智能优化算法第一次作业--------------遗传算法洪文杰S151000853 问题：用遗传算法求解f(x)=xsin(10π*x)+2.0的最大值，x取[-1,2].一、分析：遗传算法基本思路二、实例简介1. 产生初始种群s1= 13 (01101)s2= 24 (11000)s3= 8 (01000)s4= 19 (10011)2. 计算适应度假定适应度为f(s)=s^2 ，则f (s1) = f(13) = 13^2 = 169 f (s2) = f(24) = 24^2 = 576 f (s3) = f(8) = 8^2 = 64f (s4) = f(19) = 19^2 = 3613. 选择染色体的选择概率为：染色体的累计概率为：根据上面的式子，可得到：例如设从区间［0, 1］中产生4个随机数: r1 = 0.450126, r2 = 0.110347 r3 = 0.572496, r4 = 0.985034. 交叉基本遗传算法（SGA）中交叉算子采用单点交叉算子。

单点交叉运算5. 变异6. 至下一代，适应度计算→选择→交叉→变异，直至满足终止条件三、解决问题四、实验结果源代码：/*问题：用遗传算法求解f(x)=xsin(10π*x)+2.0的最大值，x取[-1,2].*/ /*洪文杰2016-3-9. 智能优化算法第一次作业*/#include<iostream>//#includ<stdio.h>#include<stdlib.h>#include<math.h>#include<time.h>#include<float.h>using namespace std;#define NUMBER 50//种群规模#define GENE_NUMBER 10000//迭代次数int Unit[NUMBER][30];//初始种群int Unit_choose[NUMBER][30];//选择、交叉、变异后的种群int Number[NUMBER];//被选择的个体编号float Fitness[NUMBER];//适应度float select_probability[NUMBER];//选择概率float accumula_probability[NUMBER] ;//积累概率float f_max=0.0;//最大值float f_x=0.0;//最大值对应的自变量int hwj_coding(int start,int end);//编码void hwj_initial_population(int num);//产生初始种群void hwj_fitness(int num);//适应度计算void hwj_choose();//选择个体int hwj_binary_search(int l, int r,float temp);//查找选择//void hwj_N_M(int a[],int b[],int N, int M);//从M个数中选N个不一样的数void hwj_cross(int num,float cross);//交叉后的得到种群void hwj_aberrance(int num,float aberrance);//变异后的得到的种群void hwj_max(int num);//找到最适应的个体int main(){int strat,end;//区间int Num;//编码大小float cross=0.8;//交叉概率float aberrance = 0.04;//变异概率int key=1;cout<<"请输入求解区间:"<<endl;cin>>strat>>end;Num=hwj_coding(strat,end);cout<<"Num:"<<Num<<endl;// cout<<"--------------------------1-----------------"<<endl;hwj_initial_population(Num);// cout<<"--------------------------2初始种群-----------------"<<endl; /* for(int i=0;i<NUMBER;i++){for(int j=0;j<Num;j++){cout<<Unit[i][j]<<' ';}cout<<endl;}*/while(key!=GENE_NUMBER){hwj_fitness(Num);// cout<<"--------------------------3适应度-----------------"<<endl;// for(int i=0;i<NUMBER;i++){// cout<<Fitness[i]<<endl;// }hwj_choose();// cout<<"--------------------------4被选择的个体-----------------"<<endl; /* for(int i=0;i<NUMBER;i++){for(int j=0;j<Num;j++){cout<<Unit_choose[i][j]<<' ';}cout<<endl;}*/hwj_cross(Num,cross);/* cout<<"--------------------------5交叉后的种群-----------------"<<endl;for(int i=0;i<NUMBER;i++){for(int j=0;j<Num;j++){cout<<Unit[i][j]<<' ';}cout<<endl;}*/hwj_aberrance(Num,aberrance);/* cout<<"--------------------------6变异后的种群-----------------"<<endl;for(int i=0;i<NUMBER;i++){for(int j=0;j<Num;j++){cout<<Unit[i][j]<<' ';}cout<<endl;}*/key++;hwj_max(Num);}cout<<"最大值是对应的x值是:"<<endl;cout<<f_x<<endl;cout<<"最大值为:"<<f_max<<endl;return 0;}int hwj_coding(int start,int end){//种群编码float precision;int temp=2;int sum;int N=1;cout<<"请输入精度范围:"<<endl;cin>>precision;if(precision==0){cout<<"对不起精度不能为零:"<<endl;return 0;}else{sum=(end-start)/precision;cout<<"sum:"<<sum<<endl;while(temp<sum){temp*=2;N++;}return N;}}void hwj_initial_population(int num){//生成初始种群srand(time(NULL));for(int i=0;i<NUMBER;i++){for(int j=0;j<num;j++){Unit[i][j]=rand()%2;}}}void hwj_fitness(int num){//计算适应度float sum;int temp;for(int i=0;i<NUMBER;i++){temp=1;sum=0.0;for(int j=num-1;j>=0;j--){sum+=Unit[i][j]*temp;temp*=2.0;}Fitness[i]=sum*3/(temp-1.0)-1.0;// cout<<Fitness[i];// cout<<"--------------+++++";Fitness[i]=Fitness[i]*sin(10*3.1415926*Fitness[i])+2.0;// cout<<Fitness[i]<<endl;}}int hwj_binary_search(int l,int r,float temp){for(int i=0;i<NUMBER;i++){if(temp<=accumula_probability[i]&&temp>accumula_probability[i-1]){return i;}}return -1;}void hwj_choose(){//选择个体float sum=0.0;float temp;int i;for(i=0;i<NUMBER;i++){sum+=Fitness[i];}select_probability[0]=Fitness[0]/sum;temp=accumula_probability[0]=select_probability[0];for(i=1;i<NUMBER;i++){select_probability[i]=Fitness[i]/sum;temp+=select_probability[i];accumula_probability[i]=temp;// cout<<accumula_probability[i]<<endl;}for(i=0;i<NUMBER;i++){// srand(time(NULL));temp=(rand()%1000000)/1000000.0;// cout<<temp;Number[i]=hwj_binary_search(0,NUMBER,temp);// cout<<Number[i]<<endl;for(int j=0;j<NUMBER;j++){Unit_choose[i][j]=Unit[Number[i]][j];}}}/*void hwj_N_M(int a[],int b[],int N,int M){//从M个数中选N个不一样的数int i=1;srand(time(NULL));a[0]=rand()%M;b[a[0]]=1;while(i!=N){a[i]=rand()%M;if(b[a[i]]==0){i++;b[a[i]]=1;cout<<a[i]<<endl;}}// cout<<a[i]<<' '<<b[a[i]]<<endl;}*/void hwj_cross(int num,float cross){//交叉后的得到种群int num_cross=NUMBER*cross;int k;//交叉点int i , j;if(num_cross%2!=0){num_cross=num_cross+1;}//需要交叉的个体数int cro[NUMBER];//被交叉的个体编号int temp[NUMBER];//是否交叉数组一览for(i=0;i<NUMBER;i++){cro[i]=-1;temp[i]=0;}// hwj_N_M(cro,temp,num_cross,NUMBER);srand(time(NULL));cro[0]=rand()%NUMBER;temp[cro[0]]=1;i=1;while(i!=num_cross){cro[i]=rand()%NUMBER;if(temp[cro[i]]==0){temp[cro[i]]=1;i++;}}// for(int i=0;i<NUMBER;i++){// cout<<temp[i]<<" "<<cro[i]<<endl;// }// cout<<num_cross<<endl;for(i=0;i<num_cross/2;i++){srand(time(NULL));k=rand()%num;for(j=0;j<num;j++){if(j<=k){Unit[i][j]=Unit_choose[cro[num_cross-i]][j];Unit[i+num_cross/2][j]=Unit_choose[cro[i]][j];}else{Unit[i][j]=Unit_choose[cro[i]][j];Unit[i+num_cross/2][j]=Unit_choose[cro[i]][j];}}}for(i=0;i<NUMBER;i++){// cout<<temp[i]<<endl;if(temp[i]==0){for(j=0;j<num;j++){Unit[num_cross][j]=Unit_choose[i][j];}num_cross++;}}}void hwj_aberrance(int num,float aberrance){//变异后的得到的种群int num_aberrance=NUMBER*aberrance;//变异的个体数int k;//变异点int abe[NUMBER];//变异的个体编号int temp[NUMBER];//是否变异数组一览int i,j,p;for(i=0;i<NUMBER;i++){abe[i]=-1;temp[i]=0;}// hwj_N_M(cro,temp,num_cross,NUMBER);srand(time(NULL));abe[0]=rand()%NUMBER;temp[abe[0]]=1;i=1;while(i!=num_aberrance){abe[i]=rand()%NUMBER;if(temp[abe[i]]==0){temp[abe[i]]=1;i++;}}for( i=0;i<NUMBER;i++){for( j=0;j<num_aberrance;j++){if(i==abe[j]){k=rand()%num;for( p=0;p<num;p++){if(p==k){if(Unit[i][p]==1){Unit[i][p]==0;}else{Unit[i][p]==1;}}}}}}}void hwj_max(int num){hwj_fitness(num);// float max=0.0;int i;int temp=1;float sum=0.0;int k;for(i=0;i<NUMBER;i++){// cout<<Fitness[i]<<endl;if(Fitness[i]>f_max){f_max=Fitness[i];k=i;}}for(int j=num-1;j>=0;j--){sum+=Unit[k][j]*temp;temp*=2.0;}f_x=sum*3/(temp-1.0)-1.0;}。