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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
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