演化计算是基于随即搜索的新算法；它的技术模型源于自然的演化。下面是一个例子，该函数是典型的多峰（震动剧烈）的函数。用的算法是郭涛算法。
问题：
求函数的最大值 :
f(x,y)=21.5+x*sin(4*PI*x)+y*sin(20*PI*y)
定义域 D: -3<=x<=12.1 , 4.1<=y<=5.8
目前最好结果：f(11.6255448,5.7250441)=38.8502944790207
程序在VC++.NET上调试，原代码如下（仅供参考）：
/*
* 类_Point表示二维空间的向量，即目标函数的自变量点
*
***************************************************************/
#pragma once
class _Point
{
public:
double x,y;
_Point(void):x(0),y(0)
{
}
_Point(double xx,double yy):x(xx),y(yy)
{
}
~_Point(void)
{
}
_Point & operator =(const _Point &point)
{
this->x=point.x;
this->y=point.y;
return *this;
}
_Point & operator +(const _Point &point)
{
this->x+=point.x;
this->y+=point.y;
return *this;
}
_Point & operator *(double k)
{
this->x*=k;
this->y*=k;
return *this;
}
};
/*
* name:percy lee
* e-mail:[email protected]
* time:2003-3-16
*
* compute the max_number of :
* f(x,y)=21.5+x*sin(4*PI*x)+y*sin(20*PI*y)
* D: -3<=x<=12.1 , 4.1<=y<=5.8
***************************************************************************/
#include <iostream>
#include <stdlib.h>
#include <time.h>
#include <math.h>
#include "_point.h"
using namespace std;
const int N=20;//种群规模
const int M=8; //子空间V的维度
const double MIN=0.000000009;//停机精确度
const double PI=3.14159265;
double Random(double min,double max);
int Random(int max);
double f(const _Point &point);
void Initialize_P();
_Point GetBestX();
_Point GetWorstX(int &i_worst);
_Point SelectX();
_Point P[N],x_best,x_worst,x_oldbest;
_Point Select[M],x;
void main()
{
clock_t start, finish;
/* Seed the random-number generator with current time so that
* the numbers will be different every time we run.
*/
srand((unsigned)time(NULL));
start=clock();
Initialize_P();
long int t=0; //迭代次数
int i_worst=0; //种群P中最差所在位置
double z_best=0.0,z_worst=0.0;
x_best=GetBestX();
x_oldbest=x_best;
x_worst=GetWorstX(i_worst);
z_best=f(x_best);
z_worst=f(x_worst);
while(z_best-z_worst>MIN)
{//迭代计算
x=SelectX();
if(x.x<-3||x.x>12.1||x.y<4.1||x.y>5.8)
continue;
if(f(x)>z_worst)
P[i_worst]=x;
else {//!
//
//
}
t++;
x_oldbest=x_best;
x_best=GetBestX();
x_worst=GetWorstX(i_worst);
z_best=f(x_best);
z_worst=f(x_worst);
//如果有提高，打印中间结果
if(z_best>f(x_oldbest)){
finish=clock();
cout<<"\nThe time is : "<<(finish-start)<<" ms..."<<endl;
cout.precision(14);
cout<<"f("<<x_best.x<<","<<x_best.y<<")="<<z_best<<endl;
}
}
finish=clock();
cout<<"\nThe time is : "<<(finish-start)<<" ms...";
cout<<"\nNow the answer(max of f) is :"<<endl;
cout.precision(14);
cout<<"f("<<x_best.x<<","<<x_best.y<<")="<<z_best<<endl<<endl;
}
/*
* 随机数产生函数（重载两个）
**/
double Random(double min,double max)
{
double randNum=0.0;
randNum=(double)rand()/RAND_MAX;
randNum*=(max-min);
randNum+=min;
return randNum;
}
int Random(int max)
{
int randNum=1;
randNum=(int)(max*((double)rand()/RAND_MAX));
return randNum;
}
/*
* 求最值的目标函数
**/
double f(const _Point &point)
{
double z=0.0;
z=point.x*sin(4*PI*point.x)+point.y*sin(20*PI*point.y)+21.5;
return z;
}
/*
* 初始化种群
**/
void Initialize_P()
{
for(int i=0;i<N;i++){
P[i].x=Random(-3,12.1);
P[i].y=Random(4.1,5.8);
}
}
/*
* 从种群p中获得最好与最坏个体
**/
_Point GetBestX()
{
_Point point=P[0];
double z=f(P[0]),zz;
for(int i=0;i<N;i++){
zz=f(P[i]);
if(z<zz){
z=zz;
point=P[i];
}
}
return point;
}
_Point GetWorstX(int &i_worst)
{
_Point point=P[0];
i_worst=0;
double z=f(P[0]),zz;
for(int i=0;i<N;i++){
zz=f(P[i]);
if(z>zz){
z=zz;
point=P[i];
i_worst=i;
}
}
return point;
}
/*
* 从种群P中随机选择M个个体，按照a[]（随机向量）要满足的条件：
* Sum(a[i])=1,i=1,2,...,M , & -0.5<=a[i]<=1.5
* 从子空间V中生成一个新个体
**/
_Point SelectX()
{
_Point point;
double a[M];
int i_rand=0；
double sum=0.0;
double MAX=1.5;
for(int i=0;i<M;i++){
i_rand=Random(N);
Select[i]=P[i_rand];
}
for(int i=0;i<M-1;i++){
a[i]=Random(-0.5,MAX);
MAX=1-a[i];
sum=sum+a[i];
}
a[M-1]=1-sum;
for(int i=0;i<M;i++)
point=point+Select[i]*a[i];
return point;
}
希望大家有兴趣的可共同研究。如果您能获得更好的结果，且您愿意与我分享，请与我e-mail联系，万分感激。
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