用c语言写遗传算法求tsp问题

以下是使用C语言实现遗传算法求解TSP问题的基本步骤：

1. 定义城市距离矩阵

#define CITY_NUM 10  // 城市数量
int distance[CITY_NUM][CITY_NUM] = {
    {0, 10, 20, 30, 40, 50, 60, 70, 80, 90},
    {10, 0, 15, 25, 35, 45, 55, 65, 75, 85},
    {20, 15, 0, 10, 50, 60, 70, 80, 90, 100},
    {30, 25, 10, 0, 40, 50, 60, 70, 80, 90},
    {40, 35, 50, 40, 0, 20, 30, 70, 80, 90},
    {50, 45, 60, 50, 20, 0, 15, 65, 75, 85},
    {60, 55, 70, 60, 30, 15, 0, 60, 70, 80},
    {70, 65, 80, 70, 70, 65, 60, 0, 20, 30},
    {80, 75, 90, 80, 80, 75, 70, 20, 0, 10},
    {90, 85, 100, 90, 90, 85, 80, 30, 10, 0}
};

2. 定义个体结构体和种群结构体

#define POPULATION_SIZE 100  // 种群大小
#define CHROMOSOME_LENGTH CITY_NUM  // 基因长度

struct chromosome {
    int genes[CHROMOSOME_LENGTH];  // 基因序列
    int fitness;  // 适应度值
};

struct population {
    struct chromosome individuals[POPULATION_SIZE];  // 个体数组
    int generation;  // 当前代数
};

3. 初始化个体和种群

void initialize_chromosome(struct chromosome *c) {
    int i, j;
    for (i = 0; i < CHROMOSOME_LENGTH; i++) {
        c->genes[i] = i;
    }
    for (i = CHROMOSOME_LENGTH - 1; i >= 1; i--) {
        j = rand() % (i + 1);
        swap(&c->genes[i], &c->genes[j]);
    }
    c->fitness = 0;
}

void initialize_population(struct population *p) {
    int i;
    for (i = 0; i < POPULATION_SIZE; i++) {
        initialize_chromosome(&p->individuals[i]);
    }
    p->generation = 0;
}

4. 计算个体适应度值

int calculate_fitness(int *genes) {
    int i, fitness = 0;
    for (i = 0; i < CHROMOSOME_LENGTH - 1; i++) {
        fitness += distance[genes[i]][genes[i+1]];
    }
    fitness += distance[genes[CHROMOSOME_LENGTH-1]][genes[0]];
    return fitness;
}

void calculate_chromosome_fitness(struct chromosome *c) {
    c->fitness = calculate_fitness(c->genes);
}

void calculate_population_fitness(struct population *p) {
    int i;
    for (i = 0; i < POPULATION_SIZE; i++) {
        calculate_chromosome_fitness(&p->individuals[i]);
    }
}

5. 选择操作

void selection(struct population *p, struct chromosome *parents) {
    int i, j, index1, index2;
    for (i = 0; i < 2; i++) {
        index1 = rand() % POPULATION_SIZE;
        index2 = rand() % POPULATION_SIZE;
        if (p->individuals[index1].fitness < p->individuals[index2].fitness) {
            parents[i] = p->individuals[index1];
        } else {
            parents[i] = p->individuals[index2];
        }
    }
}

6. 交叉操作

void crossover(struct chromosome *parent1, struct chromosome *parent2, struct chromosome *child) {
    int i, j, k, start, end;
    start = rand() % CHROMOSOME_LENGTH;
    end = rand() % CHROMOSOME_LENGTH;
    if (start > end) {
        swap(&start, &end);
    }
    for (i = 0; i < CHROMOSOME_LENGTH; i++) {
        child->genes[i] = -1;
    }
    for (i = start; i <= end; i++) {
        child->genes[i] = parent1->genes[i];
    }
    k = 0;
    for (i = 0; i < CHROMOSOME_LENGTH; i++) {
        if (child->genes[i] == -1) {
            while (k < CHROMOSOME_LENGTH) {
                for (j = 0; j <= end - start; j++) {
                    if (parent2->genes[k] == child->genes[j+start]) {
                        break;
                    }
                }
                if (j > end - start) {
                    child->genes[i] = parent2->genes[k];
                    k++;
                    break;
                }
                k++;
            }
        }
    }
}

7. 变异操作

void mutation(struct chromosome *c) {
    int i, j;
    if (rand() % 100 < MUTATION_RATE) {
        i = rand() % CHROMOSOME_LENGTH;
        j = rand() % CHROMOSOME_LENGTH;
        swap(&c->genes[i], &c->genes[j]);
    }
}

8. 进化操作

void evolve(struct population *p) {
    struct chromosome parents[2], child;
    int i, j;
    for (i = 0; i < POPULATION_SIZE; i++) {
        selection(p, parents);
        crossover(&parents[0], &parents[1], &child);
        mutation(&child);
        calculate_chromosome_fitness(&child);
        p->individuals[i] = child;
    }
    p->generation++;
}

9. 主函数

int main() {
    struct population p;
    initialize_population(&p);
    while (p.generation < MAX_GENERATION) {
        calculate_population_fitness(&p);
        evolve(&p);
    }
    printf("Best solution: ");
    for (i = 0; i < CHROMOSOME_LENGTH; i++) {
        printf("%d ", p.individuals[0].genes[i]);
    }
    printf("\nBest fitness: %d\n", p.individuals[0].fitness);
    return 0;
}

以上是使用C语言实现遗传算法求解TSP问题的基本步骤，具体实现中还需要注意一些细节问题，比如交叉、变异操作的具体实现方式等。