結果：極值點（-3.141593，5.141593）
我又算了壹下-100到100之間的極大值
結果：極值點（-97.399473,99.394504)
-1000到1000之間的極大值
結果：（999，1001）
-2000到2000之間的極大值
結果：（1998.053550，2000.053163）
以上結果我用matlab畫圖驗證了，沒問題。
希望再給加點分，呵呵
//中國電子科技集團公司
//第壹研究室
//呼文韜
//hu_hu605@163.com
//隨機初始種群
//編碼方式為格雷碼
//選擇方法為隨機遍歷
//采用了精英保存策略
//采用了自適應的交叉率和變異率
//采用了與模擬退火算法相結合的尺度變換
//采用了均勻交叉法
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <iostream.h>
#include <iomanip.h>
#include <time.h>
#include <windows.h>
#define IM1 2147483563
#define IM2 2147483399
#define AM (1.0/IM1)
#define IMM1 (IM1-1)
#define IA1 40014
#define IA2 40692
#define IQ1 53668
#define IQ2 52774
#define IR1 12211
#define IR2 3791
#define NTAB 32
#define NDIV (1+IMM1/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0-EPS)
#define zhizhenjuli 0.005
#define PI 3.14159265358
#define T0 100000//溫度要取得很高才行。
#define zhongqunshu1 200
#define zuobianjie -2000
#define youbianjie 2000
unsigned int seed=0; //seed 為種子，要設為全局變量
void mysrand(long int i) //初始化種子
{
seed = -i;
}
long a[1];
//double hundun;
//double c=4;
//設置全局變量
struct individual
{
unsigned *chrom; //染色體；
double geti;//變量值
double shiyingdu; //目標函數的值；
double fitness; //變換後的適應度值；
};
individual *zuiyougeti;//精英保存策略
int zhongqunshu; //種群大小
individual *nowpop;//當前代
individual *newpop;//新壹代
double sumfitness;//當代的總適應度fitness
double sumshiyingdu;//當代的總適應度shiyingdu
double maxfitness;//最大適應度
double avefitness;//平均適應度
double maxshiyingdu;//最大適應度
double avgshiyingdu;//平均適應度
float pc;//交叉概率
float pm;//變異概率
int lchrom;//染色體長度
int maxgen;//最大遺傳代數
int gen;//遺傳代數
//函數
int flipc(double ,double );//判斷是否交叉
int flipm(double );//判斷是否變異
int rnd(int low,int high);//產生low與high之間的任意數
void initialize();//遺傳算法初始化
void preselectfitness(); //計算sumfiness,avefitness,maxfitness
void generation();
double suijibianli();//產生隨機遍歷指針
int fuzhi(float );//選擇要復制的個體
void crossover(individual ,individual ,individual &,individual &);//交叉
void bianyi(individual &);//變異
void mubiaohanshu(individual &);//計算適應度
void chidubianhuan(individual &);//對shiyingdu進行尺度變換賦給fitness
double ran1(long *);//隨機數初始
void bianma(double bianliang,unsigned *p);//編碼
double yima(unsigned *p);
void guanjiancanshujisuan();//計算shiyingdu,根據shiyingdu計算sumshiyingdu,對shiyingdu進行尺度變換變成fitness,根據fitness計算sumfitness，avefitness，maxfitness
void jingyingbaoliu();
void glp(int n,int s,int *,int (*)[1],float (*)[1]);//glp生成函數
BOOL Exist(int Val, int Num, int *Array);//判斷壹個數在前面是否出現過
int cmpfitness(const void *p1,const void *p2)
{
float i=((individual *)p1)->shiyingdu;//現在是按照"適應度"排序，改成"個體"的話就是按照"個體"排序
float j=((individual *)p2)->shiyingdu;
return i<j ? -1:(i==j ? 0:1);//現在是按升序牌排列，將1和-1互換後就是按降序排列
}
void main()
{
initialize();
