用C语言写一段粒子群优化算法

以下是一段用C语言实现的粒子群优化算法的代码：

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

#define DIMENSION 10     // 维度
#define NUM_PARTICLES 20 // 粒子数
#define MAX_ITERATIONS 50 // 迭代次数
#define C1 2.0           // 加速系数1
#define C2 2.0           // 加速系数2
#define W 1.0            // 惯性权重

typedef struct {
    double position[DIMENSION]; // 位置
    double velocity[DIMENSION]; // 速度
    double pbest[DIMENSION];    // 个体最优解
    double fitness;             // 适应度
} Particle;

double objective_function(double *x)
{
    // 目标函数
    double sum = 0.0;
    for (int i = 0; i < DIMENSION; i++) {
        sum += x[i] * x[i];
    }
    return sum;
}

void initialize_particles(Particle *particles)
{
    // 初始化粒子
    for (int i = 0; i < NUM_PARTICLES; i++) {
        for (int j = 0; j < DIMENSION; j++) {
            particles[i].position[j] = (double)rand() / RAND_MAX * 10.0 - 5.0;
            particles[i].velocity[j] = (double)rand() / RAND_MAX * 2.0 - 1.0;
            particles[i].pbest[j] = particles[i].position[j];
        }
        particles[i].fitness = objective_function(particles[i].position);
    }
}

void update_particle(Particle *particle, double *gbest)
{
    // 更新粒子位置和速度
    for (int i = 0; i < DIMENSION; i++) {
        double r1 = (double)rand() / RAND_MAX;
        double r2 = (double)rand() / RAND_MAX;
        particle->velocity[i] = W * particle->velocity[i] +
            C1 * r1 * (particle->pbest[i] - particle->position[i]) +
            C2 * r2 * (*gbest - particle->position[i]);
        particle->position[i] += particle->velocity[i];
    }
    double fitness = objective_function(particle->position);
    if (fitness < particle->fitness) {
        // 更新个体最优解
        particle->fitness = fitness;
        for (int i = 0; i < DIMENSION; i++) {
            particle->pbest[i] = particle->position[i];
        }
    }
}

void update_gbest(Particle *particles, double *gbest)
{
    // 更新全局最优解
    double best_fitness = particles[0].fitness;
    int best_index = 0;
    for (int i = 1; i < NUM_PARTICLES; i++) {
        if (particles[i].fitness < best_fitness) {
            best_fitness = particles[i].fitness;
            best_index = i;
        }
    }
    if (best_fitness < *gbest) {
        *gbest = best_fitness;
        for (int i = 0; i < DIMENSION; i++) {
            gbest[i] = particles[best_index].position[i];
        }
    }
}

void optimize()
{
    Particle particles[NUM_PARTICLES];
    double gbest[DIMENSION];
    double best_fitness;
    
    initialize_particles(particles);
    best_fitness = particles[0].fitness;
    for (int i = 1; i < NUM_PARTICLES; i++) {
        if (particles[i].fitness < best_fitness) {
            best_fitness = particles[i].fitness;
        }
    }
    for (int i = 0; i < DIMENSION; i++) {
        gbest[i] = particles[0].position[i];
    }
    
    for (int iter = 0; iter < MAX_ITERATIONS; iter++) {
        for (int i = 0; i < NUM_PARTICLES; i++) {
            update_particle(&particles[i], gbest);
        }
        update_gbest(particles, gbest);
        printf("iteration %d: best fitness = %lf\n", iter + 1, gbest);
    }
}

int main()
{
    optimize();
    return 0;
}

该算法用于求解多维优化问题，在上述代码中，目标函数为 $f(x) = \sum_{i=1}^{10} x_i^2$，算法通过不断跟踪粒子的位置和速度，逐步优化得到最优解，本代码中设定了粒子数、迭代次数、加速系数等参数，可以根据具体问题进行调整。