遗传算法求函数极值

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)+的最大值，x取[-1,2].一、剖析：遗传算法基本思路二、实例简介产生初始种群s1=13(01101)s2=24(11000)s3=8(01000)s4=19(10011)计算适应度假设适应度为f(s)=s^2，则f(s1)=f(13)=13^2=169f(s2)=f(24)=24^2=576f(s3)=f(8)=8^2=64f(s4)=f(19)=19^2=361选择染色体的选择概率为：染色体的累计概率为：依据上边的式子，可获得：比如设从区间［0,1］中产生4个随机数:r1=,r2=r3=,r4=交错基本遗传算法（SGA）中交错算子采纳单点交错算子。单点交错运算变异至下一代，适应度计算→选择→交错→变异，直至知足停止条件三、解决问题初始化输入种群大小，交错概率，变异概率等条件依据精度编码将区间[-1,2]分红Num份，再经过Num求解种群基因个数计算每个个体的适应度，该题适应度函数就是f(X)依据适应度求解累积概率，并用轮盘赌法选着个体产生备选种群在备选种群中，利用交错概率，随机选择个体，再随机选择交错点进在交错后种群中，利用变异概率，随机选择个体，再随机选择变异点是否输出结果最大能否达到值。四、实验结果源代码：/*问题：用遗传算法求解f(x)=xsin(10π*x)+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<>#include<>#include<>#include<>#include<>usingnamespacestd;#defineNUMBER50//种群规模#defineGENE_NUMBER10000//迭代次数intUnit[NUMBER][30];//初始种群intUnit_choose[NUMBER][30];//选择、交错、变异后的种群intNumber[NUMBER];//被选择的个体编号floatFitness[NUMBER];//适应度floatselect_probability[NUMBER];//选择概率floataccumula_probability[NUMBER];//累积概率floatf_max=;//最大值floatf_x=;//最大值对应的自变量inthwj_coding(intstart,intend);//编码voidhwj_initial_population(intnum);//产生初始种群voidhwj_fitness(intnum);//适应度计算voidhwj_choose();//选择个体inthwj_binary_search(intl,intr,floattemp);//查找选择//voidhwj_N_M(inta[],intb[],intN,intM);//从M个数中选N个不同样的数voidhwj_cross(intnum,floatcross);//交错后的获得种群voidhwj_aberrance(intnum,floataberrance);//变异后的获得的种群voidhwj_max(intnum);//找到最适应的个体intmain(){intstrat,end;//区间intNum;//编码大小floatcross=;//交错概率floataberrance=;//变异概率intkey=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(inti=0;i<NUMBER;i++){for(intj=0;j<Num;j++){cout<<Unit[i][j]<<'';}cout<<endl;}*/while(key!=GENE_NUMBER){hwj_fitness(Num);//

cout<<"--------------------------3

适应度

-----------------"<<endl;for(inti=0;i<NUMBER;i++){cout<<Fitness[i]<<endl;}hwj_choose();//cout<<"--------------------------4被选择的个体-----------------"<<endl;/*for(inti=0;i<NUMBER;i++){for(intj=0;j<Num;j++){cout<<Unit_choose[i][j]<<'';}cout<<endl;}*/hwj_cross(Num,cross);/*cout<<"--------------------------5交错后的种群-----------------"<<endl;for(inti=0;i<NUMBER;i++){for(intj=0;j<Num;j++){cout<<Unit[i][j]<<'';}cout<<endl;}*/hwj_aberrance(Num,aberrance);/*

cout<<"--------------------------6

变异后的种群

-----------------"<<endl;for(inti=0;i<NUMBER;i++){for(intj=0;j<Num;j++){cout<<Unit[i][j]<<'';}cout<<endl;}*/key++;hwj_max(Num);}cout<<"最大值是对应的cout<<f_x<<endl;

x值是:"<<endl;cout<<"最大值为:"<<f_max<<endl;return0;}inthwj_coding(intstart,intend){//种群编码floatprecision;inttemp=2;intsum;intN=1;cout<<"请输入精度范围:"<<endl;cin>>precision;if(precision==0){cout<<"对不起精度不可以为零:"<<endl;return0;}else{sum=(end-start)/precision;cout<<"sum:"<<sum<<endl;while(temp<sum){temp*=2;N++;}returnN;}}voidhwj_initial_population(intnum){//srand(time(NULL));for(inti=0;i<NUMBER;i++){for(intj=0;j<num;j++){Unit[i][j]=rand()%2;

生成初始种群}}}voidhwj_fitness(intnum){//计算适应度floatsum;inttemp;for(inti=0;i<NUMBER;i++){temp=1;sum=;for(intj=num-1;j>=0;j--){sum+=Unit[i][j]*temp;temp*=;}Fitness[i]=sum*3/;cout<<Fitness[i];cout<<"--------------+++++";Fitness[i]=Fitness[i]*sin(10**Fitness[i])+;cout<<Fitness[i]<<endl;}}inthwj_binary_search(intl,intr,floattemp){for(inti=0;i<NUMBER;i++){if(temp<=accumula_probability[i]&&temp>accumula_probability[i-1]){returni;}}return-1;}voidhwj_choose(){//选择个体floatsum=;floattemp;inti;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)/;cout<<temp;Number[i]=hwj_binary_search(0,NUMBER,temp);cout<<Number[i]<<endl;for(intj=0;j<NUMBER;j++){Unit_choose[i][j]=Unit[Number[i]][j];}}}/*voidhwj_N_M(inta[],intb[],intN,intM){//从M个数中选N个不同样的数inti=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;}*/voidhwj_cross(intnum,floatcross){//交错后的获得种群intnum_cross=NUMBER*cross;intk;//交错点inti,j;if(num_cross%2!=0){num_cross=num_cross+1;}//需要交错的个体数intcro[NUMBER];//被交错的个体编号inttemp[NUMBER];//能否交错数组一览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(inti=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++;}}}voidhwj_aberrance(intnum,floataberrance){//变异后的获得的种群intnum_aberrance=NUMBER*aberrance;//变异的个体数intk;//变异点intabe[NUMBER];//变异的个体编号inttemp[NUMBER];//能否变异数组一览inti,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){i