cout<<zuiyougeti->geti<<" "<<zuiyougeti->shiyingdu<<endl;/////////////
for(gen=1;gen<maxgen;gen++)
{ generation();
}
jingyingbaoliu();
cout<<setiosflags(ios::fixed)<<setprecision(6)<<zuiyougeti->geti<<" "<<setiosflags(ios::fixed)<<setprecision(6)<<(zuiyougeti->shiyingdu)<<endl;////////////////
delete [] newpop;
delete [] nowpop;
delete [] zuiyougeti;
system("pause");
}
void initialize()
{
int q[zhongqunshu1][1],s=1;
float xx[zhongqunshu1][1];//生成的glp用x儲存
int h[1]={1};//生成向量
zuiyougeti=new individual;//最優個體的生成
zhongqunshu=200;//種群數量
nowpop=new individual[zhongqunshu1];//當代
newpop=new individual[zhongqunshu1];//新壹代
maxgen=150;//最大代數
gen=0;//起始代
lchrom=22;//基因數量的初始化
mysrand(time(0));//隨機數種子
a[0]=seed;//隨機數種子
//對最優個體的初始化
zuiyougeti->geti=0;
zuiyougeti->fitness=0;
zuiyougeti->shiyingdu=0;
//
glp(zhongqunshu,s,h,q,xx);
//for(int i=0;i<zhongqunshu1;i++)//產生初始種群
//{
// for(int j=0;j<s;j++)
// {
// nowpop[i].geti=zuobianjie+(youbianjie-zuobianjie)*xx[i][j];
// }
//}
for(int i=0;i<zhongqunshu1;i++)//產生初始種群
{
nowpop[i].geti=zuobianjie+(youbianjie-(zuobianjie))*ran1(a);
}
//nowpop[0].geti=999;//////////////////////////
guanjiancanshujisuan();
jingyingbaoliu(); //精英保留的實現
guanjiancanshujisuan();//計算shiyingdu,根據shiyingdu計算sumshiyingdu,對shiyingdu進行尺度變換變成fitness,根據fitness計算sumfitness，avefitness，maxfitness
}
void jingyingbaoliu() //精英保留的實現
{
individual *zuiyougetiguodu;
zuiyougetiguodu=new individual[zhongqunshu1];//建立壹個過渡數組
for(int i=0;i<zhongqunshu;i++)//將當代個體復制到過渡數組中
zuiyougetiguodu[i]=nowpop[i];
qsort(zuiyougetiguodu,zhongqunshu1,sizeof(individual),&cmpfitness);//按fitness升序排序
// cout<<"zuiyougetiguodu適應度:"<<zuiyougetiguodu[zhongqunshu1-1].shiyingdu<<endl;///////////
// cout<<"zuiyougeti適應度:"<<zuiyougeti->shiyingdu<<endl;///////////////////
//system("pause");
if(zuiyougetiguodu[zhongqunshu-1].shiyingdu>zuiyougeti->shiyingdu)
{
*zuiyougeti=zuiyougetiguodu[zhongqunshu1-1];//如果最優個體的fitness比當代最大的fitness小則用當代的代替之
//cout<<"zuiyougetiguodu個體:"<<zuiyougetiguodu[zhongqunshu1-1].geti<<endl;/////////////
//cout<<"zuiyougeti個體:"<<zuiyougeti->geti<<endl;/////////////
}
else
nowpop[rnd(0,(zhongqunshu1-1))]=*zuiyougeti;//否則的話從當代中隨機挑選壹個用最優個體代替之
delete [] zuiyougetiguodu;//釋放過渡數組
}
void guanjiancanshujisuan()//計算shiyingdu,根據shiyingdu計算sumshiyingdu,對shiyingdu進行尺度變換變成fitness,根據fitness計算sumfitness，avefitness，maxfitness
{
for(int i=0;i<zhongqunshu;i++)//計算shiyingdu
mubiaohanshu(nowpop[i]);
for(i=0;i<zhongqunshu;i++)//對shiyingdu進行尺度變換變成fitness
chidubianhuan(nowpop[i]);
preselectfitness();//根據fitness計算sumfitness，avefitness，maxfitness
}
void mubiaohanshu(individual &bianliang)//計算shiyingdu
{
bianliang.shiyingdu=(bianliang.geti*cos(bianliang.geti)+2.0);//目標函數
}
