pair(parents, offspring, scratch, i, n, nvar, + &p1, &p2, &off1, &off2); const bool recombine = rng_random(rng) < pair_prob; for (size_t j = 0; j < nvar; j++) { const bool swap = recombine && rng_random(rng) < swap_prob; - c1[j] = swap ? p2[j] : p1[j]; - c2[j] = swap ? p1[j] : p2[j]; + off1[j] = swap ? p2[j] : p1[j]; + off2[j] = swap ? p1[j] : p2[j]; } } free(scratch); @@ -115,15 +116,16 @@ single_point_crossover(double * restrict offspring, double * scratch = scratch_new(n, nvar); for (size_t i = 0; i < n; i += 2) { const double *p1, *p2; - double *c1, *c2; - get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); - // Cut point in [1, nvar - 1], so each child takes at least one + double *off1, *off2; + get_pair(parents, offspring, scratch, i, n, nvar, + &p1, &p2, &off1, &off2); + // Cut point in [1, nvar - 1], so each offspring takes at least one // variable from each parent. const size_t cut = 1 + rng_integer(rng, nvar - 1); - memcpy(c1, p1, cut * sizeof(*c1)); - memcpy(c1 + cut, p2 + cut, (nvar - cut) * sizeof(*c1)); - memcpy(c2, p2, cut * sizeof(*c2)); - memcpy(c2 + cut, p1 + cut, (nvar - cut) * sizeof(*c2)); + memcpy(off1, p1, cut * sizeof(*off1)); + memcpy(off1 + cut, p2 + cut, (nvar - cut) * sizeof(*off1)); + memcpy(off2, p2, cut * sizeof(*off2)); + memcpy(off2 + cut, p1 + cut, (nvar - cut) * sizeof(*off2)); } free(scratch); rng_free(rng); @@ -142,7 +144,7 @@ blend_alpha_crossover(double * restrict offspring, for (size_t i = 0; i < n; i += 2) { const double * p1 = parents + i * nvar; const double * p2 = parents + ((i + 1 < n) ? i + 1 : 0) * nvar; - double * child = offspring + (i / 2) * nvar; + double * off = offspring + (i / 2) * nvar; for (size_t j = 0; j < nvar; j++) { const double lo = fmin(p1[j], p2[j]); const double hi = fmax(p1[j], p2[j]); @@ -151,7 +153,7 @@ blend_alpha_crossover(double * restrict offspring, // bounds and sample uniformly from it. const double a = fmax(lo - alpha * span, lower[j]); const double b = fmin(hi + alpha * span, upper[j]); - child[j] = a + rng_random(rng) * (b - a); + off[j] = a + rng_random(rng) * (b - a); } } rng_free(rng); @@ -168,14 +170,15 @@ single_arithmetic_crossover(double * restrict offspring, double * scratch = scratch_new(n, nvar); for (size_t i = 0; i < n; i += 2) { const double *p1, *p2; - double *c1, *c2; - get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + double *off1, *off2; + get_pair(parents, offspring, scratch, i, n, nvar, + &p1, &p2, &off1, &off2); const bool recombine = rng_random(rng) < pair_prob; const size_t k = rng_integer(rng, nvar); - memcpy(c1, p1, nvar * sizeof(*c1)); - memcpy(c2, p2, nvar * sizeof(*c2)); + memcpy(off1, p1, nvar * sizeof(*off1)); + memcpy(off2, p2, nvar * sizeof(*off2)); if (recombine) - c1[k] = c2[k] = 0.5 * (p1[k] + p2[k]); + off1[k] = off2[k] = 0.5 * (p1[k] + p2[k]); } free(scratch); rng_free(rng); @@ -190,23 +193,25 @@ local_crossover(double * restrict offspring, const double * restrict parents, double * scratch = scratch_new(n, nvar); for (size_t i = 0; i < n; i += 2) { const double *p1, *p2; - double *c1, *c2; - get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + double *off1, *off2; + get_pair(parents, offspring, scratch, i, n, nvar, + &p1, &p2, &off1, &off2); for (size_t j = 0; j < nvar; j++) { const double a = rng_random(rng); - c1[j] = a * p1[j] + (1 - a) * p2[j]; - c2[j] = (1 - a) * p1[j] + a * p2[j]; + off1[j] = a * p1[j] + (1 - a) * p2[j]; + off2[j] = (1 - a) * p1[j] + a * p2[j]; } } free(scratch); rng_free(rng); } -/* Child of parent value X. It moves X by BETA * SPAN, where BETA follows a - two-sided exponential distribution with scale SCALE, truncated so that the - child stays within [LOWER, UPPER]. U and R are uniform in [0, 1). */ +/* Offspring value of parent value X. It moves X by BETA * SPAN, where BETA + follows a two-sided exponential distribution with scale SCALE, truncated so + that the offspring stays within [LOWER, UPPER]. U and R are uniform in + [0, 1). */ static inline double -bex_child(double x, double span, double lower, double upper, double scale, +bex_offspring(double x, double span, double lower, double upper, double scale, double u, double r) { double beta; @@ -237,31 +242,34 @@ bounded_exponential_crossover(double * restrict offspring, double * scratch = scratch_new(n, nvar); for (size_t i = 0; i < n; i += 2) { const double *p1, *p2; - double *c1, *c2; - get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &c1, &c2); + double *off1, *off2; + get_pair(parents, offspring, scratch, i, n, nvar, + &p1, &p2, &off1, &off2); if (!(rng_random(rng) < pair_prob)) { - memcpy(c1, p1, nvar * sizeof(*c1)); - memcpy(c2, p2, nvar * sizeof(*c2)); + memcpy(off1, p1, nvar * sizeof(*off1)); + memcpy(off2, p2, nvar * sizeof(*off2)); continue; } for (size_t j = 0; j < nvar; j++) { // The distance between the parents scales the move of both - // children, whichever parent is smaller. + // offspring, whichever parent is smaller. const double span = fabs(p2[j] - p1[j]); if (span == 0) { - c1[j] = p1[j]; - c2[j] = p2[j]; + off1[j] = p1[j]; + off2[j] = p2[j]; continue; } - // Both children use the same random numbers. + // Both offspring use the same random numbers. const double u = rng_random(rng); const double r = rng_random(rng); - c1[j] = bex_child(p1[j], span, lower[j], upper[j], scale, u, r); - c2[j] = bex_child(p2[j], span, lower[j], upper[j], scale, u, r); + off1[j] = bex_offspring(p1[j], span, lower[j], upper[j], + scale, u, r); + off2[j] = bex_offspring(p2[j], span, lower[j], upper[j], + scale, u, r); if (swap_prob > 0 && rng_random(rng) < swap_prob) { - const double tmp = c1[j]; - c1[j] = c2[j]; - c2[j] = tmp; + const double tmp = off1[j]; + off1[j] = off2[j]; + off2[j] = tmp; } } } @@ -288,14 +296,14 @@ de_rand_1_bin_crossover(double * restrict offspring, const double * x1 = population + r[0] * nvar; const double * x2 = population + r[1] * nvar; const double * x3 = population + r[2] * nvar; - // The child takes at least the variable JRAND from the mutant. + // The offspring takes at least the variable JRAND from the mutant. const size_t jrand = rng_integer(rng, nvar); - double * child = offspring + t * nvar; + double * off = offspring + t * nvar; for (size_t j = 0; j < nvar; j++) { const double v = (j == jrand || rng_random(rng) < crossover_rate) ? x1[j] + scaling_factor * (x2[j] - x3[j]) : x[j]; - child[j] = clamp_to_bounds(v, lower[j], upper[j]); + off[j] = clamp_to_bounds(v, lower[j], upper[j]); } } rng_free(rng); @@ -320,12 +328,12 @@ de_current_1_crossover(double * restrict offspring, sample_distinct(rng, n, excluded, 0, 2, r); const double * x1 = population + r[0] * nvar; const double * x2 = population + r[1] * nvar; - double * child = offspring + t * nvar; + double * off = offspring + t * nvar; for (size_t j = 0; j < nvar; j++) { const double v = (rng_random(rng) < crossover_rate) ? x[j] + scaling_factor * (x1[j] - x2[j]) : x[j]; - child[j] = clamp_to_bounds(v, lower[j], upper[j]); + off[j] = clamp_to_bounds(v, lower[j], upper[j]); } } rng_free(rng); @@ -398,9 +406,9 @@ parent_centric_crossover(double * restrict offspring, } const double zeta = sigma_zeta * rng_standard_normal(rng); - double * child = offspring + t * nvar; + double * off = offspring + t * nvar; for (size_t j = 0; j < nvar; j++) - child[j] = clamp_to_bounds( + off[j] = clamp_to_bounds( x[j] + zeta * direction[j] + spread * orthogonal[j], lower[j], upper[j]); } diff --git a/c/crossover.h b/c/crossover.h index cc643e81d..6e330b97b 100644 --- a/c/crossover.h +++ b/c/crossover.h @@ -29,13 +29,14 @@ BEGIN_C_DECLS All matrices are stored by rows, one decision vector per row, with NVAR variables each. OFFSPRING must be allocated by the caller. - Functions that take PARENTS (N rows) mate rows 2i and 2i+1. If N is odd, - the last row mates with row 0. Operators that produce two children per - pair write them to rows 2i and 2i+1 of OFFSPRING (N rows), dropping the - second child of the last pair when N is odd. blend_alpha_crossover() - produces one child per pair, so OFFSPRING has (N + 1) / 2 rows. - - Functions that take POPULATION (N rows) produce one child per row index in + Functions that take PARENTS (N rows) cross over rows 2i and 2i+1. If N is + odd, the last row is crossed over with row 0. Operators that produce two + offspring per pair write them to rows 2i and 2i+1 of OFFSPRING (N rows), + dropping the second offspring of the last pair when N is odd. + blend_alpha_crossover() produces one offspring per pair, so OFFSPRING has + (N + 1) / 2 rows. + + Functions that take POPULATION (N rows) produce one offspring per row index in TARGETS (NTARGETS values in [0, N)), so OFFSPRING has NTARGETS rows. They choose the other parents at random from POPULATION. From ca1cdf4ca5367314ed502b57684e65bb5959e669 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 19:29:52 +0300 Subject: [PATCH 08/30] python/ Say offspring and crossed over instead of children and mate * python/src/moocore/_crossover.py: Update docstrings. * python/src/moocore/_docsubstitute.py (COMMON_PARAMS): Likewise. * python/tests/test_crossover.py: Rename tests and variables. --- python/src/moocore/_crossover.py | 126 +++++++++++++++------------ python/src/moocore/_docsubstitute.py | 8 +- python/tests/test_crossover.py | 69 +++++++-------- 3 files changed, 107 insertions(+), 96 deletions(-) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index ef9a6f162..7ce0a4489 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -110,12 +110,12 @@ def uniform_crossover( ) -> np.ndarray: r"""Uniform crossover. - Each pair of parents produces two children. With probability - ``pair_prob``, each variable is swapped between the two children with - probability ``swap_prob``. Otherwise, the children are copies of their - parents. + Each crossover operation on a pair of parents produces two offspring. With + probability ``pair_prob``, each variable is swapped between the two + offspring with probability ``swap_prob``. Otherwise, the offspring are + copies of their parents. - The children only take values from their parents, so this operator works + The offspring only take values from their parents, so this operator works for binary, integer and real-valued variables alike. Integer and Boolean inputs keep their dtype. @@ -124,9 +124,10 @@ def uniform_crossover( parents : ${parents} swap_prob : - Probability of swapping each variable between the two children. + Probability of swapping each variable between the two offspring. pair_prob : - Probability of recombining each pair of parents. + Probability of applying the crossover operation to each pair of + parents. seed : ${random_seed} @@ -179,12 +180,13 @@ def single_point_crossover( ) -> np.ndarray: r"""Single-point crossover. - Each pair of parents produces two children. A cut point :math:`k` is drawn - uniformly from :math:`\{1, \dots, n_\text{var} - 1\}`. The first child - takes the first :math:`k` variables from the first parent and the rest from - the second parent, and the second child takes the complement. + Each crossover operation on a pair of parents produces two offspring. A + cut point :math:`k` is drawn uniformly from :math:`\{1, \dots, + n_\text{var} - 1\}`. The first offspring takes the first :math:`k` + variables from the first parent and the rest from the second parent, and + the second offspring takes the complement. - The children only take values from their parents, so this operator works + The offspring only take values from their parents, so this operator works for binary, integer and real-valued variables alike. Integer and Boolean inputs keep their dtype. @@ -245,7 +247,8 @@ def blend_alpha_crossover( ) -> np.ndarray: r"""Blend crossover (BLX-:math:`\alpha`). - Each pair of parents :math:`x, y` produces **one** child :math:`z`. For + Each crossover operation on a pair of parents :math:`x, y` produces + **one** offspring :math:`z`. For each variable :math:`j`, let :math:`m_j = \min(x_j, y_j)`, :math:`M_j = \max(x_j, y_j)` and :math:`d_j = M_j - m_j`. Then :math:`z_j` is sampled uniformly from :math:`[m_j - \alpha d_j, M_j + \alpha d_j]`, clipped to @@ -261,31 +264,31 @@ def blend_alpha_crossover( ${upper_bound} alpha : Fraction of the distance between the parents by which the sampling - interval extends beyond them on each side. With ``alpha=0``, children - lie between their parents. + interval extends beyond them on each side. With ``alpha=0``, the + offspring lie between their parents. seed : ${random_seed} Returns ------- Array with :math:`\lceil n/2 \rceil` rows, where :math:`n` is the - number of rows of ``parents``. Row ``i`` is the child of rows ``2i`` - and ``2i + 1`` of ``parents``. + number of rows of ``parents``. Row ``i`` is the offspring of rows + ``2i`` and ``2i + 1`` of ``parents``. See Also -------- - local_crossover : Children inside the box spanned by the parents. + local_crossover : Offspring inside the box spanned by the parents. Notes ----- BLX-:math:`\alpha` was proposed by :footcite:t:`EshSch1992`. Each variable - is sampled independently, so the children fill the whole (clipped) box + is sampled independently, so the offspring fill the whole (clipped) box around the parents. - To produce more than one child per pair, call the function again. If - ``seed`` is an integer, every call returns the same children. Pass the + To produce more than one offspring per pair, call the function again. If + ``seed`` is an integer, every call returns the same offspring. Pass the same :class:`numpy.random.Generator` to every call to get different - children each time, as in the example below. + offspring each time, as in the example below. References ---------- @@ -326,18 +329,19 @@ def single_arithmetic_crossover( ) -> np.ndarray: r"""Single arithmetic crossover. - Each pair of parents :math:`x, y` produces two children. With probability - ``pair_prob``, one variable :math:`k` is chosen uniformly at random and - both children get :math:`(x_k + y_k) / 2` in that variable. All other - variables are copied from the parents. Otherwise, the children are copies - of their parents. + Each crossover operation on a pair of parents :math:`x, y` produces two + offspring. With probability ``pair_prob``, one variable :math:`k` is + chosen uniformly at random and both offspring get :math:`(x_k + y_k) / 2` + in that variable. All other variables are copied from the parents. + Otherwise, the offspring are copies of their parents. Parameters ---------- parents : ${parents} pair_prob : - Probability of recombining each pair of parents. + Probability of applying the crossover operation to each pair of + parents. seed : ${random_seed} @@ -390,13 +394,14 @@ def local_crossover( ) -> np.ndarray: r"""Local crossover. - Each pair of parents :math:`x, y` produces two children + Each crossover operation on a pair of parents :math:`x, y` produces two + offspring .. math:: u_j = a_j x_j + (1 - a_j) y_j, \qquad v_j = (1 - a_j) x_j + a_j y_j, where each weight :math:`a_j` is drawn uniformly from :math:`[0, 1)`. The - children lie in the box spanned by their parents, and :math:`u + v = x + + offspring lie in the box spanned by their parents, and :math:`u + v = x + y`. Parameters @@ -460,25 +465,28 @@ def bounded_exponential_crossover( ) -> np.ndarray: r"""Bounded exponential crossover (BEX). - Each pair of parents :math:`x, y` produces two children :math:`u, v` with - probability ``pair_prob``; otherwise, the children are copies of their - parents. For each variable :math:`j` with :math:`d_j = |x_j - y_j| > 0`, + Each crossover operation on a pair of parents :math:`x, y` produces two + offspring :math:`u, v`. With probability ``pair_prob``, for each + variable :math:`j` with :math:`d_j = |x_j - y_j| > 0`, .. math:: u_j = x_j + \beta_j^x d_j, \qquad v_j = y_j + \beta_j^y d_j, where :math:`\beta_j^x` follows an exponential distribution with scale :math:`\lambda` (``scale``), truncated so that :math:`u_j` stays within - the bounds of the variable. With probability 1/2, a child moves towards - the lower bound :math:`l_j`, with :math:`\beta = \lambda \ln(e_l + r(1 - - e_l))` and :math:`e_l = \exp((l_j - x_j) / (\lambda d_j))`. Otherwise, it - moves towards the upper bound :math:`h_j`, with :math:`\beta = -\lambda - \ln(1 - r(1 - e_h))` and :math:`e_h = \exp((x_j - h_j) / (\lambda d_j))`. + the bounds of the variable. With probability 1/2, an offspring moves + towards the lower bound :math:`l_j`, with :math:`\beta = \lambda \ln(e_l + + r(1 - e_l))` and :math:`e_l = \exp((l_j - x_j) / (\lambda d_j))`. + Otherwise, it moves towards the upper bound :math:`h_j`, with :math:`\beta + = -\lambda \ln(1 - r(1 - e_h))` and :math:`e_h = \exp((x_j - h_j) / + (\lambda d_j))`. The uniform random number :math:`r` and the direction are shared by both - children. Variables where the parents are equal are copied. + offspring. Variables where the parents are equal are copied. After + that, each variable is swapped between the two offspring with probability + ``swap_prob``, as in :func:`uniform_crossover`. - After that, each variable is swapped between the two children with - probability ``swap_prob``, as in :func:`uniform_crossover`. + Otherwise, with probability ``1 - pair_prob``, the offspring are copies of + their parents. Parameters ---------- @@ -490,11 +498,12 @@ def bounded_exponential_crossover( ${upper_bound} scale : Scale :math:`\lambda > 0` of the exponential distribution. Smaller - values keep the children closer to their parents. + values keep the offspring closer to their parents. pair_prob : - Probability of recombining each pair of parents. + Probability of applying the crossover operation to each pair of + parents. swap_prob : - Probability of swapping each variable between the two children. + Probability of swapping each variable between the two offspring. seed : ${random_seed} @@ -562,10 +571,10 @@ def de_rand_1_bin_crossover( For each target :math:`x_i`, three rows :math:`x_{r_1}, x_{r_2}, x_{r_3}` are drawn from ``population``, distinct from each other and from the - target. The child takes each variable :math:`j` from the mutant + target. The offspring takes each variable :math:`j` from the mutant :math:`x_{r_1} + F (x_{r_2} - x_{r_3})` with probability :math:`CR`, and from the target otherwise. One variable chosen at random always comes - from the mutant. Finally, the child is clipped to the bounds. + from the mutant. Finally, the offspring is clipped to the bounds. Parameters ---------- @@ -587,8 +596,8 @@ def de_rand_1_bin_crossover( Returns ------- - Array with one row per target, where row ``i`` is the child of target - ``targets[i]``. + Array with one row per target, where row ``i`` is the offspring of + target ``targets[i]``. See Also -------- @@ -654,13 +663,13 @@ def de_current_1_crossover( For each target :math:`x_i`, two distinct rows :math:`x_{r_1}, x_{r_2}` are drawn from ``population``. Either of them may be the target itself. - The child takes each variable :math:`j` from :math:`x_i + F (x_{r_1} - + The offspring takes each variable :math:`j` from :math:`x_i + F (x_{r_1} - x_{r_2})` with probability :math:`CR`, and from the target otherwise. - Finally, the child is clipped to the bounds. + Finally, the offspring is clipped to the bounds. Unlike :func:`de_rand_1_bin_crossover`, the base vector is the target and no variable is forced to come from the mutant, so with :math:`CR = 0` the - child is a copy of the target. + offspring is a copy of the target. Parameters ---------- @@ -682,8 +691,8 @@ def de_current_1_crossover( Returns ------- - Array with one row per target, where row ``i`` is the child of target - ``targets[i]``. + Array with one row per target, where row ``i`` is the offspring of + target ``targets[i]``. See Also -------- @@ -755,15 +764,16 @@ def parent_centric_crossover( are drawn from ``population``, distinct from each other and from the target. Let :math:`d = x - g`, where :math:`g` is the centroid of the three parents, and let :math:`\bar{D}` be the mean distance from :math:`a` - and :math:`b` to the line through :math:`x` along :math:`d`. The child is + and :math:`b` to the line through :math:`x` along :math:`d`. The + offspring is .. math:: x + \zeta d + \bar{D} \eta, where :math:`\zeta \sim N(0, \sigma_\zeta^2)` and :math:`\eta` is a vector of independent :math:`N(0, \sigma_\eta^2)` values projected onto - the subspace orthogonal to :math:`d`. Finally, the child is clipped to the - bounds. + the subspace orthogonal to :math:`d`. Finally, the offspring is clipped to + the bounds. Parameters ---------- @@ -786,8 +796,8 @@ def parent_centric_crossover( Returns ------- - Array with one row per target, where row ``i`` is the child of index - parent ``targets[i]``. + Array with one row per target, where row ``i`` is the offspring of + index parent ``targets[i]``. Notes ----- diff --git a/python/src/moocore/_docsubstitute.py b/python/src/moocore/_docsubstitute.py index 6e39e605d..2fda2a7df 100644 --- a/python/src/moocore/_docsubstitute.py +++ b/python/src/moocore/_docsubstitute.py @@ -29,14 +29,14 @@ Maybe generated by :func:`eafdiff()` with ``rectangles=True`` or by :func:`choose_eafdiff()`.""", # ------------------------------------------------------------------------- "parents": """2D array of numerical values, where each row is a decision vector. - Rows ``2i`` and ``2i + 1`` are mated. If the number of rows is odd, the last row is mated with the first one.""", + Rows ``2i`` and ``2i + 1`` are crossed over. If the number of rows is odd, the last row is crossed over with the first one.""", # ------------------------------------------------------------------------- - "pair_offspring": """Array with the same shape as ``parents``, where rows ``2i`` and ``2i + 1`` are the two children of rows ``2i`` and ``2i + 1`` of ``parents``. - If the number of rows is odd, the second child of the last pair is dropped, so the number of rows does not change.""", + "pair_offspring": """Array with the same shape as ``parents``, where rows ``2i`` and ``2i + 1`` are the two offspring of rows ``2i`` and ``2i + 1`` of ``parents``. + If the number of rows is odd, the second offspring of the last pair is dropped, so the number of rows does not change.""", # ------------------------------------------------------------------------- "population": """2D array of numerical values, where each row is a decision vector.""", # ------------------------------------------------------------------------- - "targets": """1D vector of row indices of ``population``. Each index produces one child. ``None`` uses every row.""", + "targets": """1D vector of row indices of ``population``. Each index produces one offspring. ``None`` uses every row.""", # ------------------------------------------------------------------------- "lower_bound": """Lower bounds of the decision variables. Either a single value, which will be used for all variables, or one value per column. ``None`` means no lower bound.""", diff --git a/python/tests/test_crossover.py b/python/tests/test_crossover.py index 6ef6610cf..ffca3b017 100644 --- a/python/tests/test_crossover.py +++ b/python/tests/test_crossover.py @@ -9,14 +9,14 @@ LOWER, UPPER = 0.0, 10.0 -TWO_CHILDREN = { +TWO_OFFSPRING = { "uniform": moocore.uniform_crossover, "single_point": moocore.single_point_crossover, "single_arithmetic": moocore.single_arithmetic_crossover, "local": moocore.local_crossover, "bounded_exponential": moocore.bounded_exponential_crossover, } -PAIR_OPERATORS = {**TWO_CHILDREN, "blend_alpha": moocore.blend_alpha_crossover} +PAIR_OPERATORS = {**TWO_OFFSPRING, "blend_alpha": moocore.blend_alpha_crossover} POPULATION_OPERATORS = { "de_rand_1_bin": moocore.de_rand_1_bin_crossover, "de_current_1": moocore.de_current_1_crossover, @@ -38,22 +38,22 @@ def pairs(x): return x[0::2], x[1::2] -@pytest.mark.parametrize("name", TWO_CHILDREN) +@pytest.mark.parametrize("name", TWO_OFFSPRING) @pytest.mark.parametrize("n", [2, 3, 4, 5, 10]) -def test_two_children_per_pair_keep_row_count(name, n): +def test_two_offspring_per_pair_keep_row_count(name, n): x = random_matrix(n) - assert TWO_CHILDREN[name](x, seed=1).shape == x.shape + assert TWO_OFFSPRING[name](x, seed=1).shape == x.shape @pytest.mark.parametrize("n", [2, 3, 4, 5, 10]) -def test_blend_alpha_crossover_one_child_per_pair(n): +def test_blend_alpha_crossover_one_offspring_per_pair(n): x = random_matrix(n) out = moocore.blend_alpha_crossover(x, seed=1) assert out.shape == (math.ceil(n / 2), x.shape[1]) @pytest.mark.parametrize("name", POPULATION_OPERATORS) -def test_population_operators_one_child_per_target(name): +def test_population_operators_one_offspring_per_target(name): fun = POPULATION_OPERATORS[name] x = random_matrix(6) assert fun(x, seed=1).shape == x.shape @@ -66,7 +66,7 @@ def test_population_operators_one_child_per_target(name): def test_odd_number_of_parents_pairs_last_with_first(n): x = random_matrix(n) assert_array_equal(moocore.uniform_crossover(x, swap_prob=0, seed=1), x) - # Swapping every variable gives each child the other parent. + # Swapping every variable gives each offspring the other parent. out = moocore.uniform_crossover(x, swap_prob=1, seed=1) assert_array_equal(out[0], x[1]) assert_array_equal(out[-1], x[0]) @@ -96,7 +96,7 @@ def test_seed(name): fun(x, seed=np.random.default_rng(42)), ) assert not np.array_equal(fun(x, seed=1), fun(x, seed=2)) - # The same Generator gives new children on each call. + # The same Generator gives new offspring on each call. rng = np.random.default_rng(42) assert not np.array_equal(fun(x, seed=rng), fun(x, seed=rng)) # seed=None still works. @@ -117,10 +117,10 @@ def test_inputs_are_not_modified(name, immutable_call): def test_uniform_crossover_only_copies_parent_values(): x = random_matrix(200, nvar=6) p1, p2 = pairs(x) - c1, c2 = pairs(moocore.uniform_crossover(x, seed=1)) - from_first = c1 == p1 - assert np.all(from_first | (c1 == p2)) - assert_array_equal(c2, np.where(from_first, p2, p1)) + off1, off2 = pairs(moocore.uniform_crossover(x, seed=1)) + from_first = off1 == p1 + assert np.all(from_first | (off1 == p2)) + assert_array_equal(off2, np.where(from_first, p2, p1)) assert_array_equal(moocore.uniform_crossover(x, pair_prob=0, seed=1), x) @@ -128,7 +128,7 @@ def test_uniform_crossover_only_copies_parent_values(): def test_uniform_crossover_swap_rate(swap_prob): x = np.tile([np.zeros(10), np.ones(10)], (2000, 1)) out = moocore.uniform_crossover(x, swap_prob=swap_prob, seed=1) - # The first child gets a 1 only where it was swapped. + # The first offspring gets a 1 only where it was swapped. assert abs(out[0::2].mean() - swap_prob) < 0.02 @@ -149,10 +149,10 @@ def test_value_copying_operators_keep_dtype(fun, dtype): def test_single_point_crossover_exchanges_tails(): nvar = 5 x = np.tile([np.zeros(nvar), np.ones(nvar)], (2000, 1)) - c1, c2 = pairs(moocore.single_point_crossover(x, seed=1)) - cuts = (c1 == 0).sum(axis=1) - assert_array_equal(c1, (np.arange(nvar) >= cuts[:, None]).astype(float)) - assert_array_equal(c2, 1 - c1) + off1, off2 = pairs(moocore.single_point_crossover(x, seed=1)) + cuts = (off1 == 0).sum(axis=1) + assert_array_equal(off1, (np.arange(nvar) >= cuts[:, None]).astype(float)) + assert_array_equal(off2, 1 - off1) assert set(cuts) == set(range(1, nvar)) @@ -179,26 +179,26 @@ def test_blend_alpha_crossover_samples_variables_independently(): def test_single_arithmetic_crossover_changes_one_variable(): x = random_matrix(100, nvar=5) p1, p2 = pairs(x) - c1, c2 = pairs(moocore.single_arithmetic_crossover(x, seed=1)) - changed = c1 != p1 + off1, off2 = pairs(moocore.single_arithmetic_crossover(x, seed=1)) + changed = off1 != p1 assert np.all(changed.sum(axis=1) == 1) - assert_array_equal(changed, c2 != p2) + assert_array_equal(changed, off2 != p2) mean = 0.5 * (p1 + p2) - assert_array_equal(c1[changed], mean[changed]) - assert_array_equal(c2[changed], mean[changed]) + assert_array_equal(off1[changed], mean[changed]) + assert_array_equal(off2[changed], mean[changed]) assert_array_equal( moocore.single_arithmetic_crossover(x, pair_prob=0, seed=1), x ) -def test_local_crossover_children_lie_between_parents(): +def test_local_crossover_offspring_lie_between_parents(): x = random_matrix(100, nvar=5) p1, p2 = pairs(x) - c1, c2 = pairs(moocore.local_crossover(x, seed=1)) - assert_allclose(c1 + c2, p1 + p2) + off1, off2 = pairs(moocore.local_crossover(x, seed=1)) + assert_allclose(off1 + off2, p1 + p2) lo, hi = np.minimum(p1, p2) - 1e-12, np.maximum(p1, p2) + 1e-12 - for c in (c1, c2): - assert np.all((c >= lo) & (c <= hi)) + for off in (off1, off2): + assert np.all((off >= lo) & (off <= hi)) def test_bounded_exponential_crossover_shared_values(): @@ -231,14 +231,15 @@ def test_bounded_exponential_crossover_swap_prob(swap_prob, expected): out = moocore.bounded_exponential_crossover( x, lower=0, upper=10, swap_prob=swap_prob, seed=1 ) - # Fraction of the variables of the first child that stay near its parent. - c1 = out[0::2] - kept = (np.abs(c1 - 2) < np.abs(c1 - 8)).mean() + # Fraction of the variables of the first offspring that stay near its + # parent. + off1 = out[0::2] + kept = (np.abs(off1 - 2) < np.abs(off1 - 8)).mean() assert abs(kept - expected) < 0.02 @pytest.mark.parametrize("order", [1, -1]) -def test_bounded_exponential_crossover_children_near_their_parent(order): +def test_bounded_exponential_crossover_offspring_near_their_parent(order): pair = np.array([[3.0, 3.0], [7.0, 7.0]])[::order] x = np.tile(pair, (2000, 1)) out = moocore.bounded_exponential_crossover(x, lower=0, upper=10, seed=1) @@ -257,8 +258,8 @@ def test_de_rand_1_bin_crossover_base_is_another_row(): out = moocore.de_rand_1_bin_crossover( x, scaling_factor=1e-12, crossover_rate=1, seed=1 ) - for i, child in enumerate(out): - dist = np.abs(x - child).max(axis=1) + for i, offspring in enumerate(out): + dist = np.abs(x - offspring).max(axis=1) nearest = np.argmin(dist) assert nearest != i assert dist[nearest] < 1e-9 From de7af8e5e0f5087099a9dacae2ec922ac4fa4208 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 19:29:52 +0300 Subject: [PATCH 09/30] python/doc/ Say offspring and crossed over instead of children and mate * python/doc/source/reference/functions.variation.rst: Update. * python/examples/plot_crossover.py (mate): Rename to cross_over. Update comments. --- .../source/reference/functions.variation.rst | 21 +++--- python/examples/plot_crossover.py | 72 ++++++++++--------- 2 files changed, 49 insertions(+), 44 deletions(-) diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst index 7ce091ca8..f0f34b4ba 100644 --- a/python/doc/source/reference/functions.variation.rst +++ b/python/doc/source/reference/functions.variation.rst @@ -7,10 +7,10 @@ Variation operators .. currentmodule:: moocore Crossover operators combine decision vectors, called parents, to produce new -decision vectors, called children. Every function takes a 2D array with one +decision vectors, called offspring. Every function takes a 2D array with one decision vector per row and accepts a ``seed`` for reproducible results. The :ref:`crossover example ` shows where -each operator places its children. +each operator places its offspring. Crossover ========= @@ -28,13 +28,13 @@ Crossover parent_centric_crossover The operators differ in how many parents one crossover operation uses and how -many children it produces: +many offspring it produces: .. list-table:: :header-rows: 1 * - Function - - Children per operation + - Offspring per operation - Parents per operation * - :func:`uniform_crossover` - 2 @@ -65,14 +65,15 @@ many children it produces: - 1, plus 2 other parents chosen at random The functions that use 2 parents per operation take a matrix ``parents`` and -mate rows ``2i`` and ``2i + 1``, so the order of the rows decides which parents -mate, for example after a selection step. If the number of rows is odd, the -last row mates with the first one. When an operation produces 2 children, the -output has as many rows as ``parents``, and one child is dropped when the -number of rows is odd. :func:`blend_alpha_crossover` returns one row per pair. +cross over rows ``2i`` and ``2i + 1``, so the order of the rows decides which +parents are crossed over, for example after a selection step. If the number +of rows is odd, the last row is crossed over with the first one. When an +operation produces 2 offspring, the output has as many rows as ``parents``, and +one offspring is dropped when the number of rows is odd. +:func:`blend_alpha_crossover` returns one row per pair. The functions that use 1 parent per operation take a matrix ``population`` and -the row indices ``targets`` of the parents, and return one child per target. +the row indices ``targets`` of the parents, and return one offspring per target. They choose the other parents at random from ``population``. Differential evolution (DE) comes in two variants that are common in diff --git a/python/examples/plot_crossover.py b/python/examples/plot_crossover.py index 4cef3a46c..d64b50638 100644 --- a/python/examples/plot_crossover.py +++ b/python/examples/plot_crossover.py @@ -2,11 +2,11 @@ Crossover Operators =================== -This example shows where each crossover operator places the children of -fixed parents. Each figure mates the same parents many times and plots all -the children. Operators that use 2 parents per operation mate rows ``2i`` -and ``2i + 1``, so stacking copies of one pair of parents gives many -independent draws in a single call. +This example shows where each crossover operator places the offspring of +fixed parents. Each figure crosses over the same parents many times and +plots all the offspring. Operators that use 2 parents per operation cross +over rows ``2i`` and ``2i + 1``, so stacking copies of one pair of parents +gives many independent draws in a single call. First we define a few functions useful for plotting. """ @@ -19,8 +19,8 @@ BOUNDS = dict(lower=LOWER, upper=UPPER) -def mate(fun, a, b, n_pairs=50_000, **kwargs): - """Mate parents ``a`` and ``b`` ``n_pairs`` times.""" +def cross_over(fun, a, b, n_pairs=50_000, **kwargs): + """Cross over parents ``a`` and ``b`` ``n_pairs`` times.""" parents = np.tile(np.array([a, b], dtype=float), (n_pairs, 1)) return fun(parents, seed=42, **kwargs) @@ -45,11 +45,11 @@ def mark_parents(ax, positions): # %% # -# Where the children of two parents end up -# ---------------------------------------- +# Where the offspring of two parents end up +# ----------------------------------------- # # The parents are :math:`(3, 3)` and :math:`(7, 7)` within :math:`[0, 10]^2`. -# Each panel shows the distribution of the first variable of the children for +# Each panel shows the distribution of the first variable of the offspring for # the default parameters of each operator. Uniform and single arithmetic # crossover only produce a few distinct values, which appear as spikes. @@ -63,7 +63,7 @@ def mark_parents(ax, positions): } fig, axes = plt.subplots(len(operators), 1, figsize=(6, 8), sharex=True) for i, (ax, (name, (fun, kwargs))) in enumerate(zip(axes, operators.items())): - plot_density(ax, mate(fun, a, b, **kwargs)[:, 0], color=f"C{i}") + plot_density(ax, cross_over(fun, a, b, **kwargs)[:, 0], color=f"C{i}") mark_parents(ax, [a[0], b[0]]) ax.set_title(name, loc="left", fontsize="medium") ax.set_yticks([]) @@ -76,19 +76,19 @@ def mark_parents(ax, positions): # Bounded exponential crossover: the scale parameter # -------------------------------------------------- # -# The parameter ``scale`` (:math:`\lambda`) controls how far the children move -# from their parents. Each child stays close to one parent, and the bounds +# The parameter ``scale`` (:math:`\lambda`) controls how far the offspring move +# from their parents. Each offspring stays close to one parent, and the bounds # truncate the distribution. On a logarithmic scale, the exponential tails # become straight lines. fig, ax = plt.subplots(figsize=(6, 3.5)) for i, scale in enumerate([0.01, 0.05, 0.1, 0.5]): - children = mate( + offspring = cross_over( moocore.bounded_exponential_crossover, a, b, scale=scale, **BOUNDS ) plot_density( ax, - children[:, 0], + offspring[:, 0], color=plt.cm.viridis(i / 4), label=rf"$\lambda = {scale}$", ) @@ -111,10 +111,12 @@ def mark_parents(ax, positions): fig, ax = plt.subplots(figsize=(6, 3.5)) for i, alpha in enumerate([0.0, 0.25, 0.5, 1.0]): - children = mate(moocore.blend_alpha_crossover, a, b, alpha=alpha, **BOUNDS) + offspring = cross_over( + moocore.blend_alpha_crossover, a, b, alpha=alpha, **BOUNDS + ) plot_density( ax, - children[:, 0], + offspring[:, 0], color=plt.cm.viridis(i / 4), label=rf"$\alpha = {alpha}$", ) @@ -131,9 +133,9 @@ def mark_parents(ax, positions): # ------------------ # # With the parents at opposite corners, :math:`(2, 8)` and :math:`(8, 2)`, the -# operators differ in which regions of the decision space their children +# operators differ in which regions of the decision space their offspring # reach. Uniform and single-point crossover recombine whole variables, so -# their children land on the corners of the box spanned by the parents. +# their offspring land on the corners of the box spanned by the parents. a, b = [2.0, 8.0], [8.0, 2.0] operators = { @@ -148,8 +150,8 @@ def mark_parents(ax, positions): for i, (ax, (name, (fun, kwargs))) in enumerate( zip(axes.flat, operators.items()) ): - children = mate(fun, a, b, n_pairs=1000, **kwargs) - ax.scatter(children[:, 0], children[:, 1], s=4, alpha=0.3, color=f"C{i}") + offspring = cross_over(fun, a, b, n_pairs=1000, **kwargs) + ax.scatter(offspring[:, 0], offspring[:, 1], s=4, alpha=0.3, color=f"C{i}") ax.scatter(*np.array([a, b]).T, marker="D", s=40, color="black") ax.set_title(name, fontsize="medium") ax.set_xlim(LOWER, UPPER) @@ -169,9 +171,10 @@ def mark_parents(ax, positions): # # Uniform and single-point crossover only copy values, so they also work for # binary and integer variables. With one parent of all zeros and one of all -# ones, the share of ones in the first child shows how likely each variable is -# to come from the second parent. Uniform crossover treats all variables -# alike, whereas single-point crossover keeps neighbouring variables together. +# ones, the share of ones in the first offspring shows how likely each +# variable is to come from the second parent. Uniform crossover treats all +# variables alike, whereas single-point crossover keeps neighbouring variables +# together. nvar = 10 zeros, ones = np.zeros(nvar, dtype=int), np.ones(nvar, dtype=int) @@ -180,9 +183,9 @@ def mark_parents(ax, positions): (moocore.uniform_crossover, "Uniform"), (moocore.single_point_crossover, "Single point"), ]: - first_children = mate(fun, zeros, ones, n_pairs=4000)[0::2] + first_offspring = cross_over(fun, zeros, ones, n_pairs=4000)[0::2] ax.plot( - np.arange(1, nvar + 1), first_children.mean(axis=0), "o-", label=name + np.arange(1, nvar + 1), first_offspring.mean(axis=0), "o-", label=name ) ax.axhline(0.5, color="gray", linestyle=":", linewidth=1) ax.set_xticks(np.arange(1, nvar + 1)) @@ -198,12 +201,13 @@ def mark_parents(ax, positions): # Differential evolution and parent-centric crossover # --------------------------------------------------- # -# These operators produce one child per parent and choose the other parents at -# random from the population. Here, every member of a population of 60 points -# (circles) is a target, and each operator is called 40 times. Passing the -# same :class:`numpy.random.Generator` as ``seed`` gives new children on each -# call. Both DE variants spread their children over the region covered by -# the population, whereas PCX keeps them close to their index parents. +# These operators produce one offspring per parent and choose the other +# parents at random from the population. Here, every member of a population of +# 60 points (circles) is a target, and each operator is called 40 times. +# Passing the same :class:`numpy.random.Generator` as ``seed`` gives new +# offspring on each call. Both DE variants spread their offspring over the +# region covered by the population, whereas PCX keeps them close to their index +# parents. rng = np.random.default_rng(42) population = np.clip(rng.normal([4.0, 6.0], 1.2, size=(60, 2)), 0.2, 9.8) @@ -214,10 +218,10 @@ def mark_parents(ax, positions): } fig, axes = plt.subplots(1, 3, figsize=(10, 3.8), sharex=True, sharey=True) for i, (ax, (name, fun)) in enumerate(zip(axes, operators.items())): - children = np.vstack( + offspring = np.vstack( [fun(population, seed=rng, **BOUNDS) for _ in range(40)] ) - ax.scatter(children[:, 0], children[:, 1], s=3, alpha=0.3, color=f"C{i}") + ax.scatter(offspring[:, 0], offspring[:, 1], s=3, alpha=0.3, color=f"C{i}") ax.scatter( population[:, 0], population[:, 1], From ff8250877f3bae80af30af161212afcddfaa3ac3 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 19:44:55 +0300 Subject: [PATCH 10/30] python/ Cite the origin of the name current/1 * python/src/moocore/_crossover.py (de_current_1_crossover): Cite Tanabe and Ishibuchi (2019) and Gong et al. (2017) for the name current/1. * python/doc/source/reference/functions.variation.rst: Likewise. --- python/doc/source/reference/functions.variation.rst | 5 ++++- python/src/moocore/_crossover.py | 9 +++++++++ 2 files changed, 13 insertions(+), 1 deletion(-) diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst index f0f34b4ba..fbbda274a 100644 --- a/python/doc/source/reference/functions.variation.rst +++ b/python/doc/source/reference/functions.variation.rst @@ -83,7 +83,10 @@ multi-objective DE algorithms use :footcite:p:`BezLopStu2015emode`. :func:`de_current_1_crossover` is the operator of MOEA/D-DE :footcite:p:`LiZha2009:moead-de`. It starts from the target instead of a random row and does not force any variable to change. Its 2 other parents may -include the target itself. +include the target itself. `Tanabe and Ishibuchi (2019) +`__ call this mutation the current/1 +strategy, a term introduced by `Gong et al. (2017) +`__. Bibliography diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index 7ce0a4489..469c2c009 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -705,6 +705,10 @@ def de_current_1_crossover( operator is invariant to rotations of the decision space. MOEA/D-DE then applies polynomial mutation, which is not part of this function. + Li and Zhang do not name the mutation step. Tanabe and Ishibuchi (2019) + call it the current/1 strategy, a term introduced by Gong et al. (2017), + and find it in the source code of MOEA/D-DE, MOEA/D-DRA and MOEA/D-STM. + Li and Zhang reset values outside the bounds to a random value within them. Their own implementation clips them instead, which is what this function does, and which Tanabe and Ishibuchi (2019) found to work best @@ -720,6 +724,11 @@ def de_current_1_crossover( Computing*, 23(23):12843--12857. https://doi.org/10.1007/s00500-019-03842-6 + W. Gong, Y. Wang, Z. Cai and S. Yang (2017). A weighted biobjective + transformation technique for locating multiple optimal solutions of + nonlinear equation systems. *IEEE Transactions on Evolutionary + Computation*, 21(5):697--713. https://doi.org/10.1109/TEVC.2017.2670779 + Examples -------- >>> neighbourhood = np.array([[0.5, 0.5], [0.4, 0.9], [0.8, 0.3]]) From 405dd694786ef64ef3ffe9f58693a5b2ed2c1141 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 21:01:22 +0300 Subject: [PATCH 11/30] python/ Reword DE docstrings and pass F explicitly in a test * python/src/moocore/_crossover.py (de_rand_1_bin_crossover): Say that Storn and Price recommend F = 0.5 as a first choice. (de_current_1_crossover): Reword the crossover rate. * python/tests/test_crossover.py (test_de_current_1_crossover_two_rows): Pass scaling_factor explicitly. --- python/src/moocore/_crossover.py | 6 ++++-- python/tests/test_crossover.py | 2 +- 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index 469c2c009..1c93c1538 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -606,7 +606,8 @@ def de_rand_1_bin_crossover( Notes ----- This is the DE/rand/1/bin scheme of :footcite:t:`StoPri1997:de`, who - recommend :math:`F = 0.5` and suggest trying :math:`CR = 0.9` first. + recommend :math:`F = 0.5` as a first choice and suggest trying + :math:`CR = 0.9` first. Multi-objective DE algorithms such as GDE3 :footcite:p:`KukLam2005:gde3` and DEMO :footcite:p:`RobFil05demo` use this variant :footcite:p:`BezLopStu2015emode`. @@ -685,7 +686,8 @@ def de_current_1_crossover( scaling_factor : Scaling factor :math:`F > 0` of the difference vector. crossover_rate : - Crossover rate :math:`CR`, the probability of changing each variable. + Crossover rate :math:`CR`, the probability of crossing a decision + variable. seed : ${random_seed} diff --git a/python/tests/test_crossover.py b/python/tests/test_crossover.py index ffca3b017..46ef9748d 100644 --- a/python/tests/test_crossover.py +++ b/python/tests/test_crossover.py @@ -278,7 +278,7 @@ def test_de_current_1_crossover_two_rows(): # The donors are the two rows, in either order. x = random_matrix(2) step = 0.5 * (x[0] - x[1]) - out = moocore.de_current_1_crossover(x, seed=1) + out = moocore.de_current_1_crossover(x, scaling_factor=0.5, seed=1) for i in range(2): assert np.allclose(out[i], x[i] + step) or np.allclose( out[i], x[i] - step From d97f67f40dc8eefc5c453e53137abc4f4c67da35 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 21:01:23 +0300 Subject: [PATCH 12/30] python/doc/ Show crossover operators applied to a population * python/doc/source/reference/functions.variation.rst: Introduce mutation and crossover. Explain the order of the offspring. * python/examples/plot_crossover.py: Add figures of every crossover operator applied to a round and to a diagonal population. Remove the inheritance profile and the separate DE and PCX figure. Reword. --- .../source/reference/functions.variation.rst | 24 ++- python/examples/plot_crossover.py | 192 ++++++++++-------- 2 files changed, 127 insertions(+), 89 deletions(-) diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst index fbbda274a..a40b31766 100644 --- a/python/doc/source/reference/functions.variation.rst +++ b/python/doc/source/reference/functions.variation.rst @@ -6,11 +6,16 @@ Variation operators .. currentmodule:: moocore -Crossover operators combine decision vectors, called parents, to produce new -decision vectors, called offspring. Every function takes a 2D array with one +Variation operators produce new decision vectors, called offspring, from +existing ones, called parents. +This usually happens in two steps: first, a crossover operator combines the +parents to produce one or more offspring, and then a mutation operator randomly +changes some of the offspring's decision variables. We currently provide a +number of crossover operators. +Every operator takes a 2D array with one decision vector per row and accepts a ``seed`` for reproducible results. The -:ref:`crossover example ` shows where -each operator places its offspring. +:ref:`crossover example ` shows +the behaviour of the crossover operators. Crossover ========= @@ -67,7 +72,8 @@ many offspring it produces: The functions that use 2 parents per operation take a matrix ``parents`` and cross over rows ``2i`` and ``2i + 1``, so the order of the rows decides which parents are crossed over, for example after a selection step. If the number -of rows is odd, the last row is crossed over with the first one. When an +of rows is odd, the last row is crossed over with the first one. +When an operation produces 2 offspring, the output has as many rows as ``parents``, and one offspring is dropped when the number of rows is odd. :func:`blend_alpha_crossover` returns one row per pair. @@ -88,6 +94,14 @@ include the target itself. `Tanabe and Ishibuchi (2019) strategy, a term introduced by `Gong et al. (2017) `__. +Certain crossover operators tend to produce offspring that are close to one +or the other parent. +Operators that produce 2 offspring from 2 parents or 1 offspring from 1 parent +preserve the order, so that the index of an offspring corresponds to the index +of the parent it is closest to, assuming a parent-centric crossover operation. +For the operators that take ``population``, the parent of offspring ``i`` is +row ``targets[i]``. + Bibliography ============ diff --git a/python/examples/plot_crossover.py b/python/examples/plot_crossover.py index d64b50638..658565ab9 100644 --- a/python/examples/plot_crossover.py +++ b/python/examples/plot_crossover.py @@ -2,11 +2,9 @@ Crossover Operators =================== -This example shows where each crossover operator places the offspring of -fixed parents. Each figure crosses over the same parents many times and -plots all the offspring. Operators that use 2 parents per operation cross -over rows ``2i`` and ``2i + 1``, so stacking copies of one pair of parents -gives many independent draws in a single call. +This example shows the behaviour of the crossover operators, first with two +fixed parents and then with a whole population. Each figure crosses over the +same parents many times and plots all the offspring. First we define a few functions useful for plotting. """ @@ -45,13 +43,14 @@ def mark_parents(ax, positions): # %% # -# Where the offspring of two parents end up -# ----------------------------------------- +# Crossover behaviour with two parents +# ------------------------------------ # # The parents are :math:`(3, 3)` and :math:`(7, 7)` within :math:`[0, 10]^2`. # Each panel shows the distribution of the first variable of the offspring for # the default parameters of each operator. Uniform and single arithmetic # crossover only produce a few distinct values, which appear as spikes. +# The parent decision variables are shown as dotted vertical lines. a, b = [3.0, 3.0], [7.0, 7.0] operators = { @@ -61,13 +60,13 @@ def mark_parents(ax, positions): "Uniform": (moocore.uniform_crossover, {}), "Single arithmetic": (moocore.single_arithmetic_crossover, {}), } -fig, axes = plt.subplots(len(operators), 1, figsize=(6, 8), sharex=True) +fig, axes = plt.subplots(len(operators), 1, figsize=(6, 8), sharex=False) for i, (ax, (name, (fun, kwargs))) in enumerate(zip(axes, operators.items())): plot_density(ax, cross_over(fun, a, b, **kwargs)[:, 0], color=f"C{i}") mark_parents(ax, [a[0], b[0]]) ax.set_title(name, loc="left", fontsize="medium") ax.set_yticks([]) -axes[-1].set_xlabel("$x_1$") + ax.set_xlabel("$x_1$") fig.tight_layout() plt.show() @@ -76,10 +75,13 @@ def mark_parents(ax, positions): # Bounded exponential crossover: the scale parameter # -------------------------------------------------- # -# The parameter ``scale`` (:math:`\lambda`) controls how far the offspring move -# from their parents. Each offspring stays close to one parent, and the bounds -# truncate the distribution. On a logarithmic scale, the exponential tails -# become straight lines. +# The bounded exponential crossover operator samples from an exponential +# distribution that is truncated at the bounds. The distribution is centred on +# one parent, and the distance to the other parent scales its spread. The +# offspring moves towards either bound with equal probability. The operator is +# symmetric, so the second offspring is centred on the other parent in the same +# way. The parameter ``scale`` (:math:`\lambda`) controls the decay of the +# distribution. fig, ax = plt.subplots(figsize=(6, 3.5)) for i, scale in enumerate([0.01, 0.05, 0.1, 0.5]): @@ -93,8 +95,6 @@ def mark_parents(ax, positions): label=rf"$\lambda = {scale}$", ) mark_parents(ax, [a[0], b[0]]) -ax.set_yscale("log") -ax.set_ylim(1e-3, None) ax.set_xlabel("$x_1$") ax.set_ylabel("Density") ax.legend() @@ -129,13 +129,14 @@ def mark_parents(ax, positions): # %% # -# Offspring geometry -# ------------------ +# Offspring geometry in two dimensions +# ------------------------------------ # # With the parents at opposite corners, :math:`(2, 8)` and :math:`(8, 2)`, the # operators differ in which regions of the decision space their offspring -# reach. Uniform and single-point crossover recombine whole variables, so -# their offspring land on the corners of the box spanned by the parents. +# can reach. Note that certain operators such as uniform crossover can never +# explore all possible decision vectors, requiring the use of mutation for +# proper exploration of the decision space. a, b = [2.0, 8.0], [8.0, 2.0] operators = { @@ -166,74 +167,97 @@ def mark_parents(ax, positions): # %% # -# Which parent each variable comes from +# Crossover behaviour with a population # ------------------------------------- # -# Uniform and single-point crossover only copy values, so they also work for -# binary and integer variables. With one parent of all zeros and one of all -# ones, the share of ones in the first offspring shows how likely each -# variable is to come from the second parent. Uniform crossover treats all -# variables alike, whereas single-point crossover keeps neighbouring variables -# together. - -nvar = 10 -zeros, ones = np.zeros(nvar, dtype=int), np.ones(nvar, dtype=int) -fig, ax = plt.subplots(figsize=(6, 3.5)) -for fun, name in [ - (moocore.uniform_crossover, "Uniform"), - (moocore.single_point_crossover, "Single point"), -]: - first_offspring = cross_over(fun, zeros, ones, n_pairs=4000)[0::2] - ax.plot( - np.arange(1, nvar + 1), first_offspring.mean(axis=0), "o-", label=name - ) -ax.axhline(0.5, color="gray", linestyle=":", linewidth=1) -ax.set_xticks(np.arange(1, nvar + 1)) -ax.set_ylim(-0.05, 1.05) -ax.set_xlabel("Variable") -ax.set_ylabel("Share taken from the second parent") -ax.legend() -fig.tight_layout() -plt.show() +# In an evolutionary algorithm, crossover is applied to a whole population. +# Here, each operator is applied 40 times to a population of 60 decision +# vectors (circles), and all the offspring are plotted. For the operators that +# take ``parents``, the rows are shuffled before each call, so that different +# pairs are crossed over each time. For the operators that take +# ``population``, every row is a target. Passing the same +# :class:`numpy.random.Generator` as ``seed`` gives new offspring on each call. +# +# The first population is a round cloud. Uniform, single-point and single +# arithmetic crossover place their offspring on lines parallel to the axes, +# because each offspring copies at least one variable from a parent. Both DE +# variants spread their offspring beyond the population, whereas parent-centric +# crossover keeps them close to their index parents. + +all_operators = { + "Uniform": (moocore.uniform_crossover, {}), + "Single point": (moocore.single_point_crossover, {}), + "Blend alpha": (moocore.blend_alpha_crossover, BOUNDS), + "Single arithmetic": (moocore.single_arithmetic_crossover, {}), + "Local": (moocore.local_crossover, {}), + "Bounded exponential": (moocore.bounded_exponential_crossover, BOUNDS), + "DE/rand/1/bin": (moocore.de_rand_1_bin_crossover, BOUNDS), + "DE/current/1": (moocore.de_current_1_crossover, BOUNDS), + "Parent-centric": (moocore.parent_centric_crossover, BOUNDS), +} +takes_population = { + moocore.de_rand_1_bin_crossover, + moocore.de_current_1_crossover, + moocore.parent_centric_crossover, +} + + +def plot_population(population, n_calls=40): + """Plot the offspring of every operator applied to ``population``.""" + rng = np.random.default_rng(42) + fig, axes = plt.subplots(3, 3, figsize=(9, 9), sharex=True, sharey=True) + for i, (ax, (name, (fun, kwargs))) in enumerate( + zip(axes.flat, all_operators.items()) + ): + offspring = [] + for _ in range(n_calls): + if fun in takes_population: + x = population + else: + x = rng.permutation(population) + offspring.append(fun(x, seed=rng, **kwargs)) + offspring = np.vstack(offspring) + ax.scatter( + offspring[:, 0], offspring[:, 1], s=3, alpha=0.3, color=f"C{i}" + ) + ax.scatter( + population[:, 0], + population[:, 1], + s=15, + facecolors="none", + edgecolors="black", + linewidths=0.8, + ) + ax.set_title(name, fontsize="medium") + ax.set_xlim(LOWER, UPPER) + ax.set_ylim(LOWER, UPPER) + ax.set_aspect("equal") + for ax in axes[2]: + ax.set_xlabel("$x_1$") + for ax in axes[:, 0]: + ax.set_ylabel("$x_2$") + fig.tight_layout() + plt.show() + + +rng = np.random.default_rng(42) +round_population = np.clip(rng.normal([4.0, 6.0], 1.2, size=(60, 2)), 0.2, 9.8) +plot_population(round_population) # %% # -# Differential evolution and parent-centric crossover -# --------------------------------------------------- -# -# These operators produce one offspring per parent and choose the other -# parents at random from the population. Here, every member of a population of -# 60 points (circles) is a target, and each operator is called 40 times. -# Passing the same :class:`numpy.random.Generator` as ``seed`` gives new -# offspring on each call. Both DE variants spread their offspring over the -# region covered by the population, whereas PCX keeps them close to their index -# parents. +# The second population is stretched along a diagonal, as happens when a +# population approaches a Pareto set. Uniform and single-point crossover +# combine the variables of different parents independently, so their offspring +# fill the box around the population and lose its diagonal shape. Blend alpha, +# single arithmetic and local crossover also treat each variable separately and +# place offspring away from the diagonal. Bounded exponential crossover keeps +# the offspring close to their parents. Both DE variants and parent-centric +# crossover follow the diagonal, because they move along differences between +# parents. DE extends the population beyond its ends, whereas parent-centric +# crossover stays close to its index parents. -rng = np.random.default_rng(42) -population = np.clip(rng.normal([4.0, 6.0], 1.2, size=(60, 2)), 0.2, 9.8) -operators = { - "DE/rand/1/bin": moocore.de_rand_1_bin_crossover, - "DE/current/1": moocore.de_current_1_crossover, - "Parent-centric": moocore.parent_centric_crossover, -} -fig, axes = plt.subplots(1, 3, figsize=(10, 3.8), sharex=True, sharey=True) -for i, (ax, (name, fun)) in enumerate(zip(axes, operators.items())): - offspring = np.vstack( - [fun(population, seed=rng, **BOUNDS) for _ in range(40)] - ) - ax.scatter(offspring[:, 0], offspring[:, 1], s=3, alpha=0.3, color=f"C{i}") - ax.scatter( - population[:, 0], - population[:, 1], - s=20, - facecolors="none", - edgecolors="black", - ) - ax.set_title(name, fontsize="medium") - ax.set_xlim(LOWER, UPPER) - ax.set_ylim(LOWER, UPPER) - ax.set_aspect("equal") - ax.set_xlabel("$x_1$") -axes[0].set_ylabel("$x_2$") -fig.tight_layout() -plt.show() +t = rng.uniform(0, 1, size=60) +diagonal_population = np.column_stack([2 + 6 * t, 8 - 6 * t]) +diagonal_population += rng.normal(0, 0.25, size=(60, 2)) +plot_population(diagonal_population) From e8d7274414c500d406404a34146fcb8877c399ce Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 21:07:14 +0300 Subject: [PATCH 13/30] python/examples/plot_crossover.py: Add a population of three separate clusters. --- python/examples/plot_crossover.py | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) diff --git a/python/examples/plot_crossover.py b/python/examples/plot_crossover.py index 658565ab9..f68f02580 100644 --- a/python/examples/plot_crossover.py +++ b/python/examples/plot_crossover.py @@ -261,3 +261,22 @@ def plot_population(population, n_calls=40): diagonal_population = np.column_stack([2 + 6 * t, 8 - 6 * t]) diagonal_population += rng.normal(0, 0.25, size=(60, 2)) plot_population(diagonal_population) + +# %% +# +# The third population consists of three separate clusters of 20 members each, +# as when the Pareto set is disconnected. Crossing over members of different +# clusters produces offspring outside the clusters. Uniform and single-point +# crossover create new clusters at every combination of the clusters' variable +# values, and single arithmetic crossover adds clusters at the midpoints of one +# variable. Blend alpha and local crossover fill the space between the +# clusters. Both DE variants create new clusters by shifting the original ones +# by :math:`F` times the differences between clusters, and the offspring that +# are clipped to the bounds pile up on the edges of the box. Bounded +# exponential and parent-centric crossover keep most offspring near the cluster +# of their parent. + +centres = np.array([[2.0, 8.0], [8.0, 6.0], [5.0, 2.0]]) +clustered_population = np.repeat(centres, 20, axis=0) +clustered_population += rng.normal(0, 0.4, size=(60, 2)) +plot_population(clustered_population) From 765b92e05cb311d26575e9f1a6132477986f4951 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 21:15:34 +0300 Subject: [PATCH 14/30] python/doc/source/reference/functions.variation.rst: Explain how to seed the operators in an evolutionary algorithm. --- .../source/reference/functions.variation.rst | 21 +++++++++++++++++++ 1 file changed, 21 insertions(+) diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst index a40b31766..d213fafca 100644 --- a/python/doc/source/reference/functions.variation.rst +++ b/python/doc/source/reference/functions.variation.rst @@ -103,6 +103,27 @@ For the operators that take ``population``, the parent of offspring ``i`` is row ``targets[i]``. +Random seeds +============ + +Every operator takes a ``seed``. With an integer seed, the operator draws the +same random numbers on every call. This makes a single call reproducible, but +in an evolutionary algorithm every generation would reuse the same random +numbers. Instead, create one :class:`numpy.random.Generator` at the start of a +run and pass it as ``seed`` to every call. Each call then draws a new seed +from the generator, and the seed of the generator still reproduces the whole +run:: + + rng = np.random.default_rng(42) + for generation in range(n_generations): + parents = ... # Select and order the parents. + offspring = moocore.uniform_crossover(parents, seed=rng) + ... + +With ``seed=None``, every call uses a new random seed, so the results cannot be +reproduced. + + Bibliography ============ From be84c7f1122324c3f1a5a588236482fb2b5ed682 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Thu, 22 Oct 2026 21:41:21 +0300 Subject: [PATCH 15/30] python/doc/ Reword the crossover docs * python/doc/source/reference/functions.variation.rst: Say that variation operators are used in evolutionary algorithms. * python/examples/plot_crossover.py: Note that local crossover stays in the box spanned by the parents. Explain why uniform and single-point crossover look alike in two dimensions. Reword the captions. --- .../source/reference/functions.variation.rst | 3 +- python/examples/plot_crossover.py | 31 +++++++++++-------- 2 files changed, 20 insertions(+), 14 deletions(-) diff --git a/python/doc/source/reference/functions.variation.rst b/python/doc/source/reference/functions.variation.rst index d213fafca..6dbd4849d 100644 --- a/python/doc/source/reference/functions.variation.rst +++ b/python/doc/source/reference/functions.variation.rst @@ -6,7 +6,8 @@ Variation operators .. currentmodule:: moocore -Variation operators produce new decision vectors, called offspring, from +Variation operators are used in evolutionary algorithms to +produce new decision vectors, called offspring, from existing ones, called parents. This usually happens in two steps: first, a crossover operator combines the parents to produce one or more offspring, and then a mutation operator randomly diff --git a/python/examples/plot_crossover.py b/python/examples/plot_crossover.py index f68f02580..71ecac85c 100644 --- a/python/examples/plot_crossover.py +++ b/python/examples/plot_crossover.py @@ -72,7 +72,7 @@ def mark_parents(ax, positions): # %% # -# Bounded exponential crossover: the scale parameter +# Bounded exponential crossover # -------------------------------------------------- # # The bounded exponential crossover operator samples from an exponential @@ -136,7 +136,10 @@ def mark_parents(ax, positions): # operators differ in which regions of the decision space their offspring # can reach. Note that certain operators such as uniform crossover can never # explore all possible decision vectors, requiring the use of mutation for -# proper exploration of the decision space. +# proper exploration of the decision space. Moreover, the local crossover +# operator never produces offspring outside the bounding box defined by the +# parents, so it is not suitable for exploring the decision space beyond +# the current population. a, b = [2.0, 8.0], [8.0, 2.0] operators = { @@ -172,17 +175,18 @@ def mark_parents(ax, positions): # # In an evolutionary algorithm, crossover is applied to a whole population. # Here, each operator is applied 40 times to a population of 60 decision -# vectors (circles), and all the offspring are plotted. For the operators that -# take ``parents``, the rows are shuffled before each call, so that different -# pairs are crossed over each time. For the operators that take -# ``population``, every row is a target. Passing the same -# :class:`numpy.random.Generator` as ``seed`` gives new offspring on each call. +# vectors (circles), and all the offspring are plotted. +# Each operator gets the same population, but for each call, the population is +# randomly permuted and/or a different seed is used. # # The first population is a round cloud. Uniform, single-point and single # arithmetic crossover place their offspring on lines parallel to the axes, -# because each offspring copies at least one variable from a parent. Both DE -# variants spread their offspring beyond the population, whereas parent-centric -# crossover keeps them close to their index parents. +# because each offspring copies at least one variable from a parent. Uniform +# and single-point crossover look alike here only because, with two variables, +# the cut point always falls between them. With more variables, their +# distributions differ. Both DE variants spread their offspring beyond the +# population, whereas parent-centric and bounded exponential crossover keep +# them close to their parents. all_operators = { "Uniform": (moocore.uniform_crossover, {}), @@ -246,7 +250,7 @@ def plot_population(population, n_calls=40): # %% # -# The second population is stretched along a diagonal, as happens when a +# The second population is stretched along a diagonal, as may happen when a # population approaches a Pareto set. Uniform and single-point crossover # combine the variables of different parents independently, so their offspring # fill the box around the population and lose its diagonal shape. Blend alpha, @@ -266,8 +270,9 @@ def plot_population(population, n_calls=40): # # The third population consists of three separate clusters of 20 members each, # as when the Pareto set is disconnected. Crossing over members of different -# clusters produces offspring outside the clusters. Uniform and single-point -# crossover create new clusters at every combination of the clusters' variable +# clusters produces offspring outside the clusters, unless the operator keeps +# the offspring close to their parents. Uniform and single-point crossover +# create new clusters at every combination of the clusters' variable # values, and single arithmetic crossover adds clusters at the midpoints of one # variable. Blend alpha and local crossover fill the space between the # clusters. Both DE variants create new clusters by shifting the original ones From 83d8794ef50e8c4a0722ebdc015afcf3eefb1d19 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Fri, 23 Oct 2026 12:01:45 +0300 Subject: [PATCH 16/30] c/ Add pair_prob to every crossover operator with two parents * c/crossover.c (copy_parents): New. (single_point_crossover, blend_alpha_crossover, local_crossover): Add pair_prob. (bounded_exponential_crossover): Take swap_prob before pair_prob. Use copy_parents. * c/crossover.h: Likewise. --- c/crossover.c | 33 +++++++++++++++++++++++++++------ c/crossover.h | 11 ++++++----- 2 files changed, 33 insertions(+), 11 deletions(-) diff --git a/c/crossover.c b/c/crossover.c index f02071a2a..3f1411eb9 100644 --- a/c/crossover.c +++ b/c/crossover.c @@ -57,6 +57,15 @@ scratch_new(size_t n, size_t nvar) return (n % 2 == 1) ? MOOCORE_MALLOC(nvar, double) : NULL; } +// Offspring of a pair that is not crossed over. +static inline void +copy_parents(double * off1, double * off2, const double * p1, const double * p2, + size_t nvar) +{ + memcpy(off1, p1, nvar * sizeof(*off1)); + memcpy(off2, p2, nvar * sizeof(*off2)); +} + /* Draw K distinct indices in [0, N) that also differ from the NEXCLUDED indices in EXCLUDED. EXCLUDED must be sorted in ascending order and have room for K more values. Each draw picks among the indices not yet excluded @@ -109,7 +118,7 @@ uniform_crossover(double * restrict offspring, const double * restrict parents, void single_point_crossover(double * restrict offspring, const double * restrict parents, - size_t n, size_t nvar, uint32_t seed) + size_t n, size_t nvar, double pair_prob, uint32_t seed) { ASSUME(n >= 2 && nvar >= 2); rng_state * rng = rng_new(seed); @@ -119,6 +128,10 @@ single_point_crossover(double * restrict offspring, double *off1, *off2; get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &off1, &off2); + if (!(rng_random(rng) < pair_prob)) { + copy_parents(off1, off2, p1, p2, nvar); + continue; + } // Cut point in [1, nvar - 1], so each offspring takes at least one // variable from each parent. const size_t cut = 1 + rng_integer(rng, nvar - 1); @@ -136,7 +149,7 @@ blend_alpha_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double alpha, - uint32_t seed) + double pair_prob, uint32_t seed) { ASSUME(n >= 2 && nvar >= 1); ASSUME(alpha >= 0); @@ -145,6 +158,11 @@ blend_alpha_crossover(double * restrict offspring, const double * p1 = parents + i * nvar; const double * p2 = parents + ((i + 1 < n) ? i + 1 : 0) * nvar; double * off = offspring + (i / 2) * nvar; + // A pair that is not crossed over yields a copy of its first parent. + if (!(rng_random(rng) < pair_prob)) { + memcpy(off, p1, nvar * sizeof(*off)); + continue; + } for (size_t j = 0; j < nvar; j++) { const double lo = fmin(p1[j], p2[j]); const double hi = fmax(p1[j], p2[j]); @@ -186,7 +204,7 @@ single_arithmetic_crossover(double * restrict offspring, void local_crossover(double * restrict offspring, const double * restrict parents, - size_t n, size_t nvar, uint32_t seed) + size_t n, size_t nvar, double pair_prob, uint32_t seed) { ASSUME(n >= 2 && nvar >= 1); rng_state * rng = rng_new(seed); @@ -196,6 +214,10 @@ local_crossover(double * restrict offspring, const double * restrict parents, double *off1, *off2; get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &off1, &off2); + if (!(rng_random(rng) < pair_prob)) { + copy_parents(off1, off2, p1, p2, nvar); + continue; + } for (size_t j = 0; j < nvar; j++) { const double a = rng_random(rng); off1[j] = a * p1[j] + (1 - a) * p2[j]; @@ -233,7 +255,7 @@ bounded_exponential_crossover(double * restrict offspring, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double scale, - double pair_prob, double swap_prob, + double swap_prob, double pair_prob, uint32_t seed) { ASSUME(n >= 2 && nvar >= 1); @@ -246,8 +268,7 @@ bounded_exponential_crossover(double * restrict offspring, get_pair(parents, offspring, scratch, i, n, nvar, &p1, &p2, &off1, &off2); if (!(rng_random(rng) < pair_prob)) { - memcpy(off1, p1, nvar * sizeof(*off1)); - memcpy(off2, p2, nvar * sizeof(*off2)); + copy_parents(off1, off2, p1, p2, nvar); continue; } for (size_t j = 0; j < nvar; j++) { diff --git a/c/crossover.h b/c/crossover.h index 6e330b97b..791fb8c09 100644 --- a/c/crossover.h +++ b/c/crossover.h @@ -50,12 +50,13 @@ MOOCORE_API void uniform_crossover( MOOCORE_API void single_point_crossover( double * restrict offspring, const double * restrict parents, - size_t n, size_t nvar, uint32_t seed); + size_t n, size_t nvar, double pair_prob, uint32_t seed); MOOCORE_API void blend_alpha_crossover( double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, - const double * restrict upper, double alpha, uint32_t seed); + const double * restrict upper, double alpha, double pair_prob, + uint32_t seed); MOOCORE_API void single_arithmetic_crossover( double * restrict offspring, const double * restrict parents, @@ -63,13 +64,13 @@ MOOCORE_API void single_arithmetic_crossover( MOOCORE_API void local_crossover( double * restrict offspring, const double * restrict parents, - size_t n, size_t nvar, uint32_t seed); + size_t n, size_t nvar, double pair_prob, uint32_t seed); MOOCORE_API void bounded_exponential_crossover( double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, - const double * restrict upper, double scale, double pair_prob, - double swap_prob, uint32_t seed); + const double * restrict upper, double scale, double swap_prob, + double pair_prob, uint32_t seed); MOOCORE_API void de_rand_1_bin_crossover( double * restrict offspring, const double * restrict population, From 00caf4d0cb40a70b934ae79fc319dae016f42b92 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Fri, 23 Oct 2026 12:01:45 +0300 Subject: [PATCH 17/30] python/ Add pair_prob to every crossover operator with two parents * python/src/moocore/_crossover.py (single_point_crossover) (blend_alpha_crossover, local_crossover): Add pair_prob. (bounded_exponential_crossover): Take swap_prob before pair_prob. (de_current_1_crossover): Call the step vector the mutant. (parent_centric_crossover): Say how the orthogonal step differs from equation (2) of Deb et al. (2002). * python/src/moocore/_docsubstitute.py (COMMON_PARAMS): Add swap_prob, pair_prob, scaling_factor and crossover_rate. * python/src/moocore/libmoocore.h: Update the crossover prototypes. * python/tests/test_crossover.py: Test pair_prob for every operator with two parents. --- python/src/moocore/_crossover.py | 101 +++++++++++++++------------ python/src/moocore/_docsubstitute.py | 8 +++ python/src/moocore/libmoocore.h | 8 +-- python/tests/test_crossover.py | 24 +++++++ 4 files changed, 94 insertions(+), 47 deletions(-) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index 1c93c1538..03d2dc3e4 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -124,10 +124,9 @@ def uniform_crossover( parents : ${parents} swap_prob : - Probability of swapping each variable between the two offspring. + ${swap_prob} pair_prob : - Probability of applying the crossover operation to each pair of - parents. + ${pair_prob} seed : ${random_seed} @@ -176,15 +175,17 @@ def single_point_crossover( parents: ArrayLike, /, *, + pair_prob: float = 1.0, seed: int | np.random.Generator | None = None, ) -> np.ndarray: r"""Single-point crossover. - Each crossover operation on a pair of parents produces two offspring. A - cut point :math:`k` is drawn uniformly from :math:`\{1, \dots, - n_\text{var} - 1\}`. The first offspring takes the first :math:`k` - variables from the first parent and the rest from the second parent, and - the second offspring takes the complement. + Each crossover operation on a pair of parents produces two offspring. With + probability ``pair_prob``, a cut point :math:`k` is drawn uniformly from + :math:`\{1, \dots, n_\text{var} - 1\}`. The first offspring takes the + first :math:`k` variables from the first parent and the rest from the + second parent, and the second offspring takes the complement. Otherwise, + the offspring are copies of their parents. The offspring only take values from their parents, so this operator works for binary, integer and real-valued variables alike. Integer and Boolean @@ -194,6 +195,8 @@ def single_point_crossover( ---------- parents : ${parents} It must have at least 2 columns. + pair_prob : + ${pair_prob} seed : ${random_seed} @@ -217,19 +220,21 @@ def single_point_crossover( Examples -------- >>> parents = np.array([[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1]]) - >>> moocore.single_point_crossover(parents, seed=42) - array([[0, 0, 1, 1, 1, 1], - [1, 1, 0, 0, 0, 0]]) + >>> moocore.single_point_crossover(parents, seed=4) + array([[0, 0, 0, 1, 1, 1], + [1, 1, 1, 0, 0, 0]]) """ dtype = np.asarray(parents).dtype parents = _as_matrix(parents, "parents", min_rows=2) if parents.shape[1] < 2: raise ValueError("'parents' must have at least 2 columns") + pair_prob = _check_probability(pair_prob, "pair_prob") out = _call( lib.single_point_crossover, parents, len(parents), + pair_prob, _get_seed_for_c(seed), ) return _keep_dtype(out, dtype) @@ -243,16 +248,18 @@ def blend_alpha_crossover( lower: ArrayLike | None = None, upper: ArrayLike | None = None, alpha: float = 0.5, + pair_prob: float = 1.0, seed: int | np.random.Generator | None = None, ) -> np.ndarray: r"""Blend crossover (BLX-:math:`\alpha`). Each crossover operation on a pair of parents :math:`x, y` produces - **one** offspring :math:`z`. For - each variable :math:`j`, let :math:`m_j = \min(x_j, y_j)`, :math:`M_j = + **one** offspring :math:`z`. With probability ``pair_prob``, for each + variable :math:`j`, let :math:`m_j = \min(x_j, y_j)`, :math:`M_j = \max(x_j, y_j)` and :math:`d_j = M_j - m_j`. Then :math:`z_j` is sampled uniformly from :math:`[m_j - \alpha d_j, M_j + \alpha d_j]`, clipped to - the bounds of the variable. + the bounds of the variable. Otherwise, the offspring is a copy of the + first parent :math:`x`. Parameters ---------- @@ -266,6 +273,8 @@ def blend_alpha_crossover( Fraction of the distance between the parents by which the sampling interval extends beyond them on each side. With ``alpha=0``, the offspring lie between their parents. + pair_prob : + ${pair_prob} seed : ${random_seed} @@ -299,15 +308,16 @@ def blend_alpha_crossover( >>> parents = np.array([[0.2, 0.2], [0.6, 0.8]]) >>> rng = np.random.default_rng(42) >>> moocore.blend_alpha_crossover(parents, lower=0, upper=1, seed=rng) - array([[0.63478113, 0.52182563]]) + array([[0.4174605 , 0.81353203]]) >>> moocore.blend_alpha_crossover(parents, lower=0, upper=1, seed=rng) - array([[0.21852882, 0.04409984]]) + array([[0.03527987, 0.73987298]]) """ parents = _as_matrix(parents, "parents", min_rows=2) lower, upper = _bounds(lower, upper, parents.shape[1]) if not alpha >= 0: raise ValueError("'alpha' must be non-negative") + pair_prob = _check_probability(pair_prob, "pair_prob") return _call( lib.blend_alpha_crossover, parents, @@ -315,6 +325,7 @@ def blend_alpha_crossover( ffi.from_buffer("double []", lower), ffi.from_buffer("double []", upper), float(alpha), + pair_prob, _get_seed_for_c(seed), ) @@ -340,8 +351,7 @@ def single_arithmetic_crossover( parents : ${parents} pair_prob : - Probability of applying the crossover operation to each pair of - parents. + ${pair_prob} seed : ${random_seed} @@ -390,24 +400,27 @@ def local_crossover( parents: ArrayLike, /, *, + pair_prob: float = 1.0, seed: int | np.random.Generator | None = None, ) -> np.ndarray: r"""Local crossover. Each crossover operation on a pair of parents :math:`x, y` produces two - offspring + offspring. With probability ``pair_prob``, they are .. math:: u_j = a_j x_j + (1 - a_j) y_j, \qquad v_j = (1 - a_j) x_j + a_j y_j, where each weight :math:`a_j` is drawn uniformly from :math:`[0, 1)`. The offspring lie in the box spanned by their parents, and :math:`u + v = x + - y`. + y`. Otherwise, the offspring are copies of their parents. Parameters ---------- parents : ${parents} + pair_prob : + ${pair_prob} seed : ${random_seed} @@ -438,15 +451,17 @@ def local_crossover( -------- >>> parents = np.array([[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]]) >>> moocore.local_crossover(parents, seed=42) - array([[0.62545988, 0.04928569, 0.26800606], - [0.37454012, 0.95071431, 0.73199394]]) + array([[0.04928569, 0.26800606, 0.40134152], + [0.95071431, 0.73199394, 0.59865848]]) """ parents = _as_matrix(parents, "parents", min_rows=2) + pair_prob = _check_probability(pair_prob, "pair_prob") return _call( lib.local_crossover, parents, len(parents), + pair_prob, _get_seed_for_c(seed), ) @@ -459,8 +474,8 @@ def bounded_exponential_crossover( lower: ArrayLike | None = None, upper: ArrayLike | None = None, scale: float = 0.1, - pair_prob: float = 1.0, swap_prob: float = 0.0, + pair_prob: float = 1.0, seed: int | np.random.Generator | None = None, ) -> np.ndarray: r"""Bounded exponential crossover (BEX). @@ -499,11 +514,10 @@ def bounded_exponential_crossover( scale : Scale :math:`\lambda > 0` of the exponential distribution. Smaller values keep the offspring closer to their parents. - pair_prob : - Probability of applying the crossover operation to each pair of - parents. swap_prob : - Probability of swapping each variable between the two offspring. + ${swap_prob} + pair_prob : + ${pair_prob} seed : ${random_seed} @@ -540,8 +554,8 @@ def bounded_exponential_crossover( if np.any(parents < lower) or np.any(parents > upper): raise ValueError("'parents' must be within 'lower' and 'upper'") scale = _check_positive(scale, "scale") - pair_prob = _check_probability(pair_prob, "pair_prob") swap_prob = _check_probability(swap_prob, "swap_prob") + pair_prob = _check_probability(pair_prob, "pair_prob") return _call( lib.bounded_exponential_crossover, parents, @@ -549,8 +563,8 @@ def bounded_exponential_crossover( ffi.from_buffer("double []", lower), ffi.from_buffer("double []", upper), scale, - pair_prob, swap_prob, + pair_prob, _get_seed_for_c(seed), ) @@ -587,10 +601,9 @@ def de_rand_1_bin_crossover( upper : ${upper_bound} scaling_factor : - Scaling factor :math:`F > 0` of the difference vector. + ${scaling_factor} crossover_rate : - Crossover rate :math:`CR`, the probability of taking each variable - from the mutant. + ${crossover_rate} seed : ${random_seed} @@ -664,9 +677,9 @@ def de_current_1_crossover( For each target :math:`x_i`, two distinct rows :math:`x_{r_1}, x_{r_2}` are drawn from ``population``. Either of them may be the target itself. - The offspring takes each variable :math:`j` from :math:`x_i + F (x_{r_1} - - x_{r_2})` with probability :math:`CR`, and from the target otherwise. - Finally, the offspring is clipped to the bounds. + The offspring takes each variable :math:`j` from the mutant :math:`x_i + F + (x_{r_1} - x_{r_2})` with probability :math:`CR`, and from the target + otherwise. Finally, the offspring is clipped to the bounds. Unlike :func:`de_rand_1_bin_crossover`, the base vector is the target and no variable is forced to come from the mutant, so with :math:`CR = 0` the @@ -684,10 +697,9 @@ def de_current_1_crossover( upper : ${upper_bound} scaling_factor : - Scaling factor :math:`F > 0` of the difference vector. + ${scaling_factor} crossover_rate : - Crossover rate :math:`CR`, the probability of crossing a decision - variable. + ${crossover_rate} seed : ${random_seed} @@ -812,11 +824,14 @@ def parent_centric_crossover( Notes ----- - PCX was proposed by Deb, Anand and Joshi (2002), who sum one normal step - along each vector of an orthonormal basis of the subspace orthogonal to - :math:`d`. Projecting an isotropic normal vector onto that subspace gives - the same distribution. If :math:`x` is (almost) the centroid, the - projection is skipped. + PCX was proposed by Deb, Anand and Joshi (2002). Their equation (2) + writes the step orthogonal to :math:`d` as a sum of normal steps along + :math:`\mu - 1` orthonormal vectors, where :math:`\mu` is the number of + parents. Like pymoo, which bases its implementation on the authors' C + code, this function projects an isotropic normal vector onto the whole + subspace orthogonal to :math:`d`, so the offspring is not restricted to + the plane of the three parents. If :math:`x` is (almost) the centroid, + the projection is skipped. References ---------- diff --git a/python/src/moocore/_docsubstitute.py b/python/src/moocore/_docsubstitute.py index 2fda2a7df..2a35a0d93 100644 --- a/python/src/moocore/_docsubstitute.py +++ b/python/src/moocore/_docsubstitute.py @@ -43,6 +43,14 @@ # ------------------------------------------------------------------------- "upper_bound": """Upper bounds of the decision variables. Either a single value, which will be used for all variables, or one value per column. ``None`` means no upper bound.""", + # ------------------------------------------------------------------------- + "swap_prob": """Probability of swapping each variable between the two offspring.""", + # ------------------------------------------------------------------------- + "pair_prob": """Probability of applying the crossover operation to each pair of parents.""", + # ------------------------------------------------------------------------- + "scaling_factor": """Scaling factor :math:`F > 0` of the difference vector.""", + # ------------------------------------------------------------------------- + "crossover_rate": """Crossover rate :math:`CR`, the probability of taking each variable from the mutant.""", } diff --git a/python/src/moocore/libmoocore.h b/python/src/moocore/libmoocore.h index feae11273..dfa783685 100644 --- a/python/src/moocore/libmoocore.h +++ b/python/src/moocore/libmoocore.h @@ -88,11 +88,11 @@ double whv_hype_estimate(const double *points, size_t n, const double *ideal, co // crossover.h void uniform_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, double swap_prob, double pair_prob, uint32_t seed); -void single_point_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, uint32_t seed); -void blend_alpha_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double alpha, uint32_t seed); +void single_point_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, double pair_prob, uint32_t seed); +void blend_alpha_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double alpha, double pair_prob, uint32_t seed); void single_arithmetic_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, double pair_prob, uint32_t seed); -void local_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, uint32_t seed); -void bounded_exponential_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double scale, double pair_prob, double swap_prob, uint32_t seed); +void local_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, double pair_prob, uint32_t seed); +void bounded_exponential_crossover(double * restrict offspring, const double * restrict parents, size_t n, size_t nvar, const double * restrict lower, const double * restrict upper, double scale, double swap_prob, double pair_prob, uint32_t seed); void de_rand_1_bin_crossover(double * restrict offspring, const double * restrict population, size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, const double * restrict lower, const double * restrict upper, double scaling_factor, double crossover_rate, uint32_t seed); void de_current_1_crossover(double * restrict offspring, const double * restrict population, size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, const double * restrict lower, const double * restrict upper, double scaling_factor, double crossover_rate, uint32_t seed); void parent_centric_crossover(double * restrict offspring, const double * restrict population, size_t n, size_t nvar, const size_t * restrict targets, size_t ntargets, const double * restrict lower, const double * restrict upper, double sigma_zeta, double sigma_eta, uint32_t seed); diff --git a/python/tests/test_crossover.py b/python/tests/test_crossover.py index 46ef9748d..413a7ea62 100644 --- a/python/tests/test_crossover.py +++ b/python/tests/test_crossover.py @@ -114,6 +114,27 @@ def test_inputs_are_not_modified(name, immutable_call): immutable_call(ALL_OPERATORS[name], x, seed=3, **kwargs) +@pytest.mark.parametrize("name", PAIR_OPERATORS) +def test_pair_prob_zero_copies_parents(name): + x = random_matrix(7) + kwargs = {"lower": LOWER, "upper": UPPER} if name in BOUNDED else {} + out = PAIR_OPERATORS[name](x, pair_prob=0, seed=1, **kwargs) + # Blend alpha crossover copies the first parent of each pair. + assert_array_equal(out, x[0::2] if name == "blend_alpha" else x) + + +@pytest.mark.parametrize("name", PAIR_OPERATORS) +def test_pair_prob_rate(name): + x = random_matrix(4000, nvar=10) + kwargs = {"lower": LOWER, "upper": UPPER} if name in BOUNDED else {} + out = PAIR_OPERATORS[name](x, pair_prob=0.3, seed=1, **kwargs) + if name == "blend_alpha": + copied = np.all(out == x[0::2], axis=1) + else: + copied = np.all((out == x).reshape(-1, 2 * x.shape[1]), axis=1) + assert abs(copied.mean() - 0.7) < 0.03 + + def test_uniform_crossover_only_copies_parent_values(): x = random_matrix(200, nvar=6) p1, p2 = pairs(x) @@ -349,6 +370,9 @@ def test_errors_bounds(name): (moocore.uniform_crossover, {"swap_prob": 1.5}, "'swap_prob'"), (moocore.uniform_crossover, {"pair_prob": -0.1}, "'pair_prob'"), (moocore.single_arithmetic_crossover, {"pair_prob": 2}, "'pair_prob'"), + (moocore.single_point_crossover, {"pair_prob": 2}, "'pair_prob'"), + (moocore.blend_alpha_crossover, {"pair_prob": -1}, "'pair_prob'"), + (moocore.local_crossover, {"pair_prob": 1.5}, "'pair_prob'"), (moocore.blend_alpha_crossover, {"alpha": -1}, "'alpha'"), (moocore.bounded_exponential_crossover, {"scale": 0}, "'scale'"), (moocore.bounded_exponential_crossover, {"swap_prob": 2}, "swap_prob"), From 32c832b99735c057fb2404707ec0d23372b4fbc7 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Fri, 23 Oct 2026 12:10:33 +0300 Subject: [PATCH 18/30] python/benchmarks/ Benchmark and compare the crossover operators * python/benchmarks/bench_crossover.py: New. Time each crossover operator against pymoo, DEAP, jMetalPy and DESDEO for an increasing number of parents and of variables. * python/benchmarks/compare_crossover.py: New. Compare the offspring of each operator with those of the other packages. * python/pyproject.toml (benchmarks): Add deap. --- python/benchmarks/bench_crossover.py | 433 +++++++++++++++++++++++++ python/benchmarks/compare_crossover.py | 345 ++++++++++++++++++++ python/pyproject.toml | 1 + 3 files changed, 779 insertions(+) create mode 100644 python/benchmarks/bench_crossover.py create mode 100644 python/benchmarks/compare_crossover.py diff --git a/python/benchmarks/bench_crossover.py b/python/benchmarks/bench_crossover.py new file mode 100644 index 000000000..3bb6145d9 --- /dev/null +++ b/python/benchmarks/bench_crossover.py @@ -0,0 +1,433 @@ +"""Crossover Benchmarks +==================== + +This example benchmarks the crossover operators in ``moocore`` against the +equivalent operators in other packages, when they exist. + +Each package receives the parents in its own data structure, which is created +before the timing starts. When a package expects the caller to choose the +other parents of DE or PCX, choosing them is timed, because ``moocore`` does it +inside the call. + +""" + +import random + +from bench import Bench + +import numpy as np +import polars as pl +import matplotlib.pyplot as plt +import moocore + +from deap import tools as deap_tools +from desdeo.emo.operators import crossover as desdeo_crossover +from desdeo.problem.schema import ( + Objective, + Problem as DesdeoProblem, + Variable, + VariableTypeEnum, +) +from desdeo.tools.patterns import Publisher +from jmetal.core.solution import FloatSolution +from jmetal.operator.crossover import ( + BLXAlphaCrossover, + DifferentialEvolutionCrossover, +) +from pymoo.algorithms.moo.nsde import VariantDE +from pymoo.core.population import Population +from pymoo.core.problem import Problem as PymooProblem +from pymoo.operators.crossover.dex import DEX +from pymoo.operators.crossover.pcx import PCX +from pymoo.operators.crossover.pntx import SinglePointCrossover +from pymoo.operators.crossover.ux import UniformCrossover + +LOWER, UPPER = 0.0, 1.0 +# Number of parents for a fixed number of variables, and vice versa. +N_PARENTS = [10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000] +N_VARS = [2, 5, 10, 20, 50, 100, 200, 500, 1000] +FIXED_NVAR = 30 +FIXED_NPARENTS = 100 + +rng = np.random.default_rng(42) +# DEAP and jMetalPy draw from the random module. +random.seed(42) + + +def distinct_indices(targets, n, k, exclude_targets=True): + """Draw k distinct row indices in [0, n) for each target.""" + m = len(targets) + if exclude_targets: + excluded = targets[:, None].copy() + else: + excluded = np.empty((m, 0), dtype=int) + chosen = np.empty((m, k), dtype=int) + for j in range(k): + drawn = rng.integers(0, n - excluded.shape[1], size=m) + for col in range(excluded.shape[1]): + drawn += drawn >= excluded[:, col] + chosen[:, j] = drawn + excluded = np.sort(np.column_stack([excluded, drawn]), axis=1) + return chosen + + +def check_offspring(a, b, what, n, name): + """Check that each package returns as many offspring as moocore.""" + if hasattr(b, "to_numpy"): # DESDEO + b = b.to_numpy() + elif len(b) and hasattr(b[0], "variables"): # jMetalPy + b = [s.variables for s in b] + b = np.asarray(b, dtype=float) + assert b.shape == a.shape, ( + f"In {name}, n={n}, {what} returned shape {b.shape}, but moocore returned {a.shape}" + ) + + +# pymoo: a Population and an unbounded Problem, so that pymoo does not repair +# the offspring. Offspring are clipped as in moocore when needed. +def pymoo_setup(x): + return PymooProblem(n_var=x.shape[1]), Population.new("X", x) + + +def pymoo_bounded_setup(x): + problem = PymooProblem(n_var=x.shape[1], xl=LOWER, xu=UPPER) + return problem, Population.new("X", x) + + +def pymoo_pairs(op): + def run(problem, pop): + parents = np.arange(len(pop)).reshape(-1, 2) + return op.do(problem, pop, parents, random_state=rng).get("X") + + return run + + +pymoo_dex = DEX(F=0.5, CR=1.0, at_least_once=False) +pymoo_pcx = PCX(eta=0.1, zeta=0.1, prob=1.0) +pymoo_variant_de = VariantDE( + variant="DE/rand/1/bin", CR=0.9, F=0.5, gamma=None, de_repair="to-bounds" +) + + +def pymoo_de_rand_1_bin(problem, pop): + return pymoo_variant_de.do(problem, pop, len(pop), random_state=rng).get( + "X" + ) + + +def pymoo_de_current_1(problem, pop): + targets = np.arange(len(pop)) + donors = distinct_indices(targets, len(pop), 2, exclude_targets=False) + parents = np.column_stack([targets, donors]) + off = pymoo_dex.do(problem, pop, parents, random_state=rng) + return np.clip(off.get("X"), LOWER, UPPER) + + +def pymoo_parent_centric(problem, pop): + targets = np.arange(len(pop)) + parents = np.column_stack([targets, distinct_indices(targets, len(pop), 2)]) + off = pymoo_pcx.do(problem, pop, parents, random_state=rng) + return np.clip(off.get("X"), LOWER, UPPER) + + +# DEAP: lists of floats. The operators change both individuals in place. +def deap_setup(x): + return x.tolist() + + +def deap_pairs(fun, *args): + def run(ind): + for i in range(0, len(ind) - 1, 2): + ind[i], ind[i + 1] = fun(ind[i], ind[i + 1], *args) + return ind + + return run + + +# jMetalPy: lists of FloatSolution. +def jmetalpy_setup(x): + lower, upper = [LOWER] * x.shape[1], [UPPER] * x.shape[1] + solutions = [] + for row in x: + s = FloatSolution(lower, upper, number_of_objectives=1) + s.variables = row.tolist() + solutions.append(s) + return solutions + + +def jmetalpy_pairs(op): + def run(solutions): + offspring = [] + for i in range(0, len(solutions) - 1, 2): + offspring.extend(op.execute([solutions[i], solutions[i + 1]])) + return offspring + + return run + + +jmetalpy_de_rand = DifferentialEvolutionCrossover(CR=0.9, F=0.5) +jmetalpy_de_current = DifferentialEvolutionCrossover(CR=1.0, F=0.5) + + +def jmetalpy_de_rand_1_bin(solutions): + # execute([a, b, c]) returns c + F (a - b), crossed over with the target. + targets = np.arange(len(solutions)) + offspring = [] + for i, (r1, r2, r3) in zip( + targets, distinct_indices(targets, len(solutions), 3) + ): + jmetalpy_de_rand.current_individual = solutions[i] + offspring.extend( + jmetalpy_de_rand.execute( + [solutions[r2], solutions[r3], solutions[r1]] + ) + ) + return offspring + + +def jmetalpy_de_current_1(solutions): + targets = np.arange(len(solutions)) + donors = distinct_indices(targets, len(solutions), 2, exclude_targets=False) + offspring = [] + for i, (r1, r2) in zip(targets, donors): + jmetalpy_de_current.current_individual = solutions[i] + offspring.extend( + jmetalpy_de_current.execute( + [solutions[r1], solutions[r2], solutions[i]] + ) + ) + return offspring + + +# DESDEO: a polars DataFrame and an operator built for the problem. +def desdeo_problem(nvar, binary=False): + if binary: + kind, lower, upper = VariableTypeEnum.binary, 0, 1 + else: + kind, lower, upper = VariableTypeEnum.real, LOWER, UPPER + variables = [ + Variable( + name=f"x_{i}", + symbol=f"x_{i}", + variable_type=kind, + lowerbound=lower, + upperbound=upper, + initial_value=lower, + ) + for i in range(1, nvar + 1) + ] + objective = Objective(name="f_1", symbol="f_1", func="x_1", maximize=False) + return DesdeoProblem( + name="bench", + description="Crossover benchmark", + variables=variables, + objectives=[objective], + ) + + +def desdeo_setup(cls, binary=False, **kwargs): + def setup(x): + problem = desdeo_problem(x.shape[1], binary=binary) + op = cls( + problem=problem, + publisher=Publisher(), + verbosity=0, + seed=42, + **kwargs, + ) + symbols = [v.symbol for v in problem.get_flattened_variables()] + population = pl.DataFrame(x, schema=symbols, orient="row") + return op, population, list(range(len(x))) + + return setup + + +def desdeo_run(op, population, rows): + return op.do(population=population, to_mate=rows) + + +def moocore_blend_alpha(x): + # moocore produces one offspring per pair. Call it twice to produce as + # many offspring as the other packages. + return np.vstack( + [ + moocore.blend_alpha_crossover(x, lower=LOWER, upper=UPPER, seed=rng) + for _ in range(2) + ] + ) + + +# For each operator: (data, {package: (setup, function)}). +real = "real" +binary = "binary" +operators = { + "uniform": ( + real, + { + "moocore": (None, lambda x: moocore.uniform_crossover(x, seed=rng)), + "pymoo": (pymoo_setup, pymoo_pairs(UniformCrossover(prob=1.0))), + "deap": (deap_setup, deap_pairs(deap_tools.cxUniform, 0.5)), + "desdeo": ( + desdeo_setup(desdeo_crossover.UniformCrossover), + desdeo_run, + ), + }, + ), + "single_point": ( + binary, + { + "moocore": ( + None, + lambda x: moocore.single_point_crossover(x, seed=rng), + ), + "pymoo": (pymoo_setup, pymoo_pairs(SinglePointCrossover(prob=1.0))), + "deap": (deap_setup, deap_pairs(deap_tools.cxOnePoint)), + "desdeo": ( + desdeo_setup( + desdeo_crossover.SinglePointBinaryCrossover, binary=True + ), + desdeo_run, + ), + }, + ), + "blend_alpha": ( + real, + { + "moocore": (None, moocore_blend_alpha), + "deap": (deap_setup, deap_pairs(deap_tools.cxBlend, 0.5)), + "jMetalPy": ( + jmetalpy_setup, + jmetalpy_pairs(BLXAlphaCrossover(probability=1.0, alpha=0.5)), + ), + "desdeo": ( + desdeo_setup(desdeo_crossover.BlendAlphaCrossover), + desdeo_run, + ), + }, + ), + "single_arithmetic": ( + real, + { + "moocore": ( + None, + lambda x: moocore.single_arithmetic_crossover(x, seed=rng), + ), + "desdeo": ( + desdeo_setup(desdeo_crossover.SingleArithmeticCrossover), + desdeo_run, + ), + }, + ), + "local": ( + real, + { + "moocore": (None, lambda x: moocore.local_crossover(x, seed=rng)), + "desdeo": ( + desdeo_setup(desdeo_crossover.LocalCrossover), + desdeo_run, + ), + }, + ), + "bounded_exponential": ( + real, + { + "moocore": ( + None, + lambda x: moocore.bounded_exponential_crossover( + x, lower=LOWER, upper=UPPER, seed=rng + ), + ), + "desdeo": ( + desdeo_setup(desdeo_crossover.BoundedExponentialCrossover), + desdeo_run, + ), + }, + ), + "de_rand_1_bin": ( + real, + { + "moocore": ( + None, + lambda x: moocore.de_rand_1_bin_crossover( + x, lower=LOWER, upper=UPPER, seed=rng + ), + ), + "pymoo": (pymoo_bounded_setup, pymoo_de_rand_1_bin), + "jMetalPy": (jmetalpy_setup, jmetalpy_de_rand_1_bin), + "desdeo": ( + desdeo_setup(desdeo_crossover.DifferentialEvolutionCrossover), + desdeo_run, + ), + }, + ), + "de_current_1": ( + real, + { + "moocore": ( + None, + lambda x: moocore.de_current_1_crossover( + x, lower=LOWER, upper=UPPER, seed=rng + ), + ), + "pymoo": (pymoo_setup, pymoo_de_current_1), + "jMetalPy": (jmetalpy_setup, jmetalpy_de_current_1), + }, + ), + "parent_centric": ( + real, + { + "moocore": ( + None, + lambda x: moocore.parent_centric_crossover( + x, lower=LOWER, upper=UPPER, seed=rng + ), + ), + "pymoo": (pymoo_setup, pymoo_parent_centric), + "desdeo": ( + desdeo_setup(desdeo_crossover.ParentCentricCrossover), + desdeo_run, + ), + }, + ), +} + + +def get_parents(nparents, nvar, data): + if data == binary: + return rng.integers(0, 2, size=(nparents, nvar)).astype(float) + return rng.uniform(LOWER, UPPER, size=(nparents, nvar)) + + +file_prefix = "crossover" +for op, (data, packages) in operators.items(): + title = f"{op}_crossover()" + print(f"# Running benchmark: {title}") + sweeps = { + "nparents": ( + N_PARENTS, + "Number of parents", + lambda n: get_parents(n, FIXED_NVAR, data), + ), + "nvars": ( + N_VARS, + "Number of variables", + lambda n: get_parents(FIXED_NPARENTS, n, data), + ), + } + for sweep, (n, xlabel, get_testcase) in sweeps.items(): + bench = Bench( + name=f"{op}-{sweep}", + n=n, + bench={k: fun for k, (_, fun) in packages.items()}, + setup={k: setup for k, (setup, _) in packages.items() if setup}, + check=check_offspring, + max_time=10, + ) + bench(get_testcase) + bench.plots( + file_prefix=file_prefix, title=title, log="xy", xlabel=xlabel + ) + plt.close("all") + +if "__file__" not in globals(): # Running interactively. + plt.show() diff --git a/python/benchmarks/compare_crossover.py b/python/benchmarks/compare_crossover.py new file mode 100644 index 000000000..cec96db24 --- /dev/null +++ b/python/benchmarks/compare_crossover.py @@ -0,0 +1,345 @@ +"""Crossover Return Values +======================= + +This script compares the offspring of the crossover operators in ``moocore`` +with the offspring of the equivalent operators in other packages. + +Each operator crosses over the same parents many times. For each decision +variable, a two-sample Kolmogorov-Smirnov test compares the offspring of each +package with those of ``moocore``. The bounds are wide enough that they never +bind, so the comparison does not depend on how each package handles them. + +""" + +import random + +import numpy as np +import polars as pl +from scipy.stats import ks_2samp +import moocore + +from deap import tools as deap_tools +from desdeo.emo.operators import crossover as desdeo_crossover +from desdeo.problem.schema import ( + Objective, + Problem as DesdeoProblem, + Variable, + VariableTypeEnum, +) +from desdeo.tools.patterns import Publisher +from jmetal.core.solution import FloatSolution +from jmetal.operator.crossover import ( + BLXAlphaCrossover, + DifferentialEvolutionCrossover, +) +from pymoo.algorithms.moo.nsde import VariantDE +from pymoo.core.population import Population +from pymoo.core.problem import Problem as PymooProblem +from pymoo.operators.crossover.dex import DEX +from pymoo.operators.crossover.pcx import PCX +from pymoo.operators.crossover.pntx import SinglePointCrossover +from pymoo.operators.crossover.ux import UniformCrossover + +N = 20_000 +LOWER, UPPER = -10.0, 10.0 +# Two parents, and a population whose first row is the target. +A = np.array([0.2, 0.7, 0.95]) +B = np.array([0.6, 0.3, 0.9]) +POPULATION = np.array( + [ + [0.2, 0.7, 0.95], + [0.6, 0.3, 0.9], + [0.5, 0.5, 0.1], + [0.1, 0.9, 0.4], + [0.8, 0.2, 0.6], + [0.4, 0.4, 0.4], + [0.9, 0.1, 0.2], + [0.3, 0.6, 0.8], + ] +) + +rng = np.random.default_rng(42) +random.seed(42) + + +def pair_matrix(a, b, n=N): + return np.tile(np.array([a, b], dtype=float), (n, 1)) + + +def first_offspring(x): + """First offspring of each pair, when rows 2i and 2i+1 are a pair.""" + return np.asarray(x)[0::2] + + +# pymoo +def pymoo_pairs(op, x): + pop = Population.new("X", x) + parents = np.arange(len(x)).reshape(-1, 2) + off = op.do(PymooProblem(n_var=x.shape[1]), pop, parents, random_state=rng) + # pymoo returns all the first offspring before all the second offspring. + return off.get("X")[: len(parents)] + + +def pymoo_with_targets(op, population, others, n=N): + """Offspring of target row 0, with the other parents from `others`.""" + parents = np.column_stack([np.zeros(n, dtype=int), others(n)]) + problem = PymooProblem(n_var=population.shape[1]) + off = op.do( + problem, Population.new("X", population), parents, random_state=rng + ) + return off.get("X") + + +def random_rows(k, exclude_zero=True): + def draw(n): + start = 1 if exclude_zero else 0 + return np.array( + [ + rng.choice(np.arange(start, len(POPULATION)), k, replace=False) + for _ in range(n) + ] + ) + + return draw + + +def pymoo_de_rand_1_bin(population, n=N): + # VariantDE crosses over every row once per call, so call it repeatedly + # and keep the offspring of row 0. + op = VariantDE(variant="DE/rand/1/bin", CR=0.9, F=0.5, gamma=None) + problem = PymooProblem(n_var=population.shape[1]) + pop = Population.new("X", population) + calls = n // 4 + return np.array( + [ + op.do(problem, pop, len(pop), random_state=rng).get("X")[0] + for _ in range(calls) + ] + ) + + +# DEAP +def deap_pairs(fun, x, *args): + ind = x.tolist() + for i in range(0, len(ind) - 1, 2): + ind[i], ind[i + 1] = fun(ind[i], ind[i + 1], *args) + return first_offspring(ind) + + +# jMetalPy +def jmetalpy_solutions(x): + lower, upper = [LOWER] * x.shape[1], [UPPER] * x.shape[1] + solutions = [] + for row in x: + s = FloatSolution(lower, upper, number_of_objectives=1) + s.variables = row.tolist() + solutions.append(s) + return solutions + + +def jmetalpy_pairs(op, x): + s = jmetalpy_solutions(x) + offspring = [] + for i in range(0, len(s) - 1, 2): + offspring.extend(op.execute([s[i], s[i + 1]])) + return first_offspring([o.variables for o in offspring]) + + +def jmetalpy_de(population, current, n=N): + s = jmetalpy_solutions(population) + if current: + op = DifferentialEvolutionCrossover(CR=1.0, F=0.5) + donors = random_rows(2, exclude_zero=False)(n) + else: + op = DifferentialEvolutionCrossover(CR=0.9, F=0.5) + donors = random_rows(3)(n) + op.current_individual = s[0] + offspring = [] + for d in donors: + # execute([a, b, c]) returns c + F (a - b), crossed over with the target. + parents = ( + [s[d[0]], s[d[1]], s[0]] if current else [s[d[1]], s[d[2]], s[d[0]]] + ) + offspring.append(op.execute(parents)[0].variables) + return np.array(offspring) + + +# DESDEO +def desdeo_run(cls, x, targets=None, binary=False, **kwargs): + nvar = x.shape[1] + if binary: + kind, lower, upper = VariableTypeEnum.binary, 0, 1 + else: + kind, lower, upper = VariableTypeEnum.real, LOWER, UPPER + variables = [ + Variable( + name=f"x_{i}", + symbol=f"x_{i}", + variable_type=kind, + lowerbound=lower, + upperbound=upper, + initial_value=lower, + ) + for i in range(1, nvar + 1) + ] + objective = Objective(name="f_1", symbol="f_1", func="x_1", maximize=False) + problem = DesdeoProblem( + name="compare", + description="Crossover comparison", + variables=variables, + objectives=[objective], + ) + op = cls( + problem=problem, publisher=Publisher(), verbosity=0, seed=42, **kwargs + ) + population = pl.DataFrame( + x, schema=[v.symbol for v in variables], orient="row" + ) + if targets is None: + targets = list(range(len(x))) + return op.do(population=population, to_mate=targets).to_numpy() + + +def desdeo_pairs(cls, x, **kwargs): + # DESDEO stacks all the first offspring before all the second offspring. + return desdeo_run(cls, x, **kwargs)[: len(x) // 2] + + +x = pair_matrix(A, B) +xb = pair_matrix(np.zeros(6), np.ones(6)) +targets = np.zeros(N, dtype=int) +bounds = dict(lower=LOWER, upper=UPPER) + +comparisons = { + "uniform": ( + first_offspring(moocore.uniform_crossover(x, seed=rng)), + { + "pymoo": pymoo_pairs(UniformCrossover(prob=1.0), x), + "deap": deap_pairs(deap_tools.cxUniform, x, 0.5), + "desdeo": desdeo_pairs(desdeo_crossover.UniformCrossover, x), + }, + ), + "single_point": ( + first_offspring(moocore.single_point_crossover(xb, seed=rng)), + { + "pymoo": pymoo_pairs(SinglePointCrossover(prob=1.0), xb), + "deap": deap_pairs(deap_tools.cxOnePoint, xb), + "desdeo": desdeo_pairs( + desdeo_crossover.SinglePointBinaryCrossover, xb, binary=True + ), + }, + ), + "blend_alpha": ( + moocore.blend_alpha_crossover(x, seed=rng, **bounds), + { + "deap": deap_pairs(deap_tools.cxBlend, x, 0.5), + "jMetalPy": jmetalpy_pairs( + BLXAlphaCrossover(probability=1.0, alpha=0.5), x + ), + # DESDEO produces two independent offspring per pair. + "desdeo": desdeo_run(desdeo_crossover.BlendAlphaCrossover, x), + }, + ), + "single_arithmetic": ( + first_offspring(moocore.single_arithmetic_crossover(x, seed=rng)), + {"desdeo": desdeo_pairs(desdeo_crossover.SingleArithmeticCrossover, x)}, + ), + "local": ( + first_offspring(moocore.local_crossover(x, seed=rng)), + {"desdeo": desdeo_pairs(desdeo_crossover.LocalCrossover, x)}, + ), + "bounded_exponential": ( + first_offspring( + moocore.bounded_exponential_crossover(x, seed=rng, **bounds) + ), + { + "desdeo": desdeo_pairs( + desdeo_crossover.BoundedExponentialCrossover, x + ) + }, + ), + "de_rand_1_bin": ( + moocore.de_rand_1_bin_crossover( + POPULATION, targets=targets, seed=rng, **bounds + ), + { + "pymoo": pymoo_de_rand_1_bin(POPULATION), + "jMetalPy": jmetalpy_de(POPULATION, current=False), + "desdeo": desdeo_run( + desdeo_crossover.DifferentialEvolutionCrossover, + POPULATION, + targets=targets.tolist(), + ), + }, + ), + "de_current_1": ( + moocore.de_current_1_crossover( + POPULATION, targets=targets, seed=rng, **bounds + ), + { + "pymoo": pymoo_with_targets( + DEX(F=0.5, CR=1.0, at_least_once=False), + POPULATION, + random_rows(2, exclude_zero=False), + ), + "jMetalPy": jmetalpy_de(POPULATION, current=True), + }, + ), + "parent_centric": ( + moocore.parent_centric_crossover( + POPULATION, targets=targets, seed=rng, **bounds + ), + { + "pymoo": pymoo_with_targets( + PCX(eta=0.1, zeta=0.1, prob=1.0), POPULATION, random_rows(2) + ), + "desdeo": desdeo_run( + desdeo_crossover.ParentCentricCrossover, + POPULATION, + targets=targets.tolist(), + ), + }, + ), +} + +# Known differences from moocore. +notes = { + ("single_point", "desdeo"): "Binary variables only.", + ("blend_alpha", "deap"): "Two mirrored offspring per pair, no bounds.", + ("blend_alpha", "jMetalPy"): "Clips each sample instead of the interval.", + ( + "de_rand_1_bin", + "pymoo", + ): "Forces a mutant variable only when none was chosen, instead of a random one in every offspring.", + ( + "de_current_1", + "pymoo", + ): "Multiplies F by a random factor within 1 +/- 5e-5.", + ( + "de_current_1", + "jMetalPy", + ): "Forces a mutant variable, so it differs when CR < 1.", +} + +print( + "| Operator | Package | Offspring | Smallest KS p-value " + "| Largest mean difference / sd | sd ratio | Notes |" +) +print("|---|---|---|---|---|---|---|") +for op, (ours, others) in comparisons.items(): + ours = np.asarray(ours, dtype=float) + for package, theirs in others.items(): + theirs = np.asarray(theirs, dtype=float) + nvar = ours.shape[1] + pvalues = [ + ks_2samp(ours[:, j], theirs[:, j]).pvalue for j in range(nvar) + ] + sd = ours.std(axis=0) + sd = np.where(sd > 0, sd, 1) + mean_diff = np.abs(ours.mean(axis=0) - theirs.mean(axis=0)) / sd + sd_ratio = theirs.std(axis=0) / sd + print( + f"| {op} | {package} | {len(theirs)} | {min(pvalues):.3f} | " + f"{mean_diff.max():.3f} | {sd_ratio.min():.3f}-{sd_ratio.max():.3f} | " + f"{notes.get((op, package), '')} |" + ) diff --git a/python/pyproject.toml b/python/pyproject.toml index f36004a7d..1fff08067 100644 --- a/python/pyproject.toml +++ b/python/pyproject.toml @@ -40,6 +40,7 @@ dependencies = [ [project.optional-dependencies] benchmarks = [ "botorch", + "deap", "desdeo", "fast-pareto", "jmetalpy>=1.8", From eefeaf6edc396ed6677a2e1ccd0acba985e39637 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Fri, 23 Oct 2026 12:10:34 +0300 Subject: [PATCH 19/30] python/doc/ Add the crossover benchmarks * python/doc/source/benchmarks.inc.rst: Add the crossover operators. * python/doc/source/_static/bench/crossover_bench-*-time.png: New. --- ...ssover_bench-blend_alpha-nparents-time.png | Bin 0 -> 58081 bytes ...crossover_bench-blend_alpha-nvars-time.png | Bin 0 -> 53678 bytes ...ench-bounded_exponential-nparents-time.png | Bin 0 -> 42531 bytes ...r_bench-bounded_exponential-nvars-time.png | Bin 0 -> 41129 bytes ...sover_bench-de_current_1-nparents-time.png | Bin 0 -> 49963 bytes ...rossover_bench-de_current_1-nvars-time.png | Bin 0 -> 43045 bytes ...over_bench-de_rand_1_bin-nparents-time.png | Bin 0 -> 55033 bytes ...ossover_bench-de_rand_1_bin-nvars-time.png | Bin 0 -> 48650 bytes .../crossover_bench-local-nparents-time.png | Bin 0 -> 38477 bytes .../crossover_bench-local-nvars-time.png | Bin 0 -> 36064 bytes ...ver_bench-parent_centric-nparents-time.png | Bin 0 -> 48663 bytes ...ssover_bench-parent_centric-nvars-time.png | Bin 0 -> 45571 bytes ..._bench-single_arithmetic-nparents-time.png | Bin 0 -> 37850 bytes ...ver_bench-single_arithmetic-nvars-time.png | Bin 0 -> 36138 bytes ...sover_bench-single_point-nparents-time.png | Bin 0 -> 52863 bytes ...rossover_bench-single_point-nvars-time.png | Bin 0 -> 47892 bytes .../crossover_bench-uniform-nparents-time.png | Bin 0 -> 56013 bytes .../crossover_bench-uniform-nvars-time.png | Bin 0 -> 53410 bytes python/doc/source/benchmarks.inc.rst | 81 ++++++++++++++++++ 19 files changed, 81 insertions(+) create mode 100644 python/doc/source/_static/bench/crossover_bench-blend_alpha-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-blend_alpha-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-bounded_exponential-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-bounded_exponential-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-de_current_1-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-de_current_1-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-de_rand_1_bin-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-de_rand_1_bin-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-local-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-local-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-parent_centric-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-parent_centric-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-single_arithmetic-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-single_arithmetic-nvars-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-single_point-nparents-time.png create mode 100644 python/doc/source/_static/bench/crossover_bench-single_point-nvars-time.png create mode 100644 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following plots benchmark the speed of computing the :ref:`epsilon indicator +Crossover operators +------------------- + +The following plots compare the :ref:`crossover operators ` of `moocore`_ with the equivalent operators of `pymoo`_, `DEAP`_, `jMetalPy`_ and `DESDEO`_, when they exist. Each operator is timed for an increasing number of parents with 30 variables (left), and for an increasing number of variables with 100 parents (right). Each package receives the parents in its own data structure, which is created before the timing starts. When a package expects the caller to choose the other parents of DE or PCX, choosing them is part of the time. :func:`~moocore.blend_alpha_crossover` produces one offspring per pair, so it is called twice to produce as many offspring as the other packages. Single arithmetic, local and bounded exponential crossover are only available in `moocore`_ and `DESDEO`_. + +The script ``compare_crossover.py`` in the same folder compares the offspring of each operator with the offspring of the equivalent operators in the other packages. The distributions agree, except where the operators differ by design. The DE/rand/1/bin operator of `pymoo`_ forces a variable to come from the mutant only when no variable was chosen, instead of forcing a random variable in every offspring. The ``DEX`` operator of `pymoo`_, which matches DE/current/1, multiplies the scaling factor by a random factor within :math:`1 \pm 5 \cdot 10^{-5}`. + +|xover_uniform_parents| |xover_uniform_vars| + +.. |xover_uniform_parents| image:: _static/bench/crossover_bench-uniform-nparents-time.png + :width: 48% + +.. |xover_uniform_vars| image:: _static/bench/crossover_bench-uniform-nvars-time.png + :width: 48% + +|xover_single_point_parents| |xover_single_point_vars| + +.. |xover_single_point_parents| image:: _static/bench/crossover_bench-single_point-nparents-time.png + :width: 48% + +.. |xover_single_point_vars| image:: _static/bench/crossover_bench-single_point-nvars-time.png + :width: 48% + +|xover_blend_alpha_parents| |xover_blend_alpha_vars| + +.. |xover_blend_alpha_parents| image:: _static/bench/crossover_bench-blend_alpha-nparents-time.png + :width: 48% + +.. |xover_blend_alpha_vars| image:: _static/bench/crossover_bench-blend_alpha-nvars-time.png + :width: 48% + +|xover_single_arithmetic_parents| |xover_single_arithmetic_vars| + +.. |xover_single_arithmetic_parents| image:: _static/bench/crossover_bench-single_arithmetic-nparents-time.png + :width: 48% + +.. |xover_single_arithmetic_vars| image:: _static/bench/crossover_bench-single_arithmetic-nvars-time.png + :width: 48% + +|xover_local_parents| |xover_local_vars| + +.. |xover_local_parents| image:: _static/bench/crossover_bench-local-nparents-time.png + :width: 48% + +.. |xover_local_vars| image:: _static/bench/crossover_bench-local-nvars-time.png + :width: 48% + +|xover_bounded_exponential_parents| |xover_bounded_exponential_vars| + +.. |xover_bounded_exponential_parents| image:: _static/bench/crossover_bench-bounded_exponential-nparents-time.png + :width: 48% + +.. |xover_bounded_exponential_vars| image:: _static/bench/crossover_bench-bounded_exponential-nvars-time.png + :width: 48% + +|xover_de_rand_1_bin_parents| |xover_de_rand_1_bin_vars| + +.. |xover_de_rand_1_bin_parents| image:: _static/bench/crossover_bench-de_rand_1_bin-nparents-time.png + :width: 48% + +.. |xover_de_rand_1_bin_vars| image:: _static/bench/crossover_bench-de_rand_1_bin-nvars-time.png + :width: 48% + +|xover_de_current_1_parents| |xover_de_current_1_vars| + +.. |xover_de_current_1_parents| image:: _static/bench/crossover_bench-de_current_1-nparents-time.png + :width: 48% + +.. |xover_de_current_1_vars| image:: _static/bench/crossover_bench-de_current_1-nvars-time.png + :width: 48% + +|xover_parent_centric_parents| |xover_parent_centric_vars| + +.. |xover_parent_centric_parents| image:: _static/bench/crossover_bench-parent_centric-nparents-time.png + :width: 48% + +.. |xover_parent_centric_vars| image:: _static/bench/crossover_bench-parent_centric-nvars-time.png + :width: 48% + + + .. _BoFire: https://experimental-design.github.io/bofire/ .. _BoTorch: https://botorch.org/ .. _DEAP: https://deap.readthedocs.io/en/master/ From d72710f908b0c8730409ed467150aa2b18bd348b Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Fri, 23 Oct 2026 17:00:26 +0300 Subject: [PATCH 20/30] python/benchmarks/ Give the crossover plots plain titles * python/benchmarks/bench.py (Bench.plots): New argument add_name. * python/benchmarks/bench_crossover.py: Title each plot with the operator and the quantity that varies. --- python/benchmarks/bench.py | 4 +++- python/benchmarks/bench_crossover.py | 22 +++++++++++++++++++--- 2 files changed, 22 insertions(+), 4 deletions(-) diff --git a/python/benchmarks/bench.py b/python/benchmarks/bench.py index e9e7c409c..7e68188a9 100644 --- a/python/benchmarks/bench.py +++ b/python/benchmarks/bench.py @@ -262,6 +262,7 @@ def plots( relative=False, xlabel="n", show_ci=False, + add_name=True, ): """Plots the results after running the benchmark one or more times. @@ -366,7 +367,8 @@ def single_plot(results, ylabel, file_suffix): ax.fill_between(x, y1, y2, where=valid, alpha=0.2) plt.title(f"({self.cpu_model})", fontsize=10) - plt.suptitle(f"{title} for {self.name}", fontsize=12) + suptitle = f"{title} for {self.name}" if add_name else title + plt.suptitle(suptitle, fontsize=12) save2png(f"{file_prefix}_bench-{self.name}-{file_suffix}.png") # CPU times. diff --git a/python/benchmarks/bench_crossover.py b/python/benchmarks/bench_crossover.py index 3bb6145d9..86a6c9b24 100644 --- a/python/benchmarks/bench_crossover.py +++ b/python/benchmarks/bench_crossover.py @@ -398,10 +398,22 @@ def get_parents(nparents, nvar, data): return rng.uniform(LOWER, UPPER, size=(nparents, nvar)) +# Operator names for the plot titles. +titles = { + "uniform": "Uniform", + "single_point": "Single Point", + "blend_alpha": "Blend Alpha", + "single_arithmetic": "Single Arithmetic", + "local": "Local", + "bounded_exponential": "Bounded Exponential", + "de_rand_1_bin": "DE/rand/1/bin", + "de_current_1": "DE/current/1", + "parent_centric": "Parent-Centric", +} + file_prefix = "crossover" for op, (data, packages) in operators.items(): - title = f"{op}_crossover()" - print(f"# Running benchmark: {title}") + print(f"# Running benchmark: {op}_crossover()") sweeps = { "nparents": ( N_PARENTS, @@ -425,7 +437,11 @@ def get_parents(nparents, nvar, data): ) bench(get_testcase) bench.plots( - file_prefix=file_prefix, title=title, log="xy", xlabel=xlabel + file_prefix=file_prefix, + title=f"{titles[op]} crossover performance over {xlabel.lower()}", + log="xy", + xlabel=xlabel, + add_name=False, ) plt.close("all") From c8c63878f1447e5fea3e59c2b50e632241820292 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Fri, 23 Oct 2026 17:00:26 +0300 Subject: [PATCH 21/30] python/doc/source/_static/bench/crossover_bench-*-time.png: Regenerate. --- ...ssover_bench-blend_alpha-nparents-time.png | Bin 58081 -> 59459 bytes ...crossover_bench-blend_alpha-nvars-time.png | Bin 53678 -> 54240 bytes ...ench-bounded_exponential-nparents-time.png | Bin 42531 -> 41714 bytes ...r_bench-bounded_exponential-nvars-time.png | Bin 41129 -> 40129 bytes ...sover_bench-de_current_1-nparents-time.png | Bin 49963 -> 50541 bytes ...rossover_bench-de_current_1-nvars-time.png | Bin 43045 -> 43844 bytes ...over_bench-de_rand_1_bin-nparents-time.png | Bin 55033 -> 56202 bytes ...ossover_bench-de_rand_1_bin-nvars-time.png | Bin 48650 -> 49899 bytes .../crossover_bench-local-nparents-time.png | Bin 38477 -> 39570 bytes .../crossover_bench-local-nvars-time.png | Bin 36064 -> 37946 bytes ...ver_bench-parent_centric-nparents-time.png | Bin 48663 -> 49667 bytes ...ssover_bench-parent_centric-nvars-time.png | Bin 45571 -> 45821 bytes ..._bench-single_arithmetic-nparents-time.png | Bin 37850 -> 38177 bytes ...ver_bench-single_arithmetic-nvars-time.png | Bin 36138 -> 36737 bytes ...sover_bench-single_point-nparents-time.png | Bin 52863 -> 54787 bytes ...rossover_bench-single_point-nvars-time.png | Bin 47892 -> 47051 bytes .../crossover_bench-uniform-nparents-time.png | Bin 56013 -> 57195 bytes .../crossover_bench-uniform-nvars-time.png | Bin 53410 -> 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zdh){_9tB#eipMQCD}1vrwZkrLWPpR~=h@Pq3%TNl_>H`ysk|m< zCy*kw2E9?ora{uCai1C_(ox{L3vg+j{4x)58LjIxWG5QC9lAm=bM3=xe|g}R=z>lG zmo=z;l=T+P$30Iw5RZh^odTbqPJ9yD9=DkfgnH!ky{@LQh=_`gvyi_4fkV(T$K`c7 zPPLF1|M|K@irHjTXm+Qeut>VaOgWgZq(FZh2W$b6M+#miLY9;o<&C>xg8(g~ni1{&+Ef-I3r$9(f3eOu=Hs50%d`s*-m?5P)no0geJ58yEgUwHV|Ry z=JqD@A|;1!Z*TLn(GH=0^FbBSAFd&nc)uWi^X5%Xb+xLs_y)9g)dB40E>wxH`Ohh> z)jGu75YaF)?Pm;4Tx{%oT<#W|G2>uUv~cz*_M&kt4V@ad(u0HX9NM^-!%zdeaj}fxL9iOaJf1uj&TjicQZnMjj85; z+>#+4tZn776(wy7nTxVGlbMEp@Y%db;2Cv*3ZJ?UX8UWNP7X#sQ_L(KLch0cu9)T7 zxw(aLj24IAxmP}vXukN!LNXkLN~9`v1b(4;xcgfO6i~AAju(I$ol+b8^=lv4_ff5* z^=GJNF?J`e&Yn@XPAkd<{%I;L#>Hg0)uQy2Y+0;3ryJd2bc-n=$;{lQ{v1~d7)p~J z988I5@Fm7Ot+yM&vZIhvM*Y7pp@O;7Rg%p6=3h|>0~CMlYk zoIqZ>+O)b{_duX6Q@F+qvbUcn$)u;=u-V(TaN!fKDKB4iyrKP W@+|Vr!2$~WlaW-AC>1mG|9=3D=@=*g From 030b805c5df106ac50588597610b801d2bf3a902 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Sat, 24 Oct 2026 15:49:32 +0300 Subject: [PATCH 22/30] c/crossover.c (bex_offspring): Describe the distribution of BETA as in Thakur et al. (2014). --- c/crossover.c | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/c/crossover.c b/c/crossover.c index 3f1411eb9..2ab92074a 100644 --- a/c/crossover.c +++ b/c/crossover.c @@ -228,10 +228,11 @@ local_crossover(double * restrict offspring, const double * restrict parents, rng_free(rng); } -/* Offspring value of parent value X. It moves X by BETA * SPAN, where BETA - follows a two-sided exponential distribution with scale SCALE, truncated so - that the offspring stays within [LOWER, UPPER]. U and R are uniform in - [0, 1). */ +/* Offspring value of parent value X. It moves X by BETA * SPAN. BETA is + negative or positive with probability 1/2 each. On each side, it follows + an exponential distribution with scale SCALE, truncated at the bound on + that side, so the offspring stays within [LOWER, UPPER]. U and R are + uniform in [0, 1). */ static inline double bex_offspring(double x, double span, double lower, double upper, double scale, double u, double r) From 727f8875cb89be0d9a2e464106836a08c77ec399 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Sat, 24 Oct 2026 15:49:33 +0300 Subject: [PATCH 23/30] python/ Check the crossover operators against their papers * python/src/moocore/_crossover.py (_check_within_bounds): New. Also reject NaN. (blend_alpha_crossover): Require the parents to be within the bounds. Say what Eshelman and Schaffer recommend and do differently. (single_arithmetic_crossover): Say that this is the case alpha = 1/2 of the operator of Eiben and Smith. (bounded_exponential_crossover): Describe the two sides of the distribution. Say which settings are not from the paper. (de_rand_1_bin_crossover): Quote Storn and Price on CR in full. (de_current_1_crossover): Say where the distinct donors come from. (parent_centric_crossover): Correct the comparison with equation (2) of Deb et al. (2002). * python/tests/test_crossover.py (test_errors_operator_specific): Test parents outside the bounds in blend_alpha_crossover and NaN parents. --- python/src/moocore/_crossover.py | 95 ++++++++++++++++++++------------ python/tests/test_crossover.py | 8 +++ 2 files changed, 69 insertions(+), 34 deletions(-) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index 03d2dc3e4..52395d7c1 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -50,6 +50,14 @@ def _bounds( return np.ascontiguousarray(lower), np.ascontiguousarray(upper) +def _check_within_bounds( + parents: np.ndarray, lower: np.ndarray, upper: np.ndarray +) -> None: + # NaN fails both comparisons, so it is rejected too. + if not np.all((parents >= lower) & (parents <= upper)): + raise ValueError("'parents' must be within 'lower' and 'upper'") + + def _targets(targets: ArrayLike | None, n: int) -> np.ndarray: if targets is None: return np.arange(n, dtype=np.uintp) @@ -264,7 +272,7 @@ def blend_alpha_crossover( Parameters ---------- parents : - ${parents} + ${parents} Every value must be within the bounds. lower : ${lower_bound} upper : @@ -290,9 +298,11 @@ def blend_alpha_crossover( Notes ----- - BLX-:math:`\alpha` was proposed by :footcite:t:`EshSch1992`. Each variable - is sampled independently, so the offspring fill the whole (clipped) box - around the parents. + BLX-:math:`\alpha` was proposed by :footcite:t:`EshSch1992`, who recommend + :math:`\alpha = 0.5` because it makes an offspring as likely to lie outside + its parents as between them. Each variable is sampled independently, so + the offspring fill the whole (clipped) box around the parents. Eshelman + and Schaffer do not handle bounds, and they produce two offspring per pair. To produce more than one offspring per pair, call the function again. If ``seed`` is an integer, every call returns the same offspring. Pass the @@ -315,6 +325,7 @@ def blend_alpha_crossover( """ parents = _as_matrix(parents, "parents", min_rows=2) lower, upper = _bounds(lower, upper, parents.shape[1]) + _check_within_bounds(parents, lower, upper) if not alpha >= 0: raise ValueError("'alpha' must be non-negative") pair_prob = _check_probability(pair_prob, "pair_prob") @@ -365,8 +376,12 @@ def single_arithmetic_crossover( Notes ----- - This operator is described by :footcite:t:`EibSmi2003` and compared with - other real-coded crossover operators by Picek, Jakobovic and Golub (2013). + :footcite:t:`EibSmi2003` describe single arithmetic recombination with a + weight :math:`\alpha`, where one offspring gets :math:`\alpha y_k + (1 - + \alpha) x_k` and the other gets :math:`\alpha x_k + (1 - \alpha) y_k`. + This function is their example with :math:`\alpha = 1/2`, where both + offspring get the average. Picek, Jakobovic and Golub (2013) compare it + with other real-coded crossover operators. References ---------- @@ -487,18 +502,18 @@ def bounded_exponential_crossover( .. math:: u_j = x_j + \beta_j^x d_j, \qquad v_j = y_j + \beta_j^y d_j, - where :math:`\beta_j^x` follows an exponential distribution with scale - :math:`\lambda` (``scale``), truncated so that :math:`u_j` stays within - the bounds of the variable. With probability 1/2, an offspring moves - towards the lower bound :math:`l_j`, with :math:`\beta = \lambda \ln(e_l + - r(1 - e_l))` and :math:`e_l = \exp((l_j - x_j) / (\lambda d_j))`. - Otherwise, it moves towards the upper bound :math:`h_j`, with :math:`\beta - = -\lambda \ln(1 - r(1 - e_h))` and :math:`e_h = \exp((x_j - h_j) / - (\lambda d_j))`. - The uniform random number :math:`r` and the direction are shared by both - offspring. Variables where the parents are equal are copied. After - that, each variable is swapped between the two offspring with probability - ``swap_prob``, as in :func:`uniform_crossover`. + where :math:`\beta_j^x` is negative or positive with probability 1/2 each. + On each side, it follows an exponential distribution with scale + :math:`\lambda` (``scale``), truncated at the bound on that side, so that + :math:`u_j` stays within the bounds of the