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C++遗传算法源程序

// CMVSOGA.h : main header file for the CMVSOGA.cpp
////////////////////////////////////////////////////////////////////
/////                                                          /////
/////                沈阳航空工业学院 动力工程系               /////
/////                       作者：李立新                       /////
/////                   完成日期：2006.08.02                   /////
/////                   修改日期：2007.04.10                                       /////
////////////////////////////////////////////////////////////////////

#if !defined(AFX_CMVSOGA_H__45BECA_61EB_4A0E_9746_9A94D1CCF767__INCLUDED_)
#define AFX_CMVSOGA_H__45BECA_61EB_4A0E_9746_9A94D1CCF767__INCLUDED_

#if _MSC_VER > 1000
#pragma once
#endif // _MSC_VER > 1000
#include "Afxtempl.h"
#define variablenum 14
class CMVSOGA
{
public:
 CMVSOGA();
 ~CMVSOGA();
 void selectionoperator();
 void crossoveroperator();
 void mutationoperator();
 void initialpopulation(int, int ,double ,double,double *,double *);           //种群初始化
 void generatenextpopulation();          //生成下一代种群
 void evaluatepopulation();           //评价个体，求最佳个体
 void calculateobjectvalue();          //计算目标函数值
 void calculatefitnessvalue();          //计算适应度函数值
 void findbestandworstindividual();         //寻找最佳个体和最差个体
 void performevolution();   
 void GetResult(double *);
 void GetPopData(CList <double,double>&);
 void SetFitnessData(CList <double,double>&,CList <double,double>&,CList <double,double>&);
private:
 struct individual
 {
  double chromosome[variablenum];         //染色体编码长度应该为变量的个数
  double value;        
  double fitness;             //适应度
 };
 double variabletop[variablenum];         //变量值
 double variablebottom[variablenum];         //变量值
 int popsize;              //种群大小
// int generation;              //世代数
 int best_index;  
 int worst_index;
 double crossoverrate;            //交叉率
 double mutationrate;            //变异率
 int maxgeneration;             //最大世代数
 struct individual bestindividual;         //最佳个体
 struct individual worstindividual;         //最差个体
 struct individual current;              //当前个体
 struct individual current1;              //当前个体
 struct individual currentbest;          //当前最佳个体
 CList <struct individual,struct individual &> population;   //种群
 CList <struct individual,struct individual &> newpopulation;  //新种群
 CList <double,double> cfitness;          //存储适应度值
 //怎样使链表的数据是一个结构体????主要是想把种群作成链表。节省空间。
};
#endif

 

执行文件：

// CMVSOGA.cpp : implementation file
//

#include "stdafx.h"
//#include "vld.h"
#include "CMVSOGA.h"
#include "math.h"
#include "stdlib.h"


#ifdef _DEBUG
#define new DEBUG_NEW
#undef THIS_FILE
static char THIS_FILE[] = __FILE__;
#endif
/////////////////////////////////////////////////////////////////////////////
// CMVSOGA.cpp
CMVSOGA::CMVSOGA()
{
 best_index=0;  
 worst_index=0;
 crossoverrate=0;            //交叉率
 mutationrate=0;            //变异率
 maxgeneration=0;
}
CMVSOGA::~CMVSOGA()
{
 best_index=0;  
 worst_index=0;
 crossoverrate=0;            //交叉率
 mutationrate=0;            //变异率
 maxgeneration=0;
 population.RemoveAll();   //种群
 newpopulation.RemoveAll();  //新种群
 cfitness.RemoveAll(); 
}
void CMVSOGA::initialpopulation(int ps, int gen ,double cr ,double mr,double *xtop,double *xbottom)  //第一步，初始化。
{
 //应该采用一定的策略来保证遗传算法的初始化合理，采用产生正态分布随机数初始化？选定中心点为多少？
 int i,j;
 popsize=ps;
 maxgeneration=gen;
 crossoverrate=cr;
 mutationrate =mr;
 for (i=0;i<variablenum;i++)
 {
  variabletop[i] =xtop[i];
  variablebottom[i] =xbottom[i];
 }
 //srand( (unsigned)time( NULL ) );  //寻找一个真正的随机数生成函数。
 for(i=0;i<popsize;i++)
 { 
  for (j=0;j<variablenum ;j++)
  {
   current.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
  }
  current.fitness=0;
  current.value=0;
  population.InsertAfter(population.FindIndex(i),current);//除了初始化使用insertafter外,其他的用setat命令。
 }
}
void CMVSOGA::generatenextpopulation()//第三步，生成下一代。
{
 //srand( (unsigned)time( NULL ) );
 selectionoperator();
 crossoveroperator();
 mutationoperator();
}
//void CMVSOGA::evaluatepopulation()   //第二步，评价个体，求最佳个体
//{
// calculateobjectvalue();
// calculatefitnessvalue();   //在此步中因该按适应度值进行排序.链表的排序.
// findbestandworstindividual();
//}
void CMVSOGA:: calculateobjectvalue()  //计算函数值，应该由外部函数实现。主要因为目标函数很复杂。
{
 int i,j;
    double x[variablenum];
 for (i=0; i<popsize; i++)
 {
  current=population.GetAt(population.FindIndex(i)); 
  current.value=0;
  //使用外部函数进行，在此只做结果的传递。
  for (j=0;j<variablenum;j++)
  {
   x[j]=current.chromosome[j];
   current.value=current.value+(j+1)*pow(x[j],4);
  }
  ////使用外部函数进行，在此只做结果的传递。
  population.SetAt(population.FindIndex(i),current);
 }
}