void chidubianhuan(individual &bianliang)//對shiyingdu進行尺度變換變成fitness
{
double T;//退火溫度
T=T0*(pow(0.99,(gen+1-1)));
double sum=0;
for(int j=0;j<zhongqunshu;j++)
sum+=exp(nowpop[j].shiyingdu/T);
bianliang.fitness=exp(bianliang.shiyingdu/T)/sum;//算出fitness
}
void preselectfitness()//根據fitness計算sumfitness，avefitness，maxfitness
{
int j;
sumfitness=0;
for(j=0;j<zhongqunshu;j++)
sumfitness+=nowpop[j].fitness;
individual *guodu;
guodu=new individual[zhongqunshu1];
for(j=0;j<zhongqunshu;j++)
guodu[j]=nowpop[j];
qsort(guodu,zhongqunshu1,sizeof(individual),&cmpfitness);
maxfitness=guodu[zhongqunshu1-1].fitness;
avefitness=sumfitness/zhongqunshu1;
delete [] guodu;
}
void generation()
{
individual fuqin1,fuqin2,*pipeiguodu,*pipeichi;
int *peiduishuzu;//用來存放產生的隨機配對
pipeiguodu=new individual[zhongqunshu1];
pipeichi=new individual[zhongqunshu1];
peiduishuzu=new int[zhongqunshu1];
int member1,member2,j=0,fuzhijishu=0,i=0,temp=0,tt=0;
float zhizhen;
//隨機遍歷的實現
for(zhizhen=suijibianli();zhizhen<1;(zhizhen=zhizhen+zhizhenjuli))//設定指針1/66
{
pipeichi[fuzhijishu]=nowpop[fuzhi(zhizhen)];
fuzhijishu++;
}
//交叉與變異的實現
//交叉
for(i=0;i<zhongqunshu1;i++)
{
peiduishuzu[i]=-1;
}
for (i=0; i<zhongqunshu1; i++)
{
temp =rnd(0,zhongqunshu1-1); //產生值在0-zhongqunshu1-1的隨機數
while(Exist(temp, i, peiduishuzu))//判斷產生的隨機數是否已經產生過，如果是，則再產生壹個隨機數
{
temp =rnd(0,zhongqunshu1-1);
}
//如果沒有的話，則把產生的隨機數放在peiduishuzu中
*(peiduishuzu+i) = temp;
}
for(i=0;i<zhongqunshu1-1;i=i+2)
{
fuqin1=pipeichi[peiduishuzu[i]];
fuqin2=pipeichi[peiduishuzu[i+1]];
crossover(fuqin1,fuqin2,newpop[i],newpop[i+1]);
}
for(j=0;j<zhongqunshu1;j++)
{
//if(newpop[j].geti<-1000)
//cout<<"個體數值小於下界了";
nowpop[j].geti=newpop[j].geti;
}
//
guanjiancanshujisuan();
//變異的實現
for(j=0;j<zhongqunshu;j++)
{
bianyi(nowpop[j]);
}
//
guanjiancanshujisuan();
//精英保留的實現
jingyingbaoliu();
//
guanjiancanshujisuan();
delete [] peiduishuzu;
delete [] pipeichi;
delete [] pipeiguodu;
}
void crossover(individual parent1,individual parent2,individual &child1,individual &child2)//交叉
{
int j;
unsigned *panduan;
panduan=new unsigned[lchrom];
parent1.chrom=new unsigned[lchrom];
parent2.chrom=new unsigned[lchrom];
child1.chrom=new unsigned[lchrom];
child2.chrom=new unsigned[lchrom];
//cout<<"jiaocha"<<endl;///////////////////////
bianma(parent1.geti,parent1.chrom);
bianma(parent2.geti,parent2.chrom);
if(flipc(parent1.fitness,parent2.fitness))
{
for(j=0;j<lchrom;j++)
panduan[j]=rnd(0,1);
//for(j=0;j<lchrom;j++)////////////////
// {
// cout<<panduan[j];/////////////
// }
// cout<<endl;////////////////
// system("pause");////////////////
for(j=0;j<lchrom;j++)
{
if(panduan[j]==1)
child1.chrom[j]=parent1.chrom[j];
else
child1.chrom[j]=parent2.chrom[j];
