GA遗传算法

/* * 遗传算法求解函数的最优值问题 * 参考自《MATLAB智能算法30个案例分析》 * 本例的寻优函数为:f = -5*sin(x1)*sin(x2)*sin(x3)*sin(x4)*sin(x5) - sin(5*x1)*sin(5*x2)*sin(5*x3)*sin(5*x4)*sin(5*x5) + 8 * 其中x1,x2,x3,x4,x5是0~0.9*PI之间的实数。该函数的最小值为2,当x1,x2,x3,x4,x5都取PI/2时得到。 * update in 16/12/3 * author:Lyrichu * email:[e-mail] */#include<stdio.h>#include<stdlib.h>#include<math.h>#include<time.h>#define PI 3.1415926535897932 // 圆周率#define sizepop 500 // 种群数目#define maxgen 10000 // 进化代数#define pcross 0.6 // 交叉概率#define pmutation 0.1 // probability of mutation#define lenchrom 5 // length of chromosome = number of independent variables// 变量下界，这里因为都相同，所以就用单个值去代替了，如果每个变量上下界不同，也许需要用数组定义double bound_down[lenchrom] = {1.5, 1.5, 1.5, 1.5, 1.5};double bound_up[lenchrom] = {0.8*PI, 0.8*PI, 0.9*PI, 0.9*PI, PI};double chrom[sizepop][lenchrom]; // 种群数组double fitness[sizepop]; // 种群每个个体的适应度double fitness_prob[sizepop]; // 每个个体被选中的概率(使用轮盘赌法确定)double bestfitness[maxgen]; // 每一代最优值double gbest_pos[lenchrom]; // 取最优值的位置double average_best[maxgen+1]; // 每一代平均最优值double gbest; // 所有进化中的最优值int gbest_index; // 取得最优值的迭代次数序号//=================================================================================// 目标函数double fit_func(double * arr, int a){    double x1 = *arr;    double x2 = *(arr+1);    double x3 = *(arr+2);    double x4 = *(arr+3);    double x5 = *(arr+4);    double func_result = -5*sin(x1)*sin(x2)*sin(x3)*sin(x4)*sin(x5) - sin(5*x1)*sin(5*x2)*sin(5*x3)*sin(5*x4)*sin(5*x5) + 8 + a-a;    return func_result;}//=================================================================================// 求和函数double sum(double * fitness){    double sum_fit = 0;    for(int i=0;i<sizepop;i++)        sum_fit += *(fitness+i);    return sum_fit;}//=================================================================================// 求最小值函数double * min(double * fitness){    double min_fit = *fitness;    double min_index = 0;    static double arr[2];    for(int i=1;i<sizepop;i++)    {        if(*(fitness+i) < min_fit)        {            min_fit = *(fitness+i);            min_index = i;        }    }    arr[0] = min_index;    arr[1] = min_fit;    return arr;}//=================================================================================// 种群初始化void init_chrom(int a){    for(int i=0;i<sizepop;i++)    {        for(int j=0;j<lenchrom;j++)        {            chrom[i][j] = bound_down[j] + (bound_up[j]-bound_down[j])*(((double)rand())/RAND_MAX);        }        fitness[i] = fit_func(chrom[i],a); // 初始化适应度    }}//=================================================================================// 选择操作void Select(double chrom[sizepop][lenchrom], int a){    int index[sizepop];    for(int i=0;i<sizepop;i++)    {        double * arr = chrom[i];        fitness[i] = 1/(fit_func(arr,a)); // 本例是求最小值，适应度为目标函数的倒数，即函数值越小，适应度越大    }    double sum_fitness = 0;    for(int i=0;i<sizepop;i++)    {        sum_fitness += fitness[i]; // 适应度求和    }    for(int i=0;i<sizepop;i++)    {        fitness_prob[i] = fitness[i]/sum_fitness;    }    for(int i=0;i<sizepop;i++)    {        fitness[i] = 1/fitness[i]; // 恢复函数值    }    for(int i=0;i<sizepop;i++) // sizepop 次轮盘赌    {        double pick = ((double)rand())/RAND_MAX;        while(pick < 0.0001)            pick = ((double)rand())/RAND_MAX;        for(int j=0;j<sizepop;j++)        {            pick = pick - fitness_prob[j];            if(pick<=0)            {                index[i] = j;                break;            }        }    }    for(int i=0;i<sizepop;i++)    {        for(int j=0;j<lenchrom;j++)        {            chrom[i][j] = chrom[index[i]][j];        }        fitness[i] = fitness[index[i]];    }}//=================================================================================// 交叉操作void Cross(double chrom[sizepop][lenchrom]){    for(int i=0; i<sizepop; i++)    {        // 随机选择两个染色体进行交叉        double pick1 = ((double)rand())/RAND_MAX;        double pick2 = ((double)rand())/RAND_MAX;        int choice1 = (int)(pick1*sizepop);// 第一个随机选取的染色体序号        int choice2 = (int)(pick2*sizepop);// 