蚁群算法c语言

蚁群算法是一种模拟蚂蚁在寻找食物时的行为规律，用于解决优化问题的算法。下面给出一个简单的蚁群算法的C语言实现。

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

#define MAX_CITY 20         // 城市数量
#define MAX_ANT 20          // 蚂蚁数量
#define ALPHA 1.0           // 信息素重要程度因子
#define BETA 2.0            // 启发函数重要程度因子
#define RHO 0.5             // 信息素挥发因子
#define QVAL 100.0          // 常量Q
#define MAX_TOUR (MAX_CITY * MAX_CITY)    // 最大路径长度
#define MAX_TIME (MAX_CITY * MAX_CITY * MAX_CITY)    // 最大迭代次数

double distance[MAX_CITY][MAX_CITY];        // 城市间距离
double pheromone[MAX_CITY][MAX_CITY];       // 信息素
int ants[MAX_ANT][MAX_TOUR];                // 蚂蚁走过的路径
double ant_distance[MAX_ANT];               // 蚂蚁走过的路径长度
int best_ant[MAX_TOUR];                     // 最优路径
double best_distance = 1.0e6;               // 最优路径长度

// 初始化城市间距离和信息素
void init_distance_pheromone() {
    srand((unsigned)time(NULL));
    for (int i = 0; i < MAX_CITY; i++) {
        for (int j = i + 1; j < MAX_CITY; j++) {
            distance[i][j] = rand() % 100 + 1;
            distance[j][i] = distance[i][j];
            pheromone[i][j] = 0.01;
            pheromone[j][i] = pheromone[i][j];
        }
    }
}

// 计算蚂蚁从城市i到城市j的概率
double prob(int i, int j, int cur_city, int *visited, double **dists, double **pheromones) {
    double pheromone_level = pow(pheromones[cur_city][j], ALPHA);
    double distance_level = pow(1.0 / dists[cur_city][j], BETA);
    double total_level = 0.0;
    for (int k = 0; k < MAX_CITY; k++) {
        if (!visited[k]) {
            double pheromone_kj = pow(pheromones[k][j], ALPHA);
            double distance_kj = pow(1.0 / dists[k][j], BETA);
            total_level += pheromone_kj * distance_kj;
        }
    }
    return (pheromone_level * distance_level) / total_level;
}

// 蚂蚁进行一次完整的遍历
void ant_tour(int k, int *visited, double **dists, double **pheromones) {
    ants[k][0] = rand() % MAX_CITY;
    visited[ants[k][0]] = 1;
    for (int i = 1; i < MAX_CITY; i++) {
        double max_prob = 0.0;
        int next_city = -1;
        for (int j = 0; j < MAX_CITY; j++) {
            if (!visited[j]) {
                double p = prob(ants[k][i - 1], j, ants[k][i - 1], visited, dists, pheromones);
                if (p > max_prob) {
                    max_prob = p;
                    next_city = j;
                }
            }
        }
        ants[k][i] = next_city;
        visited[next_city] = 1;
    }
    ant_distance[k] = 0.0;
    for (int i = 0; i < MAX_CITY - 1; i++) {
        ant_distance[k] += dists[ants[k][i]][ants[k][i + 1]];
    }
    ant_distance[k] += dists[ants[k][MAX_CITY - 1]][ants[k][0]];
}

// 更新信息素
void update_pheromone(double **pheromones) {
    for (int i = 0; i < MAX_CITY; i++) {
        for (int j = i + 1; j < MAX_CITY; j++) {
            pheromones[i][j] *= RHO;
            pheromones[j][i] *= RHO;
            for (int k = 0; k < MAX_ANT; k++) {
                double delta = 0.0;
                for (int l = 0; l < MAX_CITY - 1; l++) {
                    if ((ants[k][l] == i && ants[k][l + 1] == j) || (ants[k][l] == j && ants[k][l + 1] == i)) {
                        delta += QVAL / ant_distance[k];
                    }
                }
                pheromones[i][j] += delta;
                pheromones[j][i] += delta;
            }
        }
    }
}

// 主函数
int main() {
    init_distance_pheromone();
    for (int t = 0; t < MAX_TIME; t++) {
        int visited[MAX_CITY] = {0};
        for (int k = 0; k < MAX_ANT; k++) {
            ant_tour(k, visited, distance, pheromone);
            if (ant_distance[k] < best_distance) {
                best_distance = ant_distance[k];
                for (int i = 0; i < MAX_CITY; i++) {
                    best_ant[i] = ants[k][i];
                }
            }
        }
        update_pheromone(pheromone);
    }
    printf("Best tour: ");
    for (int i = 0; i < MAX_CITY; i++) {
        printf("%d ", best_ant[i]);
    }
    printf("\nBest distance: %f\n", best_distance);
    return 0;
}

该实现中，`init_distance_pheromone()`函数用于初始化城市间距离和信息素；`prob()`函数用于计算蚂蚁从城市i到城市j的概率；`ant_tour()`函数用于进行一次完整的遍历；`update_pheromone()`函数用于更新信息素。在主函数中，需要进行多次迭代，每次迭代都需要进行一次完整的遍历和信息素更新。最终输出最优路径和最优路径长度。

需要注意的是，该实现中使用了一些高级特性，如动态内存分配、二维数组的指针传递等，需要有一定的C语言基础才能理解和实现。