}
for(j=0;j<lchrom;j++)
{
if(panduan[j]==0)
child2.chrom[j]=parent1.chrom[j];
else
child2.chrom[j]=parent2.chrom[j];
}
//for(j=0;j<lchrom;j++)////////////////
//{
// cout<<child1.chrom[j];/////////////
// }
//cout<<endl;////////////////
// system("pause");////////////////
child1.geti=yima(child1.chrom);
child2.geti=yima(child2.chrom);
delete [] child2.chrom;
delete [] child1.chrom;
delete [] parent2.chrom;
delete [] parent1.chrom;
delete [] panduan;
}
else
{
for(j=0;j<lchrom;j++)
{
child1.chrom[j]=parent1.chrom[j];
child2.chrom[j]=parent2.chrom[j];
}
child1.geti=yima(child1.chrom);
child2.geti=yima(child2.chrom);
delete [] child2.chrom;
delete [] child1.chrom;
delete [] parent2.chrom;
delete [] parent1.chrom;
delete [] panduan;
}
}
void bianyi(individual &child)//變異
{
child.chrom=new unsigned[lchrom];
//cout<<"變異"<<endl;
bianma(child.geti,child.chrom);
for(int i=0;i<lchrom;i++)
if(flipm(child.fitness))
{
if(child.chrom[i]=0)
child.chrom[i]=1;
else
child.chrom[i]=0;
}
child.geti=yima(child.chrom);
delete [] child.chrom;
}
void bianma(double bianliang,unsigned *p)//編碼
{
unsigned *q;
unsigned *gray;
q=new unsigned[lchrom];
gray=new unsigned[lchrom];
int x=0;
int i=0,j=0;
if(bianliang<zuobianjie)///////////////////
{
cout<<"bianliang:"<<bianliang<<endl;/////////
system("pause");
}
//cout<<youbianjie-(zuobianjie)<<endl;
//system("pause");
x=(bianliang-(zuobianjie))*((pow(2,lchrom)-1)/(youbianjie-(zuobianjie)));
//cout<<x<<endl;///////////
if(x<0)
system("pause");///////////
for(i=0;i<lchrom;i++)
{
q[i]=0;
p[i]=0;
}
i=0;
while (x!=0&&(i!=lchrom))
{
q[i]=(unsigned)(x%2);
x=x/2;
i++;
}
// for(i=0;i<lchrom;i++)//////////////////
// cout<<q[i];///////////////
// cout<<endl;///////////
int w=lchrom-1;
if(q[w]!=0&&q[w]!=1)
system("pause");
for(j=0;j<lchrom&&w>0;j++)
{
p[j]=q[w];
w--;
}
//cout<<"yuanma"<<endl;
//for(j=0;j<lchrom;j++)///////////
// cout<<p[j];////////
//cout<<endl;////////////////////
gray[0]=p[0];
for(j=1;j<lchrom;j++)
{
if(p[j-1]==p[j])
gray[j]=0;
else if(p[j-1]!=p[j])
gray[j]=1;
}
for(j=0;j<lchrom;j++)
p[j]=gray[j];
//cout<<"geleima"<<endl;
//for(j=0;j<lchrom;j++)///////////
// cout<<p[j];////////
//cout<<endl;////////////////////
//system("pause");///////////
delete [] gray;
delete [] q;
}
double yima(unsigned *p) //譯碼
{
int i=0;
// for(i=0;i<lchrom;i++)/////////
// {
// cout<<p[i];//////
// }
// cout<<endl;/////////
// system("pause");//////////
int x=0;
unsigned *q;
q=new unsigned[lchrom];
q[0]=p[0];
// cout<<q[0]<<endl;//////////////////
// system("pause");//////////
for(int j=1;j<lchrom;j++)
{
if(q[j-1]==p[j])
q[j]=0;
else if(q[j-1]!=p[j])
q[j]=1;
}
// for(i=0;i<lchrom;i++)//////
// {
