一道算法题,要求用c++写

2025-02-05 07:59:57
推荐回答(1个)
回答1:

简单从网上找了个算法,却发现存在一些问题,简单修改了一下,基本满足你的要求。

/***********************************************************
**             人工智能--遗传算法
**
** 求解f (x) = x + 10*sin(5*x) + 7*cos(4*x)  的最大值,x∈ [0,9]
**      
** author: CS0921 WTU
**  QQ : 2364622423   (简单修改了,有bug或任何问题请联系。)
**  代码参考了: https://blog.csdn.net/dl0914791011/article/details/8161253 
**                                                 
/**********************************************************/
 
#include     
#include 
#include 
#include 
#include  
#include 
#define TEST         0         //0:屏蔽所有的调试信息    1:开启所有的调试信息
#define TEST_FLAG    4         //1:测试randCreatePop函数 2:测试selection函数
   //3.测试crossover函数     4.测试mutation函数
 
#define CROSS_RