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+/*
+ * Copyright Nick Thompson, 2024
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#ifndef BOOST_MATH_OPTIMIZATION_DIFFERENTIAL_EVOLUTION_HPP
+#define BOOST_MATH_OPTIMIZATION_DIFFERENTIAL_EVOLUTION_HPP
+#include <atomic>
+#include <boost/math/optimization/detail/common.hpp>
+#include <cmath>
+#include <limits>
+#include <mutex>
+#include <random>
+#include <sstream>
+#include <stdexcept>
+#include <thread>
+#include <utility>
+#include <vector>
+
+namespace boost::math::optimization {
+
+// Storn, R., Price, K. (1997). Differential evolution-a simple and efficient heuristic for global optimization over
+// continuous spaces.
+// Journal of global optimization, 11, 341-359.
+// See:
+// https://www.cp.eng.chula.ac.th/~prabhas//teaching/ec/ec2012/storn_price_de.pdf
+
+// We provide the parameters in a struct-there are too many of them and they are too unwieldy to pass individually:
+template <typename ArgumentContainer> struct differential_evolution_parameters {
+ using Real = typename ArgumentContainer::value_type;
+ using DimensionlessReal = decltype(Real()/Real());
+ ArgumentContainer lower_bounds;
+ ArgumentContainer upper_bounds;
+ // mutation factor is also called scale factor or just F in the literature:
+ DimensionlessReal mutation_factor = static_cast<DimensionlessReal>(0.65);
+ DimensionlessReal crossover_probability = static_cast<DimensionlessReal>(0.5);
+ // Population in each generation:
+ size_t NP = 500;
+ size_t max_generations = 1000;
+ ArgumentContainer const *initial_guess = nullptr;
+ unsigned threads = std::thread::hardware_concurrency();
+};
+
+template <typename ArgumentContainer>
+void validate_differential_evolution_parameters(differential_evolution_parameters<ArgumentContainer> const &de_params) {
+ using std::isfinite;
+ using std::isnan;
+ std::ostringstream oss;
+ detail::validate_bounds(de_params.lower_bounds, de_params.upper_bounds);
+ if (de_params.NP < 4) {
+ oss << __FILE__ << ":" << __LINE__ << ":" << __func__;
+ oss << ": The population size must be at least 4, but requested population size of " << de_params.NP << ".";
+ throw std::invalid_argument(oss.str());
+ }
+ // From: "Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)"
+ // > The scale factor, F in (0,1+), is a positive real number that controls the rate at which the population evolves.
+ // > While there is no upper limit on F, effective values are seldom greater than 1.0.
+ // ...
+ // Also see "Limits on F", Section 2.5.1:
+ // > This discontinuity at F = 1 reduces the number of mutants by half and can result in erratic convergence...
+ auto F = de_params.mutation_factor;
+ if (isnan(F) || F >= 1 || F <= 0) {
+ oss << __FILE__ << ":" << __LINE__ << ":" << __func__;
+ oss << ": F in (0, 1) is required, but got F=" << F << ".";
+ throw std::domain_error(oss.str());
+ }
+ if (de_params.max_generations < 1) {
+ oss << __FILE__ << ":" << __LINE__ << ":" << __func__;
+ oss << ": There must be at least one generation.";
+ throw std::invalid_argument(oss.str());
+ }
+ if (de_params.initial_guess) {
+ detail::validate_initial_guess(*de_params.initial_guess, de_params.lower_bounds, de_params.upper_bounds);
+ }
+ if (de_params.threads == 0) {
+ oss << __FILE__ << ":" << __LINE__ << ":" << __func__;
+ oss << ": There must be at least one thread.";
+ throw std::invalid_argument(oss.str());
+ }
+}
+
+template <typename ArgumentContainer, class Func, class URBG>
+ArgumentContainer differential_evolution(
+ const Func cost_function, differential_evolution_parameters<ArgumentContainer> const &de_params, URBG &gen,
+ std::invoke_result_t<Func, ArgumentContainer> target_value =
+ std::numeric_limits<std::invoke_result_t<Func, ArgumentContainer>>::quiet_NaN(),
+ std::atomic<bool> *cancellation = nullptr,
+ std::atomic<std::invoke_result_t<Func, ArgumentContainer>> *current_minimum_cost = nullptr,
+ std::vector<std::pair<ArgumentContainer, std::invoke_result_t<Func, ArgumentContainer>>> *queries = nullptr) {
+ using Real = typename ArgumentContainer::value_type;
+ using DimensionlessReal = decltype(Real()/Real());
+ using ResultType = std::invoke_result_t<Func, ArgumentContainer>;
+ using std::clamp;
+ using std::isnan;
+ using std::round;
+ using std::uniform_real_distribution;
+ validate_differential_evolution_parameters(de_params);
+ const size_t dimension = de_params.lower_bounds.size();
+ auto NP = de_params.NP;
+ auto population = detail::random_initial_population(de_params.lower_bounds, de_params.upper_bounds, NP, gen);
+ if (de_params.initial_guess) {
+ population[0] = *de_params.initial_guess;
+ }
+ std::vector<ResultType> cost(NP, std::numeric_limits<ResultType>::quiet_NaN());
+ std::atomic<bool> target_attained = false;
+ // This mutex is only used if the queries are stored:
+ std::mutex mt;
+
+ std::vector<std::thread> thread_pool;
+ auto const threads = de_params.threads;
+ for (size_t j = 0; j < threads; ++j) {
+ // Note that if some members of the population take way longer to compute,
+ // then this parallelization strategy is very suboptimal.
+ // However, we tried using std::async (which should be robust to this particular problem),
+ // but the overhead was just totally unacceptable on ARM Macs (the only platform tested).
+ // As the economists say "there are no solutions, only tradeoffs".
+ thread_pool.emplace_back([&, j]() {
+ for (size_t i = j; i < cost.size(); i += threads) {
+ cost[i] = cost_function(population[i]);
+ if (current_minimum_cost && cost[i] < *current_minimum_cost) {
+ *current_minimum_cost = cost[i];
+ }
+ if (queries) {
+ std::scoped_lock lock(mt);
+ queries->push_back(std::make_pair(population[i], cost[i]));
+ }
+ if (!isnan(target_value) && cost[i] <= target_value) {
+ target_attained = true;
+ }
+ }
+ });
+ }
+ for (auto &thread : thread_pool) {
+ thread.join();
+ }
+
+ std::vector<ArgumentContainer> trial_vectors(NP);
+ for (size_t i = 0; i < NP; ++i) {
+ if constexpr (detail::has_resize_v<ArgumentContainer>) {
+ trial_vectors[i].resize(dimension);
+ }
+ }
+ std::vector<URBG> thread_generators(threads);
+ for (size_t j = 0; j < threads; ++j) {
+ thread_generators[j].seed(gen());
+ }
+ // std::vector<bool> isn't threadsafe!
+ std::vector<int> updated_indices(NP, 0);
+
+ for (size_t generation = 0; generation < de_params.max_generations; ++generation) {
+ if (cancellation && *cancellation) {
+ break;
+ }
+ if (target_attained) {
+ break;
+ }
+ thread_pool.resize(0);
+ for (size_t j = 0; j < threads; ++j) {
+ thread_pool.emplace_back([&, j]() {
+ auto& tlg = thread_generators[j];
+ uniform_real_distribution<DimensionlessReal> unif01(DimensionlessReal(0), DimensionlessReal(1));
+ for (size_t i = j; i < cost.size(); i += threads) {
+ if (target_attained) {
+ return;
+ }
+ if (cancellation && *cancellation) {
+ return;
+ }
+ size_t r1, r2, r3;
+ do {
+ r1 = tlg() % NP;
+ } while (r1 == i);
+ do {
+ r2 = tlg() % NP;
+ } while (r2 == i || r2 == r1);
+ do {
+ r3 = tlg() % NP;
+ } while (r3 == i || r3 == r2 || r3 == r1);
+
+ for (size_t k = 0; k < dimension; ++k) {
+ // See equation (4) of the reference:
+ auto guaranteed_changed_idx = tlg() % dimension;
+ if (unif01(tlg) < de_params.crossover_probability || k == guaranteed_changed_idx) {
+ auto tmp = population[r1][k] + de_params.mutation_factor * (population[r2][k] - population[r3][k]);
+ auto const &lb = de_params.lower_bounds[k];
+ auto const &ub = de_params.upper_bounds[k];
+ // Some others recommend regenerating the indices rather than clamping;
+ // I dunno seems like it could get stuck regenerating . . .
+ trial_vectors[i][k] = clamp(tmp, lb, ub);
+ } else {
+ trial_vectors[i][k] = population[i][k];
+ }
+ }
+
+ auto const trial_cost = cost_function(trial_vectors[i]);
+ if (isnan(trial_cost)) {
+ continue;
+ }
+ if (queries) {
+ std::scoped_lock lock(mt);
+ queries->push_back(std::make_pair(trial_vectors[i], trial_cost));
+ }
+ if (trial_cost < cost[i] || isnan(cost[i])) {
+ cost[i] = trial_cost;
+ if (!isnan(target_value) && cost[i] <= target_value) {
+ target_attained = true;
+ }
+ if (current_minimum_cost && cost[i] < *current_minimum_cost) {
+ *current_minimum_cost = cost[i];
+ }
+ // Can't do this! It's a race condition!
+ //population[i] = trial_vectors[i];
+ // Instead mark all the indices that need to be updated:
+ updated_indices[i] = 1;
+ }
+ }
+ });
+ }
+ for (auto &thread : thread_pool) {
+ thread.join();
+ }
+ for (size_t i = 0; i < NP; ++i) {
+ if (updated_indices[i]) {
+ population[i] = trial_vectors[i];
+ updated_indices[i] = 0;
+ }
+ }
+ }
+
+ auto it = std::min_element(cost.begin(), cost.end());
+ return population[std::distance(cost.begin(), it)];
+}
+
+} // namespace boost::math::optimization
+#endif