// cout<<q[i];//////////
// if(q[i]!=0&&q[i]!=1)
// {
// cout<<q[i];
// system("pause");
// }
// }
// cout<<endl;////////
// system("pause");///////////////////
for(i=0;i<lchrom;i++)
x=x+q[i]*pow(2,(lchrom-i-1));
if(x<0)
{
cout<<"譯碼出錯1"<<endl;
system("pause");
}
//cout<<"x:"<<x<<endl;
double bianliang;
//cout<<pow(2,22)<<endl;
//cout<<2000*x<<endl;
//cout<<(x*(2000/(pow(2,22)-1)))<<endl;
bianliang=(x*((youbianjie-(zuobianjie))/(pow(2,lchrom)-1)))+zuobianjie;
if(bianliang<zuobianjie)
{
cout<<"譯碼出錯2"<<endl;
system("pause");
}
delete [] q;
return bianliang;
}
double ran1(long *idum)
{
int j;
long k;
static long idum2=123456789;
static long iy=0;
static long iv[NTAB];
float temp;
if (*idum <= 0)
{
if (-(*idum) < 1) *idum=1;
else *idum = -(*idum);
idum2=(*idum);
for (j=NTAB+7;j>=0;j--)
{
k=(*idum)/IQ1;
*idum=IA1*(*idum-k*IQ1)-k*IR1;
if (*idum < 0) *idum += IM1;
if (j < NTAB) iv[j] = *idum;
}
iy=iv[0];
}
k=(*idum)/IQ1;
*idum=IA1*(*idum-k*IQ1)-k*IR1;
if (*idum < 0) *idum += IM1;
k=idum2/IQ2;
idum2=IA2*(idum2-k*IQ2)-k*IR2;
if (idum2 < 0) idum2 += IM2;
j=iy/NDIV;
iy=iv[j]-idum2;
iv[j] = *idum;
if (iy < 1) iy += IMM1;
if ((temp=AM*iy) > RNMX) return RNMX;
else return temp;
}
double suijibianli()//隨機遍歷
{
double i=ran1(a);
while(i>zhizhenjuli)
{
i=ran1(a);
}
//cout<<i<<endl;//////////////
return i;
}
int fuzhi(float p)//復制
{
int i;
double sum=0;
if(sumfitness!=0)
{
for(i=0;(sum<p)&&(i<zhongqunshu);i++)
sum+=nowpop[i].fitness/sumfitness;
}
else
i=rnd(1,zhongqunshu1);
return(i-1);
}
int rnd(int low, int high) /*在整數low和high之間產生壹個隨機整數*/
{
int i;
if(low >= high)
i = low;
else
{
i =(int)((ran1(a) * (high - low + 1)) + low);
if(i > high) i = high;
}
return(i);
}
int flipc(double p,double q)//判斷是否交叉
{
double pc1=0.9,pc2=0.6;
if((p-q)>0)
{
if(p>=avefitness)
{
pc=pc1-(pc1-pc2)*(p-avefitness)/(maxfitness-avefitness);
}
else
pc=pc1;
}
else
{
if(q>=avefitness)
{
pc=pc1-(pc1-pc2)*(q-avefitness)/(maxfitness-avefitness);
}
else
pc=pc1;
}
if(ran1(a)<=pc)
return(1);
else
return(0);
}
int flipm(double p)//判斷是否變異
{
double pm1=0.001,pm2=0.0001;
if(p>=avefitness)
{
pm=(pm1-(pm1-pm2)*(maxfitness-p)/(maxfitness-avefitness));
}
else
pm=pm1;
if(ran1(a)<=pm)
return(1);
else
return(0);
}
void glp(int n,int s,int *h,int (*q)[1],float (*xx)[1])//glp
{
int i=0,j=0;
//求解q
for(i=0;i<n;i++)
{
for(j=0;j<s;j++)
{
*(*(q+i)+j)=((i+1)*(*(h+j)))%n;
}
}
i=n-1;
for(j=0;j<s;j++)
{
*(*(q+i)+j)=n;
}
//求解x
for(i=0;i<n;i++)
{
for(j=0;j<s;j++)
{
*(*(xx+i)+j)=(float)(2*(*(*(q+i)+j))-1)/(2*n);
}
}
}
BOOL Exist(int Val, int Num, int *Array)//判斷壹個數是否在壹個數組的前Num個數中
{
BOOL FLAG = FALSE;
int i;
for (i=0; i<Num; i++)
if (Val == *(Array + i))
{
FLAG = TRUE;
break;
}
return FLAG;
}