void CMVSOGA::mutationoperator()  //对于浮点数编码，变异算子的选择具有决定意义。
          //需要guass正态分布函数，生成方差为sigma，均值为浮点数编码值c。
{
// srand((unsigned int) time (NULL));
 int i,j;
 double r1,r2,p,sigma;//sigma高斯变异参数
 
 for (i=0;i<popsize;i++)
 {
  current=population.GetAt(population.FindIndex(i));

  //生成均值为current.chromosome，方差为sigma的高斯分布数
  for(j=0; j<variablenum; j++)
  {   
   r1 = double(rand()%10001)/10000;
   r2 = double(rand()%10001)/10000;
   p = double(rand()%10000)/10000;
   if(p<mutationrate)
   {
    double sign;
    sign=rand()%2;
    sigma=0.01*(variabletop[j]-variablebottom [j]);
    //高斯变异
    if(sign)
    {
     current.chromosome[j] = (current.chromosome[j]
      + sigma*sqrt(-2*log(r1)/0.4323)*sin(2*3.1415926*r2));
    }
    else
    {
     current.chromosome[j] = (current.chromosome[j]
      - sigma*sqrt(-2*log(r1)/0.4323)*sin(2*3.1415926*r2));
    }
    if (current.chromosome[j]>variabletop[j])
    {
     current.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
    }
    if (current.chromosome[j]<variablebottom [j])
    {
     current.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
    }
   }
  }
  population.SetAt(population.FindIndex(i),current);
 }
}
void CMVSOGA::selectionoperator()   //从当前个体中按概率选择新种群,应该加一个复制选择,提高种群的平均适应度
{
 int i,j,pindex=0;
 double p,pc,sum;
 i=0;
 j=0;
 pindex=0;
 p=0;
 pc=0;
 sum=0.001;
 newpopulation.RemoveAll();
 cfitness.RemoveAll();
  //链表排序
// population.SetAt (population.FindIndex(0),current); //多余代码
 for (i=1;i<popsize;i++)
 { 
  current=population.GetAt(population.FindIndex(i));
  for(j=0;j<i;j++)   //从小到大用before排列。
  {
   current1=population.GetAt(population.FindIndex(j));//临时借用变量
   if(current.fitness<=current1.fitness)  
   {
    population.InsertBefore(population.FindIndex(j),current);
    population.RemoveAt(population.FindIndex(i+1));
    break;
   }
  }
//  m=population.GetCount();
 }
 //链表排序
 for(i=0;i<popsize;i++)//求适应度总值，以便归一化,是已经排序好的链。
 {
  current=population.GetAt(population.FindIndex(i)); //取出来的值出现问题.
  sum+=current.fitness;
 }
 for(i=0;i<popsize; i++)//归一化
 {
  current=population.GetAt(population.FindIndex(i)); //population 有值,为什么取出来的不正确呢??
  current.fitness=current.fitness/sum;
  cfitness.InsertAfter (cfitness .FindIndex(i),current.fitness);
 }
 