variable. Towards the lower + bound :math:`l_j`, :math:`\beta = \lambda \ln(e_l + r(1 - e_l))` with + :math:`e_l = \exp((l_j - x_j) / (\lambda d_j))`. Towards the upper bound + :math:`h_j`, :math:`\beta = -\lambda \ln(1 - r(1 - e_h))` with :math:`e_h = + \exp((x_j - h_j) / (\lambda d_j))`. The uniform random number :math:`r` + and the direction are shared by both offspring. Variables where the + parents are equal are copied. After that, each variable is swapped between + the two offspring with probability ``swap_prob``, as in + :func:`uniform_crossover`. Otherwise, with probability ``1 - pair_prob``, the offspring are copies of their parents. @@ -529,7 +544,13 @@ def bounded_exponential_crossover( ----- BEX was proposed by Thakur, Meghwani and Jalota (2014) as a bounded version of the Laplace crossover of Deep and Thakur (2007). Without - bounds, :math:`\beta` follows a Laplace distribution. + bounds, :math:`\beta` follows a Laplace distribution. A parent that sits + on a bound is copied with probability 1/2, as in the paper. + + The swap of variables (``swap_prob``) is not part of the original operator. + Thakur, Meghwani and Jalota tuned :math:`\lambda = 0.65` and a crossover + probability of 0.5 for their genetic algorithm. The defaults here keep + the offspring closer to their parents and cross over every pair. References ---------- @@ -551,8 +572,7 @@ def bounded_exponential_crossover( """ parents = _as_matrix(parents, "parents", min_rows=2) lower, upper = _bounds(lower, upper, parents.shape[1]) - if np.any(parents < lower) or np.any(parents > upper): - raise ValueError("'parents' must be within 'lower' and 'upper'") + _check_within_bounds(parents, lower, upper) scale = _check_positive(scale, "scale") swap_prob = _check_probability(swap_prob, "swap_prob") pair_prob = _check_probability(pair_prob, "pair_prob") @@ -618,9 +638,10 @@ def de_rand_1_bin_crossover( Notes ----- - This is the DE/rand/1/bin scheme of :footcite:t:`StoPri1997:de`, who - recommend :math:`F = 0.5` as a first choice and suggest trying - :math:`CR = 0.9` first. + This is the DE/rand/1/bin scheme of :footcite:t:`StoPri1997:de`. They + recommend :math:`F = 0.5` as a first choice. They call :math:`CR = 0.1` a + good first choice, but suggest first trying :math:`CR = 0.9` or 1.0 to see + whether a quick solution is possible, which gives the default here. Multi-objective DE algorithms such as GDE3 :footcite:p:`KukLam2005:gde3` and DEMO :footcite:p:`RobFil05demo` use this variant :footcite:p:`BezLopStu2015emode`. @@ -688,8 +709,9 @@ def de_current_1_crossover( Parameters ---------- population : - ${population} In MOEA/D, this is the neighbourhood of the subproblem, - and ``targets`` gives the row of the subproblem's current solution. + ${population} In MOEA/D-DE, this is the neighbourhood of the + subproblem or, with a small probability, the whole population, and + ``targets`` gives the row of the subproblem's current solution. targets : ${targets} lower : @@ -723,6 +745,10 @@ def de_current_1_crossover( call it the current/1 strategy, a term introduced by Gong et al. (2017), and find it in the source code of MOEA/D-DE, MOEA/D-DRA and MOEA/D-STM. + Li and Zhang do not require the two donors to differ. This function draws + two distinct donors, either of which may be the target, as their C++ code + does according to Tanabe and Ishibuchi (2019). + Li and Zhang reset values outside the bounds to a random value within them. Their own implementation clips them instead, which is what this function does, and which Tanabe and Ishibuchi (2019) found to work best @@ -824,14 +850,15 @@ def parent_centric_crossover( Notes ----- - PCX was proposed by Deb, Anand and Joshi (2002). Their equation (2) - writes the step orthogonal to :math:`d` as a sum of normal steps along - :math:`\mu - 1` orthonormal vectors, where :math:`\mu` is the number of - parents. Like pymoo, which bases its implementation on the authors' C - code, this function projects an isotropic normal vector onto the whole - subspace orthogonal to :math:`d`, so the offspring is not restricted to - the plane of the three parents. If :math:`x` is (almost) the centroid, - the projection is skipped. + PCX was proposed by Deb, Anand and Joshi (2002), who use three parents and + :math:`\sigma_\zeta = \sigma_\eta = 0.1`. Their equation (2) writes the + step orthogonal to :math:`d` as a sum of normal steps along :math:`\mu - 1` + orthonormal vectors, where :math:`\mu` is the number of parents. Like + pymoo, which bases its implementation on the authors' C code, this + function projects an isotropic normal vector onto the whole subspace + orthogonal to :math:`d`, so the step covers every direction orthogonal to + :math:`d`, not only :math:`\mu - 1` of them. If :math:`x` is (almost) the + centroid, the projection is skipped. References ---------- diff --git a/python/tests/test_crossover.py b/python/tests/test_crossover.py index 413a7ea62..cb93be758 100644 --- a/python/tests/test_crossover.py +++ b/python/tests/test_crossover.py @@ -400,6 +400,14 @@ def test_errors_operator_specific(): moocore.bounded_exponential_crossover( [[0.5, 2.0], [0.2, 0.3]], lower=0, upper=1 ) + with pytest.raises(ValueError, match=r"within 'lower' and 'upper'"): + moocore.bounded_exponential_crossover( + [[np.nan, 0.5], [0.2, 0.3]], lower=0, upper=1 + ) + with pytest.raises(ValueError, match=r"within 'lower' and 'upper'"): + moocore.blend_alpha_crossover( + [[1.5, 2.0], [0.2, 0.3]], lower=0, upper=1 + ) @pytest.mark.parametrize("name", POPULATION_OPERATORS) From 4a831629db0043c6f84e22c9a45460ac45ce9287 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Sat, 24 Oct 2026 15:54:16 +0300 Subject: [PATCH 24/30] python/benchmarks/compare_crossover.py: Compare every pair of packages Print and save to a CSV file one matrix of KS p-values per operator, and use 100 000 offspring per package. --- python/benchmarks/compare_crossover.py | 87 +++++++++++++------------- 1 file changed, 43 insertions(+), 44 deletions(-) diff --git a/python/benchmarks/compare_crossover.py b/python/benchmarks/compare_crossover.py index cec96db24..bd974c3c0 100644 --- a/python/benchmarks/compare_crossover.py +++ b/python/benchmarks/compare_crossover.py @@ -4,10 +4,12 @@ This script compares the offspring of the crossover operators in ``moocore`` with the offspring of the equivalent operators in other packages. -Each operator crosses over the same parents many times. For each decision -variable, a two-sample Kolmogorov-Smirnov test compares the offspring of each -package with those of ``moocore``. The bounds are wide enough that they never -bind, so the comparison does not depend on how each package handles them. +Each operator crosses over the same parents many times in each package. For +every pair of packages and every decision variable, a two-sample +Kolmogorov-Smirnov test compares their offspring. The script prints, and saves +to ``crossover_ks-.csv``, a matrix with the smallest p-value over the +variables for every pair of packages. The bounds are wide enough that they +never bind, so the comparison does not depend on how each package handles them. """ @@ -40,7 +42,7 @@ from pymoo.operators.crossover.pntx import SinglePointCrossover from pymoo.operators.crossover.ux import UniformCrossover -N = 20_000 +N = 100_000 LOWER, UPPER = -10.0, 10.0 # Two parents, and a population whose first row is the target. A = np.array([0.2, 0.7, 0.95]) @@ -302,44 +304,41 @@ def desdeo_pairs(cls, x, **kwargs): ), } -# Known differences from moocore. -notes = { - ("single_point", "desdeo"): "Binary variables only.", - ("blend_alpha", "deap"): "Two mirrored offspring per pair, no bounds.", - ("blend_alpha", "jMetalPy"): "Clips each sample instead of the interval.", - ( - "de_rand_1_bin", - "pymoo", - ): "Forces a mutant variable only when none was chosen, instead of a random one in every offspring.", - ( - "de_current_1", - "pymoo", - ): "Multiplies F by a random factor within 1 +/- 5e-5.", - ( - "de_current_1", - "jMetalPy", - ): "Forces a mutant variable, so it differs when CR < 1.", -} -print( - "| Operator | Package | Offspring | Smallest KS p-value " - "| Largest mean difference / sd | sd ratio | Notes |" -) -print("|---|---|---|---|---|---|---|") +def ks_matrix(samples): + """Smallest KS p-value over the variables, for every pair of packages.""" + names = list(samples) + p = np.full((len(names), len(names)), np.nan) + for i, a in enumerate(names): + for j, b in enumerate(names[i + 1 :], start=i + 1): + x, y = samples[a], samples[b] + p[i, j] = p[j, i] = min( + ks_2samp(x[:, k], y[:, k]).pvalue for k in range(x.shape[1]) + ) + return names, p + + +def fmt(p): + if np.isnan(p): + return "" + return "<0.001" if p < 0.001 else f"{p:.3f}" + + for op, (ours, others) in comparisons.items(): - ours = np.asarray(ours, dtype=float) - for package, theirs in others.items(): - theirs = np.asarray(theirs, dtype=float) - nvar = ours.shape[1] - pvalues = [ - ks_2samp(ours[:, j], theirs[:, j]).pvalue for j in range(nvar) - ] - sd = ours.std(axis=0) - sd = np.where(sd > 0, sd, 1) - mean_diff = np.abs(ours.mean(axis=0) - theirs.mean(axis=0)) / sd - sd_ratio = theirs.std(axis=0) / sd - print( - f"| {op} | {package} | {len(theirs)} | {min(pvalues):.3f} | " - f"{mean_diff.max():.3f} | {sd_ratio.min():.3f}-{sd_ratio.max():.3f} | " - f"{notes.get((op, package), '')} |" - ) + samples = {"moocore": np.asarray(ours, dtype=float)} + samples.update({k: np.asarray(v, dtype=float) for k, v in others.items()}) + names, p = ks_matrix(samples) + rows = [ + ["", *names], + *( + [a, *[fmt(p[i, j]) for j in range(len(names))]] + for i, a in enumerate(names) + ), + ] + with open(f"crossover_ks-{op}.csv", "w") as f: + for row in rows: + f.write(",".join(f'"{cell}"' for cell in row) + "\n") + print(f"# {op}") + for row in rows: + print(" | ".join(f"{cell:>8}" for cell in row)) + print() From 61718b3f0bcab5f3a88ffc1c89a65101a63a68dd Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Sat, 24 Oct 2026 15:55:29 +0300 Subject: [PATCH 25/30] python/doc/ Move the benchmarks to their own pages * python/doc/source/benchmarks.inc.rst: Split into ... * python/doc/source/benchmarks/index.rst: ... this, * python/doc/source/benchmarks/dominance.rst: ... this, * python/doc/source/benchmarks/indicators.rst: ... this, * python/doc/source/benchmarks/crossover/*.rst: ... and one page per crossover operator, with a matrix of KS test results. * python/doc/source/benchmarks-links.inc.rst: New. * python/doc/source/_static/bench/crossover_ks-*.csv: New. * python/doc/source/index.rst: Link to the benchmarks instead of including them. * python/doc/source/my_unused_images.py (check_unused_images): Also resolve image paths relative to the source directory. * python/benchmarks/README.md: Update the link to the benchmarks. --- python/benchmarks/README.md | 2 +- .../bench/crossover_ks-blend_alpha.csv | 5 + .../crossover_ks-bounded_exponential.csv | 3 + .../bench/crossover_ks-de_current_1.csv | 4 + .../bench/crossover_ks-de_rand_1_bin.csv | 5 + .../_static/bench/crossover_ks-local.csv | 3 + .../bench/crossover_ks-parent_centric.csv | 4 + .../bench/crossover_ks-single_arithmetic.csv | 3 + .../bench/crossover_ks-single_point.csv | 5 + .../_static/bench/crossover_ks-uniform.csv | 5 + python/doc/source/benchmarks-links.inc.rst | 22 ++ python/doc/source/benchmarks.inc.rst | 366 ------------------ .../benchmarks/crossover/blend_alpha.rst | 55 +++ .../crossover/bounded_exponential.rst | 38 ++ .../benchmarks/crossover/de_current_1.rst | 50 +++ .../benchmarks/crossover/de_rand_1_bin.rst | 48 +++ .../doc/source/benchmarks/crossover/index.rst | 44 +++ .../doc/source/benchmarks/crossover/local.rst | 38 ++ .../benchmarks/crossover/parent_centric.rst | 42 ++ .../crossover/single_arithmetic.rst | 36 ++ .../benchmarks/crossover/single_point.rst | 42 ++ .../source/benchmarks/crossover/uniform.rst | 41 ++ python/doc/source/benchmarks/dominance.rst | 117 ++++++ python/doc/source/benchmarks/index.rst | 47 +++ python/doc/source/benchmarks/indicators.rst | 114 ++++++ python/doc/source/index.rst | 4 +- python/doc/source/my_unused_images.py | 3 + 27 files changed, 778 insertions(+), 368 deletions(-) create mode 100644 python/doc/source/_static/bench/crossover_ks-blend_alpha.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-bounded_exponential.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-de_current_1.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-de_rand_1_bin.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-local.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-parent_centric.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-single_arithmetic.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-single_point.csv create mode 100644 python/doc/source/_static/bench/crossover_ks-uniform.csv create mode 100644 python/doc/source/benchmarks-links.inc.rst delete mode 100644 python/doc/source/benchmarks.inc.rst create mode 100644 python/doc/source/benchmarks/crossover/blend_alpha.rst create mode 100644 python/doc/source/benchmarks/crossover/bounded_exponential.rst create mode 100644 python/doc/source/benchmarks/crossover/de_current_1.rst create mode 100644 python/doc/source/benchmarks/crossover/de_rand_1_bin.rst create mode 100644 python/doc/source/benchmarks/crossover/index.rst create mode 100644 python/doc/source/benchmarks/crossover/local.rst create mode 100644 python/doc/source/benchmarks/crossover/parent_centric.rst create mode 100644 python/doc/source/benchmarks/crossover/single_arithmetic.rst create mode 100644 python/doc/source/benchmarks/crossover/single_point.rst create mode 100644 python/doc/source/benchmarks/crossover/uniform.rst create mode 100644 python/doc/source/benchmarks/dominance.rst create mode 100644 python/doc/source/benchmarks/index.rst create mode 100644 python/doc/source/benchmarks/indicators.rst diff --git a/python/benchmarks/README.md b/python/benchmarks/README.md index 002b7186c..b9e505b63 100644 --- a/python/benchmarks/README.md +++ b/python/benchmarks/README.md @@ -4,4 +4,4 @@ Install dependencies with: python3 -m pip install moocore[benchmarks] -Benchmark results: https://multi-objective.github.io/moocore/python/#benchmarks +Benchmark results: https://multi-objective.github.io/moocore/python/benchmarks/index.html diff --git a/python/doc/source/_static/bench/crossover_ks-blend_alpha.csv b/python/doc/source/_static/bench/crossover_ks-blend_alpha.csv new file mode 100644 index 000000000..72c43fdd4 --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-blend_alpha.csv @@ -0,0 +1,5 @@ +"","moocore","deap","jMetalPy","desdeo" +"moocore","","0.517","0.064","0.513" +"deap","0.517","","0.118","0.814" +"jMetalPy","0.064","0.118","","0.014" +"desdeo","0.513","0.814","0.014","" diff --git a/python/doc/source/_static/bench/crossover_ks-bounded_exponential.csv b/python/doc/source/_static/bench/crossover_ks-bounded_exponential.csv new file mode 100644 index 000000000..2f174e87c --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-bounded_exponential.csv @@ -0,0 +1,3 @@ +"","moocore","desdeo" +"moocore","","0.199" +"desdeo","0.199","" diff --git a/python/doc/source/_static/bench/crossover_ks-de_current_1.csv b/python/doc/source/_static/bench/crossover_ks-de_current_1.csv new file mode 100644 index 000000000..a5291d899 --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-de_current_1.csv @@ -0,0 +1,4 @@ +"","moocore","pymoo","jMetalPy" +"moocore","","<0.001","0.905" +"pymoo","<0.001","","<0.001" +"jMetalPy","0.905","<0.001","" diff --git a/python/doc/source/_static/bench/crossover_ks-de_rand_1_bin.csv b/python/doc/source/_static/bench/crossover_ks-de_rand_1_bin.csv new file mode 100644 index 000000000..6fd181c10 --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-de_rand_1_bin.csv @@ -0,0 +1,5 @@ +"","moocore","pymoo","jMetalPy","desdeo" +"moocore","","<0.001","0.275","0.786" +"pymoo","<0.001","","<0.001","<0.001" +"jMetalPy","0.275","<0.001","","0.549" +"desdeo","0.786","<0.001","0.549","" diff --git a/python/doc/source/_static/bench/crossover_ks-local.csv b/python/doc/source/_static/bench/crossover_ks-local.csv new file mode 100644 index 000000000..dadb780c2 --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-local.csv @@ -0,0 +1,3 @@ +"","moocore","desdeo" +"moocore","","0.496" +"desdeo","0.496","" diff --git a/python/doc/source/_static/bench/crossover_ks-parent_centric.csv b/python/doc/source/_static/bench/crossover_ks-parent_centric.csv new file mode 100644 index 000000000..b859f4f5e --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-parent_centric.csv @@ -0,0 +1,4 @@ +"","moocore","pymoo","desdeo" +"moocore","","0.233","0.736" +"pymoo","0.233","","0.343" +"desdeo","0.736","0.343","" diff --git a/python/doc/source/_static/bench/crossover_ks-single_arithmetic.csv b/python/doc/source/_static/bench/crossover_ks-single_arithmetic.csv new file mode 100644 index 000000000..1081baac3 --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-single_arithmetic.csv @@ -0,0 +1,3 @@ +"","moocore","desdeo" +"moocore","","0.999" +"desdeo","0.999","" diff --git a/python/doc/source/_static/bench/crossover_ks-single_point.csv b/python/doc/source/_static/bench/crossover_ks-single_point.csv new file mode 100644 index 000000000..4b6156d9d --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-single_point.csv @@ -0,0 +1,5 @@ +"","moocore","pymoo","deap","desdeo" +"moocore","","0.995","0.996","0.650" +"pymoo","0.995","","0.531","0.422" +"deap","0.996","0.531","","0.177" +"desdeo","0.650","0.422","0.177","" diff --git a/python/doc/source/_static/bench/crossover_ks-uniform.csv b/python/doc/source/_static/bench/crossover_ks-uniform.csv new file mode 100644 index 000000000..0cf2da533 --- /dev/null +++ b/python/doc/source/_static/bench/crossover_ks-uniform.csv @@ -0,0 +1,5 @@ +"","moocore","pymoo","deap","desdeo" +"moocore","","0.249","0.765","1.000" +"pymoo","0.249","","0.658","0.699" +"deap","0.765","0.658","","0.987" +"desdeo","1.000","0.699","0.987","" diff --git a/python/doc/source/benchmarks-links.inc.rst b/python/doc/source/benchmarks-links.inc.rst new file mode 100644 index 000000000..2b03a5714 --- /dev/null +++ b/python/doc/source/benchmarks-links.inc.rst @@ -0,0 +1,22 @@ +.. _BoFire: https://experimental-design.github.io/bofire/ +.. _BoTorch: https://botorch.org/ +.. _DEAP: https://deap.readthedocs.io/en/master/ +.. _DESDEO: https://desdeo.readthedocs.io/en/latest/ +.. _Nevergrad: https://facebookresearch.github.io/nevergrad/ +.. _Numba: https://numba.pydata.org/numba-doc/dev/index.html +.. _Optuna: https://optuna.org/ +.. _Xopt: https://xopt.xopt.org/index.html +.. _fast-pareto: https://github.com/nabenabe0928/fast-pareto +.. _jMetalPy: https://jmetal.github.io/jMetalPy/index.html +.. _dmosopt: https://dmosopt.github.io/dmosopt/ +.. _moarchiving: https://cma-es.github.io/moarchiving/ +.. _moocore: https://multi-objective.github.io/moocore/python/ +.. _paretobench: https://github.com/electronsandstuff/ParetoBench +.. _paretoset: https://github.com/tommyod/paretoset +.. _patatune: https://cms-patatrack.github.io/patatune/ +.. _platypus: https://github.com/Project-Platypus/Platypus +.. _pygmo: https://esa.github.io/pygmo2/ +.. _pymoo: https://pymoo.org/ +.. _pysamoo: https://anyoptimization.com/projects/pysamoo/ +.. _seqme: https://seqme.readthedocs.io +.. _trieste: https://secondmind-labs.github.io/trieste diff --git a/python/doc/source/benchmarks.inc.rst b/python/doc/source/benchmarks.inc.rst deleted file mode 100644 index 85d73f373..000000000 --- a/python/doc/source/benchmarks.inc.rst +++ /dev/null @@ -1,366 +0,0 @@ -Benchmarks -========== - -The following plots compare the performance of `moocore`_, `pymoo`_, `BoTorch`_, `DESDEO`_, `paretoset`_, `Nevergrad`_, `jMetalPy`_, `fast-pareto`_, `Optuna`_, `moarchiving`_, and `patatune`_. - -Other Python packages are not included in the comparison because they are based -on these packages for the functionality benchmarked, so they are **at least as -slow** as them. For example `Xopt`_ and `BoFire`_ use `BoTorch`_, `pysamoo`_ is -an extension of `pymoo`_. We do not include functions from the Bayesian -optimization toolbox `trieste`_, because it is much slower than `BoTorch`_ and -too slow to run the benchmarks in a reasonable time -(https://github.com/secondmind-labs/trieste/issues/917). Similarly, we do not -include `paretobench`_ because it is always slower than `BoTorch`_ for -identifying nondominated points and more than 2000 times slower than `moocore`_ -for computing the hypervolume in 3D -(https://github.com/electronsandstuff/ParetoBench/issues/57), which is too slow -to include in the benchmarks. - -Not all packages provide the same functionality. For example, `pymoo`_ does not -provide the :ref:`epsilon indicator `. `BoTorch`_ and -`paretobench`_ only provide the hypervolume. `paretoset`_ and `fast-pareto`_ -only identify nondominated points. `DESDEO`_, `DEAP`_, and `jMetalPy`_ use -`moocore`_ for computing the hypervolume, but other functionality, such as -filtering dominated points, is still slower than `moocore`_. Recent versions -of `seqme`_ and `pymoo`_ (≥0.6.2) already use `moocore`_ for most functionality -benchmarked here. - -We would like to benchmark `pygmo`_, however, it is currently impossible to install using ``pip`` (See https://github.com/esa/pygmo2/issues/152). - -We would also like to benchmark `platypus`_, but its API is too different from -other packages. For example, it only supports filtering dominated points by -creating a new list of points, but it cannot identify their position in the -input. It cannot calculate hypervolume without normalization. It doesn't -support :obj:`~numpy.typing.ArrayLike` inputs. - -The source code for the benchmarks below can be found at https://github.com/multi-objective/moocore/tree/main/python/benchmarks . - -.. _bench-ndom: - -Identifying nondominated points -------------------------------- - -The following plots compare the speed of finding nondominated solutions, equivalent to :func:`moocore.is_nondominated`. We test both ``keep_weakly=False`` (the default) and ``keep_weakly=True``. The former is only supported by `BoTorch`_ and `paretoset`_. Thus, for the purpose of benchmarking the other packages with ``keep_weakly=False``, we remove duplicated points from the data and exclude this time from the results. This makes all packages, except `moocore`_, `BoTorch`_ and `paretoset`_, seem faster than they actually are, because the user is forced to remove duplicated points when using them. - -For 2D and 3D, the plots show that `moocore`_ is 10 times faster than `DESDEO`_ and `paretoset`_ and 100-1000 times faster than the other packages. `fast-pareto`_ claims to implement a :math:`O(n\log n)` algorithm for 3D, but the benchmarks below indicate a :math:`O(n^2)` complexity, similar to other packages and significantly slower than `moocore`_. - -|ndom_bench-test2D-200k| |ndom_bench-ran3d-40k| - -.. |ndom_bench-test2D-200k| image:: _static/bench/ndom_bench-test2D-200k-time.png - :width: 49% - -.. |ndom_bench-ran3d-40k| image:: _static/bench/ndom_bench-ran3d-40k-time.png - :width: 49% - -|wndom_bench-test2D-200k| |wndom_bench-ran3d-40k| - -.. |wndom_bench-test2D-200k| image:: _static/bench/wndom_bench-test2D-200k-time.png - :width: 49% - -.. |wndom_bench-ran3d-40k| image:: _static/bench/wndom_bench-ran3d-40k-time.png - :width: 49% - - -For dimensions larger than 3, :func:`moocore.is_nondominated` uses the -best-known :math:`O(n\log^{m-2} n)` algorithm. `fast-pareto`_ claims to be -using a :math:`O(n\log^{m-2} n)` algorithm, but the benchmarks suggest that it -uses a :math:`O(m n^2)` algorithm, although slower than most other packages and -almost 100 times slower than `moocore`_. The following plots with -``keep_weakly=True`` show that `moocore`_ is at least 10 times faster than the -other packages, even for 10D. - -|wndom_bench-sphere-4d| |wndom_bench-convex-4d| - -|wndom_bench-sphere-5d| |wndom_bench-rmnk-10d| - -.. |wndom_bench-sphere-4d| image:: _static/bench/wndom_bench-sphere-4d-time.png - :width: 49% - -.. |wndom_bench-convex-4d| image:: _static/bench/wndom_bench-convex-4d-time.png - :width: 49% - -.. |wndom_bench-sphere-5d| image:: _static/bench/wndom_bench-sphere-5d-time.png - :width: 49% - -.. |wndom_bench-rmnk-10d| image:: _static/bench/wndom_bench-rmnk-10d-time.png - :width: 49% - - -Similar results are obtained with ``keep_weakly=False``, however, this setting -is only supported by `moocore`_, `BoTorch`_ and `paretoset`_, thus the other -packages are actually slower to use than reported here, because the user is -forced to remove duplicated points when using them. - -|ndom_bench-sphere-4d| |ndom_bench-convex-4d| - -|ndom_bench-sphere-5d| |ndom_bench-rmnk-10d| - -.. |ndom_bench-sphere-4d| image:: _static/bench/ndom_bench-sphere-4d-time.png - :width: 49% - -.. |ndom_bench-convex-4d| image:: _static/bench/ndom_bench-convex-4d-time.png - :width: 49% - -.. |ndom_bench-sphere-5d| image:: _static/bench/ndom_bench-sphere-5d-time.png - :width: 49% - -.. |ndom_bench-rmnk-10d| image:: _static/bench/ndom_bench-rmnk-10d-time.png - :width: 49% - - -.. _bench-ndsort: - -Nondominated Sorting (Pareto ranking) -------------------------------------- - -Nondominated sorting (or Pareto ranking) assigns a rank to each point according -to Pareto-optimality. It can be used to split a set of points into layers of -nondominated fronts. For more details, see :func:`moocore.pareto_rank`. This -function in `moocore`_ uses a :math:`O(n \log n)` algorithm for 2 dimensions -and a :math:`O(n^2\log n)` algorithm for 3 dimensions. As the plots show, this -makes `moocore`_ significantly faster than `paretoset`_, `pymoo`_ and -`DESDEO`_. With higher dimensions, `moocore`_ uses a :math:`O(n^2\log^{m-2}n)` -algorithm instead of the :math:`O(n^3)` algorithm in `paretoset`_ and `DESDEO`_ -(latter is compiled with `Numba`_). In these benchmarks points