第二个染色体序号        while(choice1 > sizepop-1)        {            pick1 = ((double)rand())/RAND_MAX;            choice1 = (int)(pick1*sizepop); //防止选取位置过界        }        while(choice2 > sizepop-1)        {            pick2 = ((double)rand())/RAND_MAX;            choice2 = (int)(pick2*sizepop);        }        double pick = ((double)rand())/RAND_MAX;// 用于判断是否进行交叉操作        if(pick>pcross)            continue;        int flag = 0; // 判断交叉是否有效的标记        while(flag == 0)        {            double pick = ((double)rand())/RAND_MAX;            int pos = (int)(pick*lenchrom);            while(pos > lenchrom-1)            {                double pick = ((double)rand())/RAND_MAX;                int pos = (int)(pick*lenchrom); // 处理越界            }            // 交叉开始            double r = ((double)rand())/RAND_MAX;            double v1 = chrom[choice1][pos];            double v2 = chrom[choice2][pos];            chrom[choice1][pos] = r*v2 + (1-r)*v1;            chrom[choice2][pos] = r*v1 + (1-r)*v2; // 交叉结束            if(chrom[choice1][pos] >=bound_down[pos] && chrom[choice1][pos]<=bound_up[pos]            && chrom[choice2][pos] >=bound_down[pos] && chrom[choice2][pos]<=bound_up[pos])            {                flag = 1; // 交叉有效，退出交叉，否则继续下一次交叉            }        }    }}//=================================================================================// 变异操作void Mutation(double chrom[sizepop][lenchrom]){    for(int i=0;i<sizepop;i++)    {        double pick = ((double)rand())/RAND_MAX; // 随机选择一个染色体进行变异        int choice = (int)(pick*sizepop);        while(choice > sizepop-1)        {            pick = ((double)rand())/RAND_MAX;            int choice = (int)(pick*sizepop);  // 处理下标越界        }        pick = ((double)rand())/RAND_MAX; // 用于决定该轮是否进行变异        if(pick>pmutation)            continue;        pick = ((double)rand())/RAND_MAX;        int pos = (int)(pick*lenchrom);        while(pos > lenchrom-1)        {        }        double v = chrom[i][pos];        double v1 = v - bound_up[pos];        double v2 = bound_down[pos] - v;        double r = ((double)rand())/RAND_MAX;        double r1 = ((double)rand())/RAND_MAX;        if(r >= 0.5)            chrom[i][pos] = v - v1*r1*(1-((double)i)/maxgen)*(1-((double)i)/maxgen);        else            chrom[i][pos] = v + v2*r1*(1-((double)i)/maxgen)*(1-((double)i)/maxgen); // 注意这里写法是不会越界的，所以只用一次变异就可以了    }}//=================================================================================//=================================================================================// 主函数int main(void){int AA=20;    time_t start,finish;    start = clock(); // 程序开始计时    srand((unsigned)time(NULL)); // 初始化随机数种子    init_chrom(AA); // 初始化种群    double * best_fit_index = min(fitness);    int best_index =(int)(*best_fit_index);    gbest = *(best_fit_index+1); // 最优值    gbest_index = 0;    average_best[0] = sum(fitness)/sizepop; //初始平均最优值    for(int i=0;i<lenchrom;i++)        gbest_pos[i] = chrom[best_index][i];    // 进化开始    for(int i=0;i<maxgen;i++)    {        Select(chrom,AA); // 选择        Cross(chrom); //交叉        Mutation(chrom); //变异        for(int j=0;j<sizepop;j++)        {            fitness[j] = fit_func(chrom[j],AA);        }        double sum_fit = sum(fitness);        average_best[i+1] = sum_fit/sizepop; // 平均最优值        double * arr = min(fitness);        double new_best = *(arr+1);        int new_best_index = (int)(*arr); // 新最优值序号        if(new_best < gbest)        {            gbest = new_best;            for(int j=0;j<lenchrom;j++)            {                gbest_pos[j] = chrom[new_best_index][j];            }            gbest_index = i+1;        }    }    finish = clock(); // 程序计算结束    double duration = ((double)(finish-start))/CLOCKS_PER_SEC;    printf("程序计算耗时:%lf秒\n.",duration);    printf("遗传算法进化了%d次，最优值为:%lf,最优值在第%d代取得,此代的平均最优值为%lf.\n",maxgen,gbest,gbest_index,average_best[gbest_index]);    printf("取得最优值的地方为(%lf,%lf,%lf,%lf,%lf).\n",gbest_pos[0],gbest_pos[1],gbest_pos[2],gbest_pos[3],gbest_pos[4]);    return 0;}