アニーリング法のC言語実装

参考文献

しっかり学ぶ数理最適化　モデルからアルゴリズムまで
梅谷俊治・著
発行 2020/10/23

準備

オンラインコンパイラを使用します。

ソースコード

sample.c

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

// 目的関数の定義
double objective(double x) {
    return 2 * sin(x) + 3 * cos(2 * x) + 5 * sin(2.0 / 3.0 * x);
}

// 受け入れ確率を計算する関数
double acceptance_probability(double old_cost, double new_cost, double temperature) {
    if (new_cost < old_cost) {
        return 1.0;
    } else {
        return exp((old_cost - new_cost) / temperature);
    }
}

// シミュレーテッド・アニーリングによる最適化
void simulated_annealing(double (*objective)(double), double initial_state, double initial_temperature, double cooling_rate, double min_temperature, int num_iterations, double *best_state, double *best_cost) {
    double current_state = initial_state;
    double current_cost = objective(current_state);

    *best_state = current_state;
    *best_cost = current_cost;

    double temperature = initial_temperature;

    for (int i = 0; i < num_iterations; i++) {
        double new_state = current_state + ((double)rand() / RAND_MAX) * 0.2 - 0.1;
        double new_cost = objective(new_state);

        if (acceptance_probability(current_cost, new_cost, temperature) > (double)rand() / RAND_MAX) {
            current_state = new_state;
            current_cost = new_cost;
        }

        if (new_cost < *best_cost) {
            *best_state = new_state;
            *best_cost = new_cost;
        }

        temperature *= cooling_rate;
        if (temperature < min_temperature) {
            break;
        }
    }
}

int main() {
    srand(time(0));

    // パラメータの設定
    double initial_state = 0.0;
    double initial_temperature = 100.0;
    double cooling_rate = 0.9999;
    double min_temperature = 0.01;
    int num_iterations = 100000;

    // 最適化の実行
    double best_state, best_cost;
    simulated_annealing(objective, initial_state, initial_temperature, cooling_rate, min_temperature, num_iterations, &best_state, &best_cost);

    printf("Best state: %f\n", best_state);
    printf("Best cost: %f\n", best_cost);

    return 0;
}