 for(i=1;i<popsize; i++)//概率值从小到大;
 {
  current.fitness=cfitness.GetAt (cfitness.FindIndex(i-1))
   +cfitness.GetAt(cfitness.FindIndex(i));   //归一化
  cfitness.SetAt (cfitness .FindIndex(i),current.fitness);
  population.SetAt(population.FindIndex(i),current);
 }
 for (i=0;i<popsize;)//轮盘赌概率选择。本段还有问题。
 {
  p=double(rand()%999)/1000+0.0001;  //随机生成概率
  pindex=0;  //遍历索引
  pc=cfitness.GetAt(cfitness.FindIndex(1));  //为什么取不到数值???20060910
  while(p>=pc&&pindex<popsize) //问题所在。
  {
   pc=cfitness.GetAt(cfitness .FindIndex(pindex));
   pindex++;
  }
  //必须是从index~popsize，选择高概率的数。即大于概率p的数应该被选择，选择不满则进行下次选择。
  for (j=popsize-1;j<pindex&&i<popsize;j--)
  {
   newpopulation.InsertAfter (newpopulation.FindIndex(0),
    population.GetAt (population.FindIndex(j)));
   i++;
  }
 }
 for(i=0;i<popsize; i++)
 {
  population.SetAt (population.FindIndex(i),
   newpopulation.GetAt (newpopulation.FindIndex(i)));
 }
// j=newpopulation.GetCount();
// j=population.GetCount();
 newpopulation.RemoveAll();
}

//current   变化后，以上没有问题了。


void CMVSOGA:: crossoveroperator()   //非均匀算术线性交叉，浮点数适用,alpha ,beta是(0，1)之间的随机数
          //对种群中两两交叉的个体选择也是随机选择的。也可取beta=1-alpha;
          //current的变化会有一些改变。
{
 int i,j;
 double alpha,beta;
 CList <int,int> index;
 int point,temp;
 double p;
// srand( (unsigned)time( NULL ) );
 for (i=0;i<popsize;i++)//生成序号
 {
  index.InsertAfter (index.FindIndex(i),i);
 }
 for (i=0;i<popsize;i++)//打乱序号
 {
  point=rand()%(popsize-1);
  temp=index.GetAt(index.FindIndex(i));
  index.SetAt(index.FindIndex(i),
   index.GetAt(index.FindIndex(point)));  
  index.SetAt(index.FindIndex(point),temp);
 }
 for (i=0;i<popsize-1;i+=2)
 {//按顺序序号,按序号选择两个母体进行交叉操作。
  p=double(rand()%10000)/10000.0;
  if (p<crossoverrate)
  {  
   alpha=double(rand()%10000)/10000.0;
   beta=double(rand()%10000)/10000.0;
   current=population.GetAt(population.FindIndex(index.GetAt(index.FindIndex(i))));
   current1=population.GetAt(population.FindIndex(index.GetAt(index.FindIndex(i+1))));//临时使用current1代替
   for(j=0;j<variablenum;j++)
   { 
    //交叉
    double sign;
    sign=rand()%2;
    if(sign)
    {
     current.chromosome[j]=(1-alpha)*current.chromosome[j]+
      beta*current1.chromosome[j];
    }
    else
    {
     current.chromosome[j]=(1-alpha)*current.chromosome[j]-
      beta*current1.chromosome[j];
    }
    if (current.chromosome[j]>variabletop[j])  //判断是否超界.
    {
     current.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
    }
    if (current.chromosome[j]<variablebottom [j])
    {
     current.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
    }
    if(sign)
    {
     current1.chromosome[j]=alpha*current.chromosome[j]+
      (1- beta)*current1.chromosome[j];
    }
    else
    {
     current1.chromosome[j]=alpha*current.chromosome[j]-
      (1- beta)*current1.chromosome[j];
    }
    if (current1.chromosome[j]>variabletop[j])
    {
     current1.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
    }
    if (current1.chromosome[j]<variablebottom [j])
    {
     current1.chromosome[j]=double(rand()%10000)/10000*(variabletop[j]-variablebottom[j])+variablebottom[j];
    }
   }
   //回代
  }
  newpopulation.InsertAfter  (newpopulation.FindIndex(i),current);
  newpopulation.InsertAfter  (newpopulation.FindIndex(i),current1);
 }
 ASSERT(newpopulation.GetCount()==popsize);
 for (i=0;i<popsize;i++)
 {
  population.SetAt (population.FindIndex(i),
   newpopulation.GetAt (newpopulation.FindIndex(i)));
 }
 newpopulation.RemoveAll();
 index.RemoveAll();
}
void CMVSOGA:: findbestandworstindividual( )  
{
 int i;
 bestindividual=population.GetAt(population.FindIndex(best_index));
 worstindividual=population.GetAt(population.FindIndex(worst_index));
 for (i=1;i<popsize; i++)
 {
  current=population.GetAt(population.FindIndex(i));
  if (current.fitness>bestindividual.fitness)
  {
   bestindividual=current;
   best_index=i;
  }
  else if (current.fitness<worstindividual.fitness)
  {
   worstindividual=current;
   worst_index=i;
  }
 }
 population.SetAt(population.FindIndex(worst_index),
  population.GetAt(population.FindIndex(best_index)));
 //用最好的替代最差的。
 if (maxgeneration==0)
 {
  currentbest=bestindividual;
 }
 else
 {
  if(bestindividual.fitness>=currentbest.fitness)
  {
   currentbest=bestindividual;
  }
 }
}
void CMVSOGA:: calculatefitnessvalue() //适应度函数值计算，关键是适应度函数的设计
          //current变化，这段程序变化较大，特别是排序。
{
 int  i;
 double temp;//alpha,beta;//适应度函数的尺度变化系数
 double cmax=100;
 for(i=0;i<popsize;i++)
 {
  current=population.GetAt(population.FindIndex(i));
  if(current.value<cmax)
  {
   temp=cmax-current.value;
  }
  else
  {
   temp=0.0;
  }
  /*
  if((population[i].value+cmin)>0.0)
  {temp=cmin+population[i].value;}
 else
 {temp=0.0;
   }
  */
  current.fitness=temp;
  population.SetAt(population.FindIndex(i),current); 
 }
}
void CMVSOGA:: performevolution() //演示评价结果,有冗余代码,current变化，程序应该改变较大
{
 if (bestindividual.fitness>currentbest.fitness)
 {
  currentbest=population.GetAt(population.FindIndex(best_index));
 }
 else
 {
  population.SetAt(population.FindIndex(worst_index),currentbest);
 }
}
void CMVSOGA::GetResult(double *Result)
{
 int i;
 for (i=0;i<variablenum;i++)
 {
  Result[i]=currentbest.chromosome[i];
 }
 Result[i]=currentbest.value;
}

void CMVSOGA::GetPopData(CList <double,double>&PopData) 
{
 PopData.RemoveAll();
 int i,j;
 for (i=0;i<popsize;i++)
 {
  current=population.GetAt(population.FindIndex(i));
  for (j=0;j<variablenum;j++)
  {
   PopData.AddTail(current.chromosome[j]);
  }
 }
}
void CMVSOGA::SetFitnessData(CList <double,double>&PopData,CList <double,double>&FitnessData,CList <double,double>&ValueData)
{
 int i,j;
 for (i=0;i<popsize;i++)
 { 
  current=population.GetAt(population.FindIndex(i)); //就因为这一句，出现了很大的问题。 
  for (j=0;j<variablenum;j++)
  {
   current.chromosome[j]=PopData.GetAt(PopData.FindIndex(i*variablenum+j));
  }
  current.fitness=FitnessData.GetAt(FitnessData.FindIndex(i));
  current.value=ValueData.GetAt(ValueData.FindIndex(i));
  population.SetAt(population.FindIndex(i),current);
 }
 FitnessData.RemoveAll();
 PopData.RemoveAll();
 ValueData.RemoveAll();
}

posted on 2007-05-26 08:14 唯月释怀 阅读(15027) 评论(7)  编辑 收藏 引用

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# re: C++遗传算法源程序 2007-05-26 17:38 pass86