are sampled -uniformly at random within the hypercube. - -|ndsort_bench-ran-2d| |ndsort_bench-ran-3d| - -|ndsort_bench-ran-4d| |ndsort_bench-ran-5d| - -|ndsort_bench-ran-9d| |ndsort_bench-ran-10d| - -.. |ndsort_bench-ran-2d| image:: _static/bench/ndsort_bench-ran-2d-time.png - :width: 49% - -.. |ndsort_bench-ran-3d| image:: _static/bench/ndsort_bench-ran-3d-time.png - :width: 49% - -.. |ndsort_bench-ran-4d| image:: _static/bench/ndsort_bench-ran-4d-time.png - :width: 49% - -.. |ndsort_bench-ran-5d| image:: _static/bench/ndsort_bench-ran-5d-time.png - :width: 49% - -.. |ndsort_bench-ran-9d| image:: _static/bench/ndsort_bench-ran-9d-time.png - :width: 49% - -.. |ndsort_bench-ran-10d| image:: _static/bench/ndsort_bench-ran-10d-time.png - :width: 49% - - -.. _bench-hv: - -Exact computation of hypervolume --------------------------------- - -The following plots compare the speed of computing the :ref:`hypervolume indicator ` in 3D, 4D, 5D and 6D. As the plots show, `moocore`_ is 100 times faster than the other packages and 1000 times faster than `BoTorch`_ and, by extension, `Xopt`_ and `BoFire`_. - -For 3D, `Optuna`_ uses a :math:`O(n^2)` algorithm, while `moocore`_ uses the best-known :math:`O(n\log n)` one, so the gap between the two will get significantly larger with a larger number of points than those tested here. `moarchiving`_ uses the same algorithms as `moocore`_ for 3D and 4D, but a pure Python implementation, so it is still 10-100 times slower than `moocore`_'s C implementation. `BoTorch`_ and `fast-pareto`_ are not included for more than 3 objectives because **they are tens of thousands of times slower** than `moocore`_. - -Recent versions of `DESDEO`_, `DEAP`_ (≥1.4.4), `pymoo`_ (≥0.6.1.6) and `jMetalPy`_ (≥1.9.0) already use `moocore`_ for hypervolume computation. -The implementation in `patatune`_ appears to be wrong (https://github.com/cms-patatrack/patatune/issues/52). - -|hv_bench-DTLZLinearShape-3d| |hv_bench-DTLZLinearShape-4d| - -|hv_bench-DTLZLinearShape-5d| |hv_bench-DTLZLinearShape-6d| - -.. |hv_bench-DTLZLinearShape-3d| image:: _static/bench/hv_bench-DTLZLinearShape.3d-time.png - :width: 49% - -.. |hv_bench-DTLZLinearShape-4d| image:: _static/bench/hv_bench-DTLZLinearShape.4d-time.png - :width: 49% - -.. |hv_bench-DTLZLinearShape-5d| image:: _static/bench/hv_bench-DTLZLinearShape.5d-time.png - :width: 49% - -.. |hv_bench-DTLZLinearShape-6d| image:: _static/bench/hv_bench-DTLZLinearShape.6d-time.png - :width: 49% - -.. _bench-hvapprox: - -Approximation of the hypervolume --------------------------------- - -The following plots compare the accuracy and speed of approximating the -hypervolume with the various methods provided by :func:`moocore.hv_approx`. The -plots show that there is no clear winner, in terms of approximation error, -between methods ``Rphi-FWE+`` (default) and ``DZ2019-HW``, but both produce -consistently lower approximation errors than method ``DZ2019-MC``. However, ``Rphi-FWE+`` is as fast as ``DZ2019-MC`` and both are consistently faster than ``DZ2019-HW``, in particular with higher number of objectives. - -The exact computation of the hypervolume for less than 5D takes milliseconds -for thousands of points, whereas approximating the hypervolume is significantly -slower and, thus, not worth doing. - -Approximating the hypervolume becomes more useful for dimensions higher than 5, -where the exact computation becomes noticeably slower with hundreds of points. -For such problems, method ``DZ2019-HW`` becomes significantly slower than -``Rphi-FWE+``. - -|hvapprox_bench-DTLZLinearShape-6d-values| |hvapprox_bench-DTLZLinearShape-6d-time| - -|hvapprox_bench-DTLZSphereShape-6d-values| |hvapprox_bench-DTLZSphereShape-6d-time| - -|hvapprox_bench-ran-6d-values| |hvapprox_bench-ran-6d-time| - -|hvapprox_bench-DTLZLinearShape-9d-values| |hvapprox_bench-DTLZLinearShape-9d-time| - -|hvapprox_bench-ran-9d-values| |hvapprox_bench-ran-9d-time| - -|hvapprox_bench-DTLZSphereShape-10d-values| |hvapprox_bench-DTLZSphereShape-10d-time| - -.. |hvapprox_bench-DTLZSphereShape-6d-values| image:: _static/bench/hvapprox_bench-DTLZSphereShape.6d-values.png - :width: 49% - -.. |hvapprox_bench-DTLZSphereShape-6d-time| image:: _static/bench/hvapprox_bench-DTLZSphereShape.6d-time.png - :width: 49% - -.. |hvapprox_bench-DTLZLinearShape-6d-values| image:: _static/bench/hvapprox_bench-DTLZLinearShape.6d-values.png - :width: 49% - -.. |hvapprox_bench-DTLZLinearShape-6d-time| image:: _static/bench/hvapprox_bench-DTLZLinearShape.6d-time.png - :width: 49% - -.. |hvapprox_bench-ran-6d-values| image:: _static/bench/hvapprox_bench-ran.6d-values.png - :width: 49% - -.. |hvapprox_bench-ran-6d-time| image:: _static/bench/hvapprox_bench-ran.6d-time.png - :width: 49% - -.. |hvapprox_bench-DTLZLinearShape-9d-values| image:: _static/bench/hvapprox_bench-DTLZLinearShape.9d-values.png - :width: 49% - -.. |hvapprox_bench-DTLZLinearShape-9d-time| image:: _static/bench/hvapprox_bench-DTLZLinearShape.9d-time.png - :width: 49% - -.. |hvapprox_bench-ran-9d-values| image:: _static/bench/hvapprox_bench-ran.9d-values.png - :width: 49% - -.. |hvapprox_bench-ran-9d-time| image:: _static/bench/hvapprox_bench-ran.9d-time.png - :width: 49% - -.. |hvapprox_bench-DTLZSphereShape-10d-values| image:: _static/bench/hvapprox_bench-DTLZSphereShape.10d-values.png - :width: 49% - -.. |hvapprox_bench-DTLZSphereShape-10d-time| image:: _static/bench/hvapprox_bench-DTLZSphereShape.10d-time.png - :width: 49% - - -Epsilon and IGD+ indicators ---------------------------- - -The following plots benchmark the speed of computing the :ref:`epsilon indicator ` metric and :ref:`IGD+ indicator `. Although the algorithms for computing these metrics are relatively simple and easy to vectorize in Python, the `moocore`_ implementation is still 10 to 100 times faster. - -|fig_eps_bench| |fig_igd_plus_bench| - -.. |fig_eps_bench| image:: _static/bench/eps_bench-rmnk_10D_random_search-time.png - :width: 48% - -.. |fig_igd_plus_bench| image:: _static/bench/igd_plus_bench-ran.1000pts.3d-time.png - :width: 48% - - - -Crossover operators -------------------- - -The following plots compare the :ref:`crossover operators ` of `moocore`_ with the equivalent operators of `pymoo`_, `DEAP`_, `jMetalPy`_ and `DESDEO`_, when they exist. Each operator is timed for an increasing number of parents with 30 variables (left), and for an increasing number of variables with 100 parents (right). Each package receives the parents in its own data structure, which is created before the timing starts. When a package expects the caller to choose the other parents of DE or PCX, choosing them is part of the time. :func:`~moocore.blend_alpha_crossover` produces one offspring per pair, so it is called twice to produce as many offspring as the other packages. Single arithmetic, local and bounded exponential crossover are only available in `moocore`_ and `DESDEO`_. - -The script ``compare_crossover.py`` in the same folder compares the offspring of each operator with the offspring of the equivalent operators in the other packages. The distributions agree, except where the operators differ by design. The DE/rand/1/bin operator of `pymoo`_ forces a variable to come from the mutant only when no variable was chosen, instead of forcing a random variable in every offspring. The ``DEX`` operator of `pymoo`_, which matches DE/current/1, multiplies the scaling factor by a random factor within :math:`1 \pm 5 \cdot 10^{-5}`. - -|xover_uniform_parents| |xover_uniform_vars| - -.. |xover_uniform_parents| image:: _static/bench/crossover_bench-uniform-nparents-time.png - :width: 48% - -.. |xover_uniform_vars| image:: _static/bench/crossover_bench-uniform-nvars-time.png - :width: 48% - -|xover_single_point_parents| |xover_single_point_vars| - -.. |xover_single_point_parents| image:: _static/bench/crossover_bench-single_point-nparents-time.png - :width: 48% - -.. |xover_single_point_vars| image:: _static/bench/crossover_bench-single_point-nvars-time.png - :width: 48% - -|xover_blend_alpha_parents| |xover_blend_alpha_vars| - -.. |xover_blend_alpha_parents| image:: _static/bench/crossover_bench-blend_alpha-nparents-time.png - :width: 48% - -.. |xover_blend_alpha_vars| image:: _static/bench/crossover_bench-blend_alpha-nvars-time.png - :width: 48% - -|xover_single_arithmetic_parents| |xover_single_arithmetic_vars| - -.. |xover_single_arithmetic_parents| image:: _static/bench/crossover_bench-single_arithmetic-nparents-time.png - :width: 48% - -.. |xover_single_arithmetic_vars| image:: _static/bench/crossover_bench-single_arithmetic-nvars-time.png - :width: 48% - -|xover_local_parents| |xover_local_vars| - -.. |xover_local_parents| image:: _static/bench/crossover_bench-local-nparents-time.png - :width: 48% - -.. |xover_local_vars| image:: _static/bench/crossover_bench-local-nvars-time.png - :width: 48% - -|xover_bounded_exponential_parents| |xover_bounded_exponential_vars| - -.. |xover_bounded_exponential_parents| image:: _static/bench/crossover_bench-bounded_exponential-nparents-time.png - :width: 48% - -.. |xover_bounded_exponential_vars| image:: _static/bench/crossover_bench-bounded_exponential-nvars-time.png - :width: 48% - -|xover_de_rand_1_bin_parents| |xover_de_rand_1_bin_vars| - -.. |xover_de_rand_1_bin_parents| image:: _static/bench/crossover_bench-de_rand_1_bin-nparents-time.png - :width: 48% - -.. |xover_de_rand_1_bin_vars| image:: _static/bench/crossover_bench-de_rand_1_bin-nvars-time.png - :width: 48% - -|xover_de_current_1_parents| |xover_de_current_1_vars| - -.. |xover_de_current_1_parents| image:: _static/bench/crossover_bench-de_current_1-nparents-time.png - :width: 48% - -.. |xover_de_current_1_vars| image:: _static/bench/crossover_bench-de_current_1-nvars-time.png - :width: 48% - -|xover_parent_centric_parents| |xover_parent_centric_vars| - -.. |xover_parent_centric_parents| image:: _static/bench/crossover_bench-parent_centric-nparents-time.png - :width: 48% - -.. |xover_parent_centric_vars| image:: _static/bench/crossover_bench-parent_centric-nvars-time.png - :width: 48% - - - -.. _BoFire: https://experimental-design.github.io/bofire/ -.. _BoTorch: https://botorch.org/ -.. _DEAP: https://deap.readthedocs.io/en/master/ -.. _DESDEO: https://desdeo.readthedocs.io/en/latest/ -.. _Nevergrad: https://facebookresearch.github.io/nevergrad/ -.. _Numba: https://numba.pydata.org/numba-doc/dev/index.html -.. _Optuna: https://optuna.org/ -.. _Xopt: https://xopt.xopt.org/index.html -.. _fast-pareto: https://github.com/nabenabe0928/fast-pareto -.. _jMetalPy: https://jmetal.github.io/jMetalPy/index.html -.. _dmosopt: https://dmosopt.github.io/dmosopt/ -.. _moarchiving: https://cma-es.github.io/moarchiving/ -.. _moocore: https://multi-objective.github.io/moocore/python/ -.. _paretobench: https://github.com/electronsandstuff/ParetoBench -.. _paretoset: https://github.com/tommyod/paretoset -.. _patatune: https://cms-patatrack.github.io/patatune/ -.. _platypus: https://github.com/Project-Platypus/Platypus -.. _pygmo: https://esa.github.io/pygmo2/ -.. _pymoo: https://pymoo.org/ -.. _pysamoo: https://anyoptimization.com/projects/pysamoo/ -.. _seqme: https://seqme.readthedocs.io -.. _trieste: https://secondmind-labs.github.io/trieste diff --git a/python/doc/source/benchmarks/crossover/blend_alpha.rst b/python/doc/source/benchmarks/crossover/blend_alpha.rst new file mode 100644 index 000000000..756dcb0ac --- /dev/null +++ b/python/doc/source/benchmarks/crossover/blend_alpha.rst @@ -0,0 +1,55 @@ +.. _bench-crossover-blend-alpha: + +Blend crossover (BLX-α) +======================= + +:func:`~moocore.blend_alpha_crossover` samples each variable of the offspring +uniformly from the interval between the parents, widened on each side by +``alpha`` times its length. `DEAP`_ (``cxBlend``), `jMetalPy`_ +(``BLXAlphaCrossover``) and `DESDEO`_ (``BlendAlphaCrossover``) provide it. + +`moocore`_ produces one offspring per pair of parents, and the other packages +produce two. The two offspring of `DEAP`_ mirror each other, so the KS tests +use the first offspring of each pair from `DEAP`_ and `jMetalPy`_, and every +offspring from `DESDEO`_, whose offspring are independent. The timings call +`moocore`_ twice, so that every package produces the same number of offspring. + +The packages handle bounds differently. `moocore`_ and `DESDEO`_ clip the +sampling interval to the bounds, `jMetalPy`_ clips each sampled value, and +`DEAP`_ ignores the bounds. The KS tests use bounds that never bind. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-blend_alpha.csv + :header-rows: 1 + :stub-columns: 1 + +All implementations produce the same distribution of offspring. The p-value of +0.014 between `jMetalPy`_ and `DESDEO`_ is one of the low values expected by +chance: with two other random seeds, it was 0.07 and 0.31. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-blend_alpha-nparents-time.png + :width: 80% + +With 10 parents, `DEAP`_ is faster than the two calls to `moocore`_. From 20 +parents on, `moocore`_ is the fastest. With 10 000 parents, it takes 2.1 ms, +while `DEAP`_, `DESDEO`_ and `jMetalPy`_ take 7.8, 15 and 51 times as long. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-blend_alpha-nvars-time.png + :width: 80% + +With 2 variables, `DEAP`_ is faster than `moocore`_. With more variables, +`moocore`_ is the fastest. With 1000 variables, `DEAP`_, `DESDEO`_ and +`jMetalPy`_ take 6.8, 8.1 and 170 times as long. The time of `jMetalPy`_ grows +much faster than linearly with the number of variables, because its solutions +copy their list of variables on every access. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/bounded_exponential.rst b/python/doc/source/benchmarks/crossover/bounded_exponential.rst new file mode 100644 index 000000000..ce5ce033b --- /dev/null +++ b/python/doc/source/benchmarks/crossover/bounded_exponential.rst @@ -0,0 +1,38 @@ +.. _bench-crossover-bounded-exponential: + +Bounded exponential crossover (BEX) +=================================== + +:func:`~moocore.bounded_exponential_crossover` moves each offspring away from +its parent by a random step that follows an exponential distribution truncated +at the bounds. Only `DESDEO`_ (``BoundedExponentialCrossover``) provides this +operator. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-bounded_exponential.csv + :header-rows: 1 + :stub-columns: 1 + +Both implementations produce the same distribution of offspring. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-bounded_exponential-nparents-time.png + :width: 80% + +`DESDEO`_ takes 20 times as long as `moocore`_ with 10 parents, and 1.2 times +as long with 10 000 parents. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-bounded_exponential-nvars-time.png + :width: 80% + +`DESDEO`_ takes 3.7 to 15 times as long as `moocore`_. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/de_current_1.rst b/python/doc/source/benchmarks/crossover/de_current_1.rst new file mode 100644 index 000000000..b22cc4b0f --- /dev/null +++ b/python/doc/source/benchmarks/crossover/de_current_1.rst @@ -0,0 +1,50 @@ +.. _bench-crossover-de-current-1: + +Differential evolution: DE/current/1 +==================================== + +:func:`~moocore.de_current_1_crossover` adds a scaled difference of two random +members of the population to the target, as in MOEA/D-DE. `pymoo`_ provides +it as ``DEX`` with ``at_least_once=False``, when the target is given as the +first parent. `jMetalPy`_ provides it through the order of the parents of +``DifferentialEvolutionCrossover``, as its MOEA/D does. `jMetalPy`_ always +takes one random variable from the mutant, so it equals this operator only +with :math:`CR = 1`, which is the default. The version of `DESDEO`_ on PyPI +does not provide this operator. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-de_current_1.csv + :header-rows: 1 + :stub-columns: 1 + +`moocore`_ and `jMetalPy`_ produce the same distribution of offspring. +`pymoo`_ multiplies the scaling factor by a random factor within :math:`1 \pm +5 \cdot 10^{-5}`, so its offspring are within :math:`2 \cdot 10^{-5}` of the +values that the other packages produce, but never equal to them. The KS test +detects this. After rounding the offspring to three decimals, the p-values +between `moocore`_ and `pymoo`_ are 0.43, 0.59 and 0.98 for the three +variables. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-de_current_1-nparents-time.png + :width: 80% + +`moocore`_ is the fastest for every number of parents. With 10 000 parents, +it takes 1.2 ms, while `pymoo`_ and `jMetalPy`_ take 33 and 230 times as +long. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-de_current_1-nvars-time.png + :width: 80% + +`moocore`_ is the fastest for every number of variables. With 1000 variables, +`pymoo`_ and `jMetalPy`_ take 2.7 and 950 times as long. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/de_rand_1_bin.rst b/python/doc/source/benchmarks/crossover/de_rand_1_bin.rst new file mode 100644 index 000000000..20b9f8bc2 --- /dev/null +++ b/python/doc/source/benchmarks/crossover/de_rand_1_bin.rst @@ -0,0 +1,48 @@ +.. _bench-crossover-de-rand-1-bin: + +Differential evolution: DE/rand/1/bin +===================================== + +:func:`~moocore.de_rand_1_bin_crossover` adds a scaled difference of two random +members of the population to a third one, and takes each variable of the +offspring from this mutant or from the target. One random variable always +comes from the mutant. `pymoo`_ (``VariantDE``), `jMetalPy`_ +(``DifferentialEvolutionCrossover``) and `DESDEO`_ +(``DifferentialEvolutionCrossover``) provide this operator. `pymoo`_ forces a +variable to come from the mutant only when no variable was chosen, instead of +forcing a random variable in every offspring. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-de_rand_1_bin.csv + :header-rows: 1 + :stub-columns: 1 + +`moocore`_, `jMetalPy`_ and `DESDEO`_ produce the same distribution of +offspring. `pymoo`_ differs from all three because of its rule for the +forced variable. With 3 variables and :math:`CR = 0.9`, it keeps the value of +the target in 13% to 14% of the variables, against 9% to 11% in the other +packages. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-de_rand_1_bin-nparents-time.png + :width: 80% + +`moocore`_ is the fastest for every number of parents. With 10 000 parents, +it takes 1.9 ms, while `DESDEO`_, `pymoo`_ and `jMetalPy`_ take 2.2, 17 and 140 +times as long. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-de_rand_1_bin-nvars-time.png + :width: 80% + +`moocore`_ is the fastest for every number of variables. With 1000 variables, +`pymoo`_, `DESDEO`_ and `jMetalPy`_ take 2.6, 6.5 and 550 times as long. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/index.rst b/python/doc/source/benchmarks/crossover/index.rst new file mode 100644 index 000000000..780913c9d --- /dev/null +++ b/python/doc/source/benchmarks/crossover/index.rst @@ -0,0 +1,44 @@ +.. _bench-crossover: + +Crossover operators +=================== + +These pages compare the :ref:`crossover operators ` of +`moocore`_ with the equivalent operators of `pymoo`_, `DEAP`_, `jMetalPy`_ and +`DESDEO`_, when they exist. Each page compares the offspring that the packages +produce and the time they take. + +The KS test results show whether two packages produce offspring with the same +distribution. Each package crosses over the same parents 100 000 times, with +bounds wide enough that they never bind, so the results do not depend on how +each package handles bounds. For every pair of packages and every decision +variable, a two-sample Kolmogorov-Smirnov test compares their offspring. Each +table shows the smallest p-value over the variables. A p-value below 0.001 +means that the distributions differ. Among this many tests, a few p-values +between 0.001 and 0.05 are expected even when the distributions are equal. +Rerunning with other random seeds moves those values, whereas real differences +stay below 0.001. + +The performance plots time each operator for an increasing number of parents +with 30 variables, and for an increasing number of variables with 100 parents. +Each package receives the parents in its own data structure, which is created +before the timing starts. When a package expects the caller to choose the +other parents of DE or PCX, choosing them is part of the time. + +The scripts ``compare_crossover.py`` and ``bench_crossover.py`` produce the +tables and the plots. + +.. toctree:: + :maxdepth: 1 + + uniform + single_point + blend_alpha + single_arithmetic + local + bounded_exponential + de_rand_1_bin + de_current_1 + parent_centric + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/local.rst b/python/doc/source/benchmarks/crossover/local.rst new file mode 100644 index 000000000..16674bd1b --- /dev/null +++ b/python/doc/source/benchmarks/crossover/local.rst @@ -0,0 +1,38 @@ +.. _bench-crossover-local: + +Local crossover +=============== + +:func:`~moocore.local_crossover` draws a random weight for each variable and +sets the two offspring to the two weighted averages of the parents. Only +`DESDEO`_ (``LocalCrossover``) provides this operator. The +``ArithmeticCrossover`` of `jMetalPy`_ draws one weight for all the variables, +so it is a different operator. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-local.csv + :header-rows: 1 + :stub-columns: 1 + +Both implementations produce the same distribution of offspring. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-local-nparents-time.png + :width: 80% + +`DESDEO`_ takes 39 to 70 times as long as `moocore`_. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-local-nvars-time.png + :width: 80% + +`DESDEO`_ takes 28 to 71 times as long as `moocore`_. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/parent_centric.rst b/python/doc/source/benchmarks/crossover/parent_centric.rst new file mode 100644 index 000000000..01a239c4c --- /dev/null +++ b/python/doc/source/benchmarks/crossover/parent_centric.rst @@ -0,0 +1,42 @@ +.. _bench-crossover-parent-centric: + +Parent-centric crossover (PCX) +============================== + +:func:`~moocore.parent_centric_crossover` creates an offspring around each +target, from two more parents chosen at random. `pymoo`_ (``PCX``) and +`DESDEO`_ (``ParentCentricCrossover``) provide the same operator. `pymoo`_ +replaces values outside the bounds by random values, while `moocore`_ and +`DESDEO`_ clip them. The KS tests use bounds that never bind. The PCX of +`platypus`_ keeps the offspring in the plane of the three parents and has half +the spread, so it is a different operator. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-parent_centric.csv + :header-rows: 1 + :stub-columns: 1 + +All implementations produce the same distribution of offspring. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-parent_centric-nparents-time.png + :width: 80% + +`moocore`_ is the fastest for every number of parents. With 10 000 parents, +it takes 4.0 ms, while `DESDEO`_ and `pymoo`_ take 3.7 and 12 times as long. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-parent_centric-nvars-time.png + :width: 80% + +`moocore`_ is the fastest for every number of variables. With 1000 variables, +`pymoo`_ and `DESDEO`_ take 2.1 and 3.8 times as long. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/single_arithmetic.rst b/python/doc/source/benchmarks/crossover/single_arithmetic.rst new file mode 100644 index 000000000..0fdcd44b8 --- /dev/null +++ b/python/doc/source/benchmarks/crossover/single_arithmetic.rst @@ -0,0 +1,36 @@ +.. _bench-crossover-single-arithmetic: + +Single arithmetic crossover +=========================== + +:func:`~moocore.single_arithmetic_crossover` sets one random variable of both +offspring to the average of the parents and copies the other variables. Only +`DESDEO`_ (``SingleArithmeticCrossover``) provides this operator. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-single_arithmetic.csv + :header-rows: 1 + :stub-columns: 1 + +Both implementations produce the same distribution of offspring. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-single_arithmetic-nparents-time.png + :width: 80% + +`DESDEO`_ takes 16 to 69 times as long as `moocore`_. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-single_arithmetic-nvars-time.png + :width: 80% + +`DESDEO`_ takes 31 to 164 times as long as `moocore`_. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/single_point.rst b/python/doc/source/benchmarks/crossover/single_point.rst new file mode 100644 index 000000000..bb1466006 --- /dev/null +++ b/python/doc/source/benchmarks/crossover/single_point.rst @@ -0,0 +1,42 @@ +.. _bench-crossover-single-point: + +Single-point crossover +====================== + +:func:`~moocore.single_point_crossover` draws a cut point and exchanges the +tails of the two parents. `pymoo`_ (``SinglePointCrossover``), `DEAP`_ +(``cxOnePoint``) and `DESDEO`_ (``SinglePointBinaryCrossover``) provide the +same operator. The operator of `DESDEO`_ only accepts binary variables, so all +packages cross over binary parents here: a parent of zeros and a parent of ones +in the KS tests, and random binary parents in the timings. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-single_point.csv + :header-rows: 1 + :stub-columns: 1 + +All implementations produce the same distribution of offspring. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-single_point-nparents-time.png + :width: 80% + +With 10 and 20 parents, `DEAP`_ is faster than `moocore`_. From 50 parents +on, `moocore`_ is the fastest. With 10 000 parents, it takes 0.14 ms, while +`DESDEO`_, `DEAP`_ and `pymoo`_ take 9.8, 18 and 270 times as long. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-single_point-nvars-time.png + :width: 80% + +`moocore`_ is the fastest for every number of variables. `DEAP`_ takes 2.5 to +5 times as long, and `pymoo`_ and `DESDEO`_ take 24 to 144 times as long. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/uniform.rst b/python/doc/source/benchmarks/crossover/uniform.rst new file mode 100644 index 000000000..145137bd6 --- /dev/null +++ b/python/doc/source/benchmarks/crossover/uniform.rst @@ -0,0 +1,41 @@ +.. _bench-crossover-uniform: + +Uniform crossover +================= + +:func:`~moocore.uniform_crossover` swaps each variable between the two +offspring with probability ``swap_prob``, which is 0.5 by default. `pymoo`_ +(``UniformCrossover``), `DEAP`_ (``cxUniform``) and `DESDEO`_ +(``UniformCrossover``) provide the same operator. + +KS test results +--------------- + +.. csv-table:: + :file: /_static/bench/crossover_ks-uniform.csv + :header-rows: 1 + :stub-columns: 1 + +All implementations produce the same distribution of offspring. + +Performance over number of parents +---------------------------------- + +.. image:: /_static/bench/crossover_bench-uniform-nparents-time.png + :width: 80% + +With 10 parents, the Python loop of `DEAP`_ over five pairs takes less time +than the fixed cost of a call to `moocore`_. From 20 parents on, `moocore`_ is +the fastest. With 10 000 parents, it takes 1.4 ms, while `DESDEO`_, `DEAP`_ +and `pymoo`_ take 1.7, 4.4 and 20 times as long. + +Performance over number of variables +------------------------------------ + +.. image:: /_static/bench/crossover_bench-uniform-nvars-time.png + :width: 80% + +`moocore`_ is the fastest for every number of variables. With 1000 variables, +`pymoo`_, `DEAP`_ and `DESDEO`_ take 2.0, 3.9 and 7.4 times as long. + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/dominance.rst b/python/doc/source/benchmarks/dominance.rst new file mode 100644 index 000000000..2041e4329 --- /dev/null +++ b/python/doc/source/benchmarks/dominance.rst @@ -0,0 +1,117 @@ +Nondominated points and sorting +=============================== + +.. _bench-ndom: + +Identifying nondominated points +------------------------------- + +The following plots compare the speed of finding nondominated solutions, equivalent to :func:`moocore.is_nondominated`. We test both ``keep_weakly=False`` (the default) and ``keep_weakly=True``. The former is only supported by `BoTorch`_ and `paretoset`_. Thus, for the purpose of benchmarking the other packages with ``keep_weakly=False``, we remove duplicated points from the data and exclude this time from the results. This makes all packages, except `moocore`_, `BoTorch`_ and `paretoset`_, seem faster than they actually are, because the user is forced to remove duplicated points when using them. + +For 2D and 3D, the plots show that `moocore`_ is 10 times faster than `DESDEO`_ and `paretoset`_ and 100-1000 times faster than the other packages. `fast-pareto`_ claims to implement a :math:`O(n\log n)` algorithm for 3D, but the benchmarks below indicate a :math:`O(n^2)` complexity, similar to other packages and significantly slower than `moocore`_. + +|ndom_bench-test2D-200k| |ndom_bench-ran3d-40k| + +.. |ndom_bench-test2D-200k| image:: /_static/bench/ndom_bench-test2D-200k-time.png + :width: 49% + +.. |ndom_bench-ran3d-40k| image:: /_static/bench/ndom_bench-ran3d-40k-time.png + :width: 49% + +|wndom_bench-test2D-200k| |wndom_bench-ran3d-40k| + +.. |wndom_bench-test2D-200k| image:: /_static/bench/wndom_bench-test2D-200k-time.png + :width: 49% + +.. |wndom_bench-ran3d-40k| image:: /_static/bench/wndom_bench-ran3d-40k-time.png + :width: 49% + + +For dimensions larger than 3, :func:`moocore.is_nondominated` uses the +best-known :math:`O(n\log^{m-2} n)` algorithm. `fast-pareto`_ claims to be +using a :math:`O(n\log^{m-2} n)` algorithm, but the benchmarks suggest that it +uses a :math:`O(m n^2)` algorithm, although slower than most other packages and +almost 100 times slower than `moocore`_. The following plots with +``keep_weakly=True`` show that `moocore`_ is at least 10 times faster than the +other packages, even for 10D. + +|wndom_bench-sphere-4d| |wndom_bench-convex-4d| + +|wndom_bench-sphere-5d| |wndom_bench-rmnk-10d| + +.. |wndom_bench-sphere-4d| image:: /_static/bench/wndom_bench-sphere-4d-time.png + :width: 49% + +.. |wndom_bench-convex-4d| image:: /_static/bench/wndom_bench-convex-4d-time.png + :width: 49% + +.. |wndom_bench-sphere-5d| image:: /_static/bench/wndom_bench-sphere-5d-time.png + :width: 49% + +.. |wndom_bench-rmnk-10d| image:: /_static/bench/wndom_bench-rmnk-10d-time.png + :width: 49% + + +Similar results are obtained with ``keep_weakly=False``, however, this setting +is only supported by `moocore`_, `BoTorch`_ and `paretoset`_, thus the other +packages are actually slower to use than reported here, because the user is +forced to remove duplicated points when using them. + +|ndom_bench-sphere-4d| |ndom_bench-convex-4d| + +|ndom_bench-sphere-5d| |ndom_bench-rmnk-10d| + +.. |ndom_bench-sphere-4d| image:: /_static/bench/ndom_bench-sphere-4d-time.png + :width: 49% + +.. |ndom_bench-convex-4d| image:: /_static/bench/ndom_bench-convex-4d-time.png + :width: 49% + +.. |ndom_bench-sphere-5d| image:: /_static/bench/ndom_bench-sphere-5d-time.png + :width: 49% + +.. |ndom_bench-rmnk-10d| image:: /_static/bench/ndom_bench-rmnk-10d-time.png + :width: 49% + + +.. _bench-ndsort: + +Nondominated Sorting (Pareto ranking) +------------------------------------- + +Nondominated sorting (or Pareto ranking) assigns a rank to each point according +to Pareto-optimality. It can be used to split a set of points into layers of +nondominated fronts. For more details, see :func:`moocore.pareto_rank`. This +function in `moocore`_ uses a :math:`O(n \log n)` algorithm for 2 dimensions +and a :math:`O(n^2\log n)` algorithm for 3 dimensions. As the plots show, this +makes `moocore`_ significantly faster than `paretoset`_, `pymoo`_ and +`DESDEO`_. With higher dimensions, `moocore`_ uses a :math:`O(n^2\log^{m-2}n)` +algorithm instead of the :math:`O(n^3)` algorithm in `paretoset`_ and `DESDEO`_ +(latter is compiled with `Numba`_). In these benchmarks points are sampled +uniformly at random within the hypercube. + +|ndsort_bench-ran-2d| |ndsort_bench-ran-3d| + +|ndsort_bench-ran-4d| |ndsort_bench-ran-5d| + +|ndsort_bench-ran-9d| |ndsort_bench-ran-10d| + +.. |ndsort_bench-ran-2d| image:: /_static/bench/ndsort_bench-ran-2d-time.png + :width: 49% + +.. |ndsort_bench-ran-3d| image:: /_static/bench/ndsort_bench-ran-3d-time.png + :width: 49% + +.. |ndsort_bench-ran-4d| image:: /_static/bench/ndsort_bench-ran-4d-time.png + :width: 49% + +.. |ndsort_bench-ran-5d| image:: /_static/bench/ndsort_bench-ran-5d-time.png + :width: 49% + +.. |ndsort_bench-ran-9d| image:: /_static/bench/ndsort_bench-ran-9d-time.png + :width: 49% + +.. |ndsort_bench-ran-10d| image:: /_static/bench/ndsort_bench-ran-10d-time.png + :width: 49% + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/index.rst b/python/doc/source/benchmarks/index.rst new file mode 100644 index 000000000..35ac32f46 --- /dev/null +++ b/python/doc/source/benchmarks/index.rst @@ -0,0 +1,47 @@ +.. _benchmarks: + +Benchmarks +========== + +The following pages compare the performance of `moocore`_, `pymoo`_, `BoTorch`_, `DEAP`_, `DESDEO`_, `paretoset`_, `Nevergrad`_, `jMetalPy`_, `fast-pareto`_, `Optuna`_, `moarchiving`_, and `patatune`_. + +Other Python packages are not included in the comparison because they are based +on these packages for the functionality benchmarked, so they are **at least as +slow** as them. For example `Xopt`_ and `BoFire`_ use `BoTorch`_, `pysamoo`_ is +an extension of `pymoo`_. We do not include functions from the Bayesian +optimization toolbox `trieste`_, because it is much slower than `BoTorch`_ and +too slow to run the benchmarks in a reasonable time +(https://github.com/secondmind-labs/trieste/issues/917). Similarly, we do not +include `paretobench`_ because it is always slower than `BoTorch`_ for +identifying nondominated points and more than 2000 times slower than `moocore`_ +for computing the hypervolume in 3D +(https://github.com/electronsandstuff/ParetoBench/issues/57), which is too slow +to include in the benchmarks. + +Not all packages provide the same functionality. For example, `pymoo`_ does not +provide the :ref:`epsilon indicator `. `BoTorch`_ and +`paretobench`_ only provide the hypervolume. `paretoset`_ and `fast-pareto`_ +only identify nondominated points. `DESDEO`_, `DEAP`_, and `jMetalPy`_ use +`moocore`_ for computing the hypervolume, but other functionality, such as +filtering dominated points, is still slower than `moocore`_. Recent versions +of `seqme`_ and `pymoo`_ (≥0.6.2) already use `moocore`_ for most functionality +benchmarked here. + +We would like to benchmark `pygmo`_, however, it is currently impossible to install using ``pip`` (See https://github.com/esa/pygmo2/issues/152). + +We would also like to benchmark `platypus`_, but its API is too different from +other packages. For example, it only supports filtering dominated points by +creating a new list of points, but it cannot identify their position in the +input. It cannot calculate hypervolume without normalization. It doesn't +support :obj:`~numpy.typing.ArrayLike` inputs. + +The source code for the benchmarks below can be found at https://github.com/multi-objective/moocore/tree/main/python/benchmarks . + +.. toctree:: + :maxdepth: 2 + + dominance + indicators + crossover/index + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/indicators.rst b/python/doc/source/benchmarks/indicators.rst new file mode 100644 index 000000000..587d0c929 --- /dev/null +++ b/python/doc/source/benchmarks/indicators.rst @@ -0,0 +1,114 @@ +Quality indicators +================== + +.. _bench-hv: + +Exact computation of hypervolume +-------------------------------- + +The following plots compare the speed of computing the :ref:`hypervolume indicator ` in 3D, 4D, 5D and 6D. As the plots show, `moocore`_ is 100 times faster than the other packages and 1000 times faster than `BoTorch`_ and, by extension, `Xopt`_ and `BoFire`_. + +For 3D, `Optuna`_ uses a :math:`O(n^2)` algorithm, while `moocore`_ uses the best-known :math:`O(n\log n)` one, so the gap between the two will get significantly larger with a larger number of points than those tested here. `moarchiving`_ uses the same algorithms as `moocore`_ for 3D and 4D, but a pure Python implementation, so it is still 10-100 times slower than `moocore`_'s C implementation. `BoTorch`_ and `fast-pareto`_ are not included for more than 3 objectives because **they are tens of thousands of times slower** than `moocore`_. + +Recent versions of `DESDEO`_, `DEAP`_ (≥1.4.4), `pymoo`_ (≥0.6.1.6) and `jMetalPy`_ (≥1.9.0) already use `moocore`_ for hypervolume computation. +The implementation in `patatune`_ appears to be wrong (https://github.com/cms-patatrack/patatune/issues/52). + +|hv_bench-DTLZLinearShape-3d| |hv_bench-DTLZLinearShape-4d| + +|hv_bench-DTLZLinearShape-5d| |hv_bench-DTLZLinearShape-6d| + +.. |hv_bench-DTLZLinearShape-3d| image:: /_static/bench/hv_bench-DTLZLinearShape.3d-time.png + :width: 49% + +.. |hv_bench-DTLZLinearShape-4d| image:: /_static/bench/hv_bench-DTLZLinearShape.4d-time.png + :width: 49% + +.. |hv_bench-DTLZLinearShape-5d| image:: /_static/bench/hv_bench-DTLZLinearShape.5d-time.png + :width: 49% + +.. |hv_bench-DTLZLinearShape-6d| image:: /_static/bench/hv_bench-DTLZLinearShape.6d-time.png + :width: 49% + +.. _bench-hvapprox: + +Approximation of the hypervolume +-------------------------------- + +The following plots compare the accuracy and speed of approximating the +hypervolume with the various methods provided by :func:`moocore.hv_approx`. The +plots show that there is no clear winner, in terms of approximation error, +between methods ``Rphi-FWE+`` (default) and ``DZ2019-HW``, but both produce +consistently lower approximation errors than method ``DZ2019-MC``. However, ``Rphi-FWE+`` is as fast as ``DZ2019-MC`` and both are consistently faster than ``DZ2019-HW``, in particular with higher number of objectives. + +The exact computation of the hypervolume for less than 5D takes milliseconds +for thousands of points, whereas approximating the hypervolume is significantly +slower and, thus, not worth doing. + +Approximating the hypervolume becomes more useful for dimensions higher than 5, +where the exact computation becomes noticeably slower with hundreds of points. +For such problems, method ``DZ2019-HW`` becomes significantly slower than +``Rphi-FWE+``. + +|hvapprox_bench-DTLZLinearShape-6d-values| |hvapprox_bench-DTLZLinearShape-6d-time| + +|hvapprox_bench-DTLZSphereShape-6d-values| |hvapprox_bench-DTLZSphereShape-6d-time| + +|hvapprox_bench-ran-6d-values| |hvapprox_bench-ran-6d-time| + +|hvapprox_bench-DTLZLinearShape-9d-values| |hvapprox_bench-DTLZLinearShape-9d-time| + +|hvapprox_bench-ran-9d-values| |hvapprox_bench-ran-9d-time| + +|hvapprox_bench-DTLZSphereShape-10d-values| |hvapprox_bench-DTLZSphereShape-10d-time| + +.. |hvapprox_bench-DTLZSphereShape-6d-values| image:: /_static/bench/hvapprox_bench-DTLZSphereShape.6d-values.png + :width: 49% + +.. |hvapprox_bench-DTLZSphereShape-6d-time| image:: /_static/bench/hvapprox_bench-DTLZSphereShape.6d-time.png + :width: 49% + +.. |hvapprox_bench-DTLZLinearShape-6d-values| image:: /_static/bench/hvapprox_bench-DTLZLinearShape.6d-values.png + :width: 49% + +.. |hvapprox_bench-DTLZLinearShape-6d-time| image:: /_static/bench/hvapprox_bench-DTLZLinearShape.6d-time.png + :width: 49% + +.. |hvapprox_bench-ran-6d-values| image:: /_static/bench/hvapprox_bench-ran.6d-values.png + :width: 49% + +.. |hvapprox_bench-ran-6d-time| image:: /_static/bench/hvapprox_bench-ran.6d-time.png + :width: 49% + +.. |hvapprox_bench-DTLZLinearShape-9d-values| image:: /_static/bench/hvapprox_bench-DTLZLinearShape.9d-values.png + :width: 49% + +.. |hvapprox_bench-DTLZLinearShape-9d-time| image:: /_static/bench/hvapprox_bench-DTLZLinearShape.9d-time.png + :width: 49% + +.. |hvapprox_bench-ran-9d-values| image:: /_static/bench/hvapprox_bench-ran.9d-values.png + :width: 49% + +.. |hvapprox_bench-ran-9d-time| image:: /_static/bench/hvapprox_bench-ran.9d-time.png + :width: 49% + +.. |hvapprox_bench-DTLZSphereShape-10d-values| image:: /_static/bench/hvapprox_bench-DTLZSphereShape.10d-values.png + :width: 49% + +.. |hvapprox_bench-DTLZSphereShape-10d-time| image:: /_static/bench/hvapprox_bench-DTLZSphereShape.10d-time.png + :width: 49% + + +Epsilon and IGD+ indicators +--------------------------- + +The following plots benchmark the speed of computing the :ref:`epsilon indicator ` metric and :ref:`IGD+ indicator `. Although the algorithms for computing these metrics are relatively simple and easy to vectorize in Python, the `moocore`_ implementation is still 10 to 100 times faster. + +|fig_eps_bench| |fig_igd_plus_bench| + +.. |fig_eps_bench| image:: /_static/bench/eps_bench-rmnk_10D_random_search-time.png + :width: 48% + +.. |fig_igd_plus_bench| image:: /_static/bench/igd_plus_bench-ran.1000pts.3d-time.png + :width: 48% + +.. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/index.rst b/python/doc/source/index.rst index f7e3cfaeb..abec66d90 100644 --- a/python/doc/source/index.rst +++ b/python/doc/source/index.rst @@ -10,6 +10,7 @@ moocore: Core Algorithms for Multi-Objective Optimization API reference Examples + Benchmarks whatsnew/index contribute/index @@ -63,7 +64,8 @@ performance measures, performance assessment Detailed examples and tutorials. -.. include:: benchmarks.inc.rst +The :ref:`benchmarks ` compare the speed of moocore with other +Python packages. .. This is not really the index page, that is found in diff --git a/python/doc/source/my_unused_images.py b/python/doc/source/my_unused_images.py index b440e3cb1..ec5cce5c1 100644 --- a/python/doc/source/my_unused_images.py +++ b/python/doc/source/my_unused_images.py @@ -23,7 +23,10 @@ def check_unused_images(app, exception): if "://" in uri or uri.startswith("data:"): continue + # Sphinx stores the URI relative to the source directory, which is + # not the folder of the document for documents in subfolders. used.add((document.parent / uri).resolve()) + used.add((Path(app.srcdir) / uri).resolve()) for image in Path(app.srcdir).rglob("*.png"): if "auto_examples" in image.parts: From f4e9c68688db982ec61563a13a4223a357bc1968 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Sat, 24 Oct 2026 15:55:29 +0300 Subject: [PATCH 26/30] python/doc/source/_static/bench/crossover_bench-*-time.png: Regenerate. --- ...ssover_bench-blend_alpha-nparents-time.png | Bin 59459 -> 59030 bytes 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zW!bGY^2uy*Immw=X~slF=VWAjL7C&I(B=ltG;Kz&^-vn))778FN%TSD!V7Gdmo8ZG z){w!1E=4D4x?wU7ktcet7J)FB9vO1}h}41I1kV zwUJ>O1UD1Zq*-T~VBrDCw*u$=6vgvcWUr|r@QC55il$UE`il2?v`Y3HbIM49YK7@2 zJtcC7*8n43)y|IGvQc0RvwQB1u-Hg|p$;n{qIA#i&!CT7+=eS11t1F$s`k;6zrVi< znpnb*hK2@$Y1pw8D4V@YOKFW7({G3oy8;G!(t%YctYg)8E7@A;FiN?DxP}vIA7BJ% zf=Gqwu;!Oi8dz$t9`_C>^ vCG!8-JN$2F@qcep{eNpb{>O*c^`1#wgHt$IMb&Jfz#l2`k7DH_2LAsG^3qC= From ea9b80935ba89e4aeda474a204b3fbfde53cba37 Mon Sep 17 00:00:00 2001 From: Bhupinder Saini Date: Sat, 24 Oct 2026 16:36:18 +0300 Subject: [PATCH 27/30] python/doc/source/benchmarks/crossover/*.rst: Shorten the descriptions. --- python/doc/source/benchmarks/crossover/blend_alpha.rst | 7 ++----- .../source/benchmarks/crossover/bounded_exponential.rst | 3 +-- python/doc/source/benchmarks/crossover/de_current_1.rst | 9 +++------ python/doc/source/benchmarks/crossover/index.rst | 8 +------- python/doc/source/benchmarks/crossover/local.rst | 4 +--- .../doc/source/benchmarks/crossover/parent_centric.rst | 4 +--- 6 files changed, 9 insertions(+), 26 deletions(-) diff --git a/python/doc/source/benchmarks/crossover/blend_alpha.rst b/python/doc/source/benchmarks/crossover/blend_alpha.rst index 756dcb0ac..4ec10ea9e 100644 --- a/python/doc/source/benchmarks/crossover/blend_alpha.rst +++ b/python/doc/source/benchmarks/crossover/blend_alpha.rst @@ -16,7 +16,7 @@ offspring from `DESDEO`_, whose offspring are independent. The timings call The packages handle bounds differently. `moocore`_ and `DESDEO`_ clip the sampling interval to the bounds, `jMetalPy`_ clips each sampled value, and -`DEAP`_ ignores the bounds. The KS tests use bounds that never bind. +`DEAP`_ ignores the bounds. KS test results --------------- @@ -47,9 +47,6 @@ Performance over number of variables :width: 80% With 2 variables, `DEAP`_ is faster than `moocore`_. With more variables, -`moocore`_ is the fastest. With 1000 variables, `DEAP`_, `DESDEO`_ and -`jMetalPy`_ take 6.8, 8.1 and 170 times as long. The time of `jMetalPy`_ grows -much faster than linearly with the number of variables, because its solutions -copy their list of variables on every access. +`moocore`_ is the fastest. .. include:: /benchmarks-links.inc.rst diff --git a/python/doc/source/benchmarks/crossover/bounded_exponential.rst b/python/doc/source/benchmarks/crossover/bounded_exponential.rst index ce5ce033b..cfc82f733 100644 --- a/python/doc/source/benchmarks/crossover/bounded_exponential.rst +++ b/python/doc/source/benchmarks/crossover/bounded_exponential.rst @@ -5,8 +5,7 @@ Bounded exponential crossover (BEX) :func:`~moocore.bounded_exponential_crossover` moves each offspring away from its parent by a random step that follows an exponential distribution truncated -at the bounds. Only `DESDEO`_ (``BoundedExponentialCrossover``) provides this -operator. +at the bounds. KS test results --------------- diff --git a/python/doc/source/benchmarks/crossover/de_current_1.rst b/python/doc/source/benchmarks/crossover/de_current_1.rst index b22cc4b0f..fd5afc62d 100644 --- a/python/doc/source/benchmarks/crossover/de_current_1.rst +++ b/python/doc/source/benchmarks/crossover/de_current_1.rst @@ -9,8 +9,7 @@ it as ``DEX`` with ``at_least_once=False``, when the target is given as the first parent. `jMetalPy`_ provides it through the order of the parents of ``DifferentialEvolutionCrossover``, as its MOEA/D does. `jMetalPy`_ always takes one random variable from the mutant, so it equals this operator only -with :math:`CR = 1`, which is the default. The version of `DESDEO`_ on PyPI -does not provide this operator. +with :math:`CR = 1`, which is the default. KS test results --------------- @@ -23,10 +22,8 @@ KS test results `moocore`_ and `jMetalPy`_ produce the same distribution of offspring. `pymoo`_ multiplies the scaling factor by a random factor within :math:`1 \pm 5 \cdot 10^{-5}`, so its offspring are within :math:`2 \cdot 10^{-5}` of the -values that the other packages produce, but never equal to them. The KS test -detects this. After rounding the offspring to three decimals, the p-values -between `moocore`_ and `pymoo`_ are 0.43, 0.59 and 0.98 for the three -variables. +values that the other packages produce, but never equal to them, which is enough +difference to be detected by the KS test. Performance over number of parents ---------------------------------- diff --git a/python/doc/source/benchmarks/crossover/index.rst b/python/doc/source/benchmarks/crossover/index.rst index 780913c9d..7b1f9a31d 100644 --- a/python/doc/source/benchmarks/crossover/index.rst +++ b/python/doc/source/benchmarks/crossover/index.rst @@ -14,10 +14,7 @@ bounds wide enough that they never bind, so the results do not depend on how each package handles bounds. For every pair of packages and every decision variable, a two-sample Kolmogorov-Smirnov test compares their offspring. Each table shows the smallest p-value over the variables. A p-value below 0.001 -means that the distributions differ. Among this many tests, a few p-values -between 0.001 and 0.05 are expected even when the distributions are equal. -Rerunning with other random seeds moves those values, whereas real differences -stay below 0.001. +means that the distributions differ. The performance plots time each operator for an increasing number of parents with 30 variables, and for an increasing number of variables with 100 parents. @@ -25,9 +22,6 @@ Each package receives the parents in its own data structure, which is created before the timing starts. When a package expects the caller to choose the other parents of DE or PCX, choosing them is part of the time. -The scripts ``compare_crossover.py`` and ``bench_crossover.py`` produce the -tables and the plots. - .. toctree:: :maxdepth: 1 diff --git a/python/doc/source/benchmarks/crossover/local.rst b/python/doc/source/benchmarks/crossover/local.rst index 16674bd1b..9a42d18ff 100644 --- a/python/doc/source/benchmarks/crossover/local.rst +++ b/python/doc/source/benchmarks/crossover/local.rst @@ -5,9 +5,7 @@ Local crossover :func:`~moocore.local_crossover` draws a random weight for each variable and sets the two offspring to the two weighted averages of the parents. Only -`DESDEO`_ (``LocalCrossover``) provides this operator. The -``ArithmeticCrossover`` of `jMetalPy`_ draws one weight for all the variables, -so it is a different operator. +`DESDEO`_ (``LocalCrossover``) provides this operator. KS test results --------------- diff --git a/python/doc/source/benchmarks/crossover/parent_centric.rst b/python/doc/source/benchmarks/crossover/parent_centric.rst index 01a239c4c..49c8d6f5b 100644 --- a/python/doc/source/benchmarks/crossover/parent_centric.rst +++ b/python/doc/source/benchmarks/crossover/parent_centric.rst @@ -7,9 +7,7 @@ Parent-centric crossover (PCX) target, from two more parents chosen at random. `pymoo`_ (``PCX``) and `DESDEO`_ (``ParentCentricCrossover``) provide the same operator. `pymoo`_ replaces values outside the bounds by random values, while `moocore`_ and -`DESDEO`_ clip them. The KS tests use bounds that never bind. The PCX of -`platypus`_ keeps the offspring in the plane of the three parents and has half -the spread, so it is a different operator. +`DESDEO`_ clip them. KS test results --------------- From 87af12bdc8915d905d38bffc473395ef2de6f967 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Manuel=20L=C3=B3pez-Ib=C3=A1=C3=B1ez?= <2620021+MLopez-Ibanez@users.noreply.github.com> Date: Mon, 26 Oct 2026 07:47:59 +0000 Subject: [PATCH 28/30] Add type ignore for unresolved import in _crossover.py Added type ignore comment for unresolved import. --- python/src/moocore/_crossover.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index 52395d7c1..aaadb2d1c 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -5,7 +5,7 @@ from numpy.typing import ArrayLike from ._docsubstitute import DocSubstitute -from ._libmoocore import ffi, lib +from ._libmoocore import ffi, lib # ty: ignore[unresolved-import] from ._utils import _get_seed_for_c, array_1d_of_length_n, np2d_to_double_array From 1b0fb4388265089edb8e9cc03f40593deefcfa55 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Mon, 26 Oct 2026 07:48:30 +0000 Subject: [PATCH 29/30] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- python/src/moocore/_crossover.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index aaadb2d1c..c6d71468d 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -5,7 +5,7 @@ from numpy.typing import ArrayLike from ._docsubstitute import DocSubstitute -from ._libmoocore import ffi, lib # ty: ignore[unresolved-import] +from ._libmoocore import ffi, lib # ty: ignore[unresolved-import] from ._utils import _get_seed_for_c, array_1d_of_length_n, np2d_to_double_array From 091913c10dfcdd72f7be7583be75849d98ef7c34 Mon Sep 17 00:00:00 2001 From: MLopez-Ibanez <2620021+MLopez-Ibanez@users.noreply.github.com> Date: Mon, 26 Oct 2026 12:58:09 +0000 Subject: [PATCH 30/30] Fix documentation --- python/src/moocore/_crossover.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/python/src/moocore/_crossover.py b/python/src/moocore/_crossover.py index c6d71468d..627ce32dd 100644 --- a/python/src/moocore/_crossover.py +++ b/python/src/moocore/_crossover.py @@ -1,3 +1,5 @@ +from __future__ import annotations + from collections.abc import Callable from typing import Any

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