我也写过一点，从书上改编的。
/********************************************************************
Filename: aiWorld.h
Purpose: 遗传算法，花朵演化。
Author: pass86
E-mail: pass86@gmail.com
Created: 2007/03/29
Id:
Copyright:
Licence:
*********************************************************************/
#ifndef AIWORLD_H_
#define AIWORLD_H_

#include <iostream>
#include <ctime>
#include <cstdlib>
#include <cmath>

#define kMaxFlowers 10

using std::cout;
using std::endl;

class ai_World
{
public:
ai_World()
{
srand(time(0));
}
~ai_World() {}

int temperature[kMaxFlowers]; //温度
int water[kMaxFlowers]; //水质
int sunlight[kMaxFlowers]; //阳光
int nutrient[kMaxFlowers]; //养分
int beneficialInsect[kMaxFlowers]; //益虫
int harmfulInsect[kMaxFlowers]; //害虫

int currentTemperature;
int currentWater;
int currentSunlight;
int currentNutrient;
int currentBeneficialInsect;
int currentHarmfulInsect;

/**
第一代花朵
*/
void Encode();

/**
花朵适合函数
*/
int Fitness(int flower);

/**
花朵演化
*/
void Evolve();

/**
返回区间[start, end]的随机数
*/
inline int tb_Rnd(int start, int end)
{
if (start > end)
return 0;
else
{
//srand(time(0));
return (rand() % (end + 1) + start);
}
}

/**
显示数值
*/
void show();
};
// ----------------------------------------------------------------- //
void ai_World::Encode()
// ----------------------------------------------------------------- //

{
int i;

for (i=0;i<kMaxFlowers;i++)
{
temperature[i]=tb_Rnd(1,75);
water[i]=tb_Rnd(1,75);
sunlight[i]=tb_Rnd(1,75);
nutrient[i]=tb_Rnd(1,75);
beneficialInsect[i]=tb_Rnd(1,75);
harmfulInsect[i]=tb_Rnd(1,75);
}

currentTemperature=tb_Rnd(1,75);
currentWater=tb_Rnd(1,75);
currentSunlight=tb_Rnd(1,75);
currentNutrient=tb_Rnd(1,75);
currentBeneficialInsect=tb_Rnd(1,75);
currentHarmfulInsect=tb_Rnd(1,75);

currentTemperature=tb_Rnd(1,75);
currentWater=tb_Rnd(1,75);
currentSunlight=tb_Rnd(1,75);
currentNutrient=tb_Rnd(1,75);
currentBeneficialInsect=tb_Rnd(1,75);
currentHarmfulInsect=tb_Rnd(1,75);

}
// ----------------------------------------------------------------- //
int ai_World::Fitness(int flower)
// ----------------------------------------------------------------- //

{
int theFitness;


theFitness=abs(temperature[flower]-currentTemperature);
theFitness=theFitness+abs(water[flower]-currentWater);
theFitness=theFitness+abs(sunlight[flower]-currentSunlight);
theFitness=theFitness+abs(nutrient[flower]-currentNutrient);
theFitness=theFitness+abs(beneficialInsect[flower]-currentBeneficialInsect);
theFitness=theFitness+abs(harmfulInsect[flower]-currentHarmfulInsect);

return (theFitness);

}
// ----------------------------------------------------------------- //
void ai_World::Evolve()
// ----------------------------------------------------------------- //

{
int fitTemperature[kMaxFlowers];
int fitWater[kMaxFlowers];
int fitSunlight[kMaxFlowers];
int fitNutrient[kMaxFlowers];
int fitBeneficialInsect[kMaxFlowers];
int fitHarmfulInsect[kMaxFlowers];
int fitness[kMaxFlowers];
int i;
int leastFit=0;
int leastFitIndex;

for (i=0;i<kMaxFlowers;i++)
if (Fitness(i)>leastFit)
{
leastFit=Fitness(i);
leastFitIndex=i;
}

temperature[leastFitIndex]=temperature[tb_Rnd(0,kMaxFlowers - 1)];
water[leastFitIndex]=water[tb_Rnd(0,kMaxFlowers - 1)];
sunlight[leastFitIndex]=sunlight[tb_Rnd(0,kMaxFlowers - 1)];
nutrient[leastFitIndex]=nutrient[tb_Rnd(0,kMaxFlowers - 1)];
beneficialInsect[leastFitIndex]=beneficialInsect[tb_Rnd(0,kMaxFlowers - 1)];
harmfulInsect[leastFitIndex]=harmfulInsect[tb_Rnd(0,kMaxFlowers - 1)];

for (i=0;i<kMaxFlowers;i++)
{
fitTemperature[i]=temperature[tb_Rnd(0,kMaxFlowers - 1)];
fitWater[i]=water[tb_Rnd(0,kMaxFlowers - 1)];
fitSunlight[i]=sunlight[tb_Rnd(0,kMaxFlowers - 1)];
fitNutrient[i]=nutrient[tb_Rnd(0,kMaxFlowers - 1)];
fitBeneficialInsect[i]=beneficialInsect[tb_Rnd(0,kMaxFlowers - 1)];
fitHarmfulInsect[i]=harmfulInsect[tb_Rnd(0,kMaxFlowers - 1)];
}

for (i=0;i<kMaxFlowers;i++)
{
temperature[i]=fitTemperature[i];
water[i]=fitWater[i];
sunlight[i]=fitSunlight[i];
nutrient[i]=fitNutrient[i];
beneficialInsect[i]=fitBeneficialInsect[i];
harmfulInsect[i]=fitHarmfulInsect[i];
}

for (i=0;i<kMaxFlowers;i++)
{
if (tb_Rnd(1,100)==1)
temperature[i]=tb_Rnd(1,75);
if (tb_Rnd(1,100)==1)
water[i]=tb_Rnd(1,75);
if (tb_Rnd(1,100)==1)
sunlight[i]=tb_Rnd(1,75);
if (tb_Rnd(1,100)==1)
nutrient[i]=tb_Rnd(1,75);
if (tb_Rnd(1,100)==1)
beneficialInsect[i]=tb_Rnd(1,75);
if (tb_Rnd(1,100)==1)
harmfulInsect[i]=tb_Rnd(1,75);
}

}
void ai_World::show()
{
// cout << "\t temperature water sunlight nutrient beneficialInsect harmfulInsect\n";
cout << "current\t " << currentTemperature << "\t " << currentWater << "\t ";
cout << currentSunlight << "\t " << currentNutrient << "\t ";
cout << currentBeneficialInsect << "\t " << currentHarmfulInsect << "\n";
for (int i=0;i<kMaxFlowers;i++)
{
cout << "Flower " << i << ": ";
cout << temperature[i] << "\t ";
cout << water[i] << "\t ";
cout << sunlight[i] << "\t ";
cout << nutrient[i] << "\t ";
cout << beneficialInsect[i] << "\t ";
cout << harmfulInsect[i] << "\t ";
cout << endl;
}
}
#endif // AIWORLD_H_

//test.cpp
#include <iostream>
#include "ai_World.h"

using namespace std;

int main()
{
ai_World a;
a.Encode();
// a.show();
for (int i = 0; i < 10; i++)
{
cout << "Generation " << i << endl;
a.Evolve();
a.show();
}

system("PAUSE");
return 0;
}
  回复  更多评论   

# re: C++遗传算法源程序 2007-05-27 19:04 江水兽

啊哈 当初我也写过 只是没有像这样如此具有遗传算法的特点 当时只是为了选修课写的一个具有基本功能的GA Program  回复  更多评论   

# re: C++遗传算法源程序 2007-06-25 17:33 7777

垃圾 什么你都往上传  回复  更多评论   

# re: C++遗传算法源程序 2007-10-21 08:15 starlet

作者不知道有没有联系方式，有问题请教  回复  更多评论   

# re: C++遗传算法源程序 2008-04-20 02:33 阿毛

你好，我在做遗传算法解决vrp问题的毕业论文，有问题想指教，有偿求助，急，望回复，我的q是267497220  回复  更多评论   

# re: C++遗传算法源程序 2008-10-19 21:57 禇

谢谢，我如果有新的代码，也给大家传上来共享！  回复  更多评论   

# re: C++遗传算法源程序 2011-04-20 16:28 sjiao888

你好，我在做遗传算法的毕业论文，有问题想指教，我的QQ是709375489  回复  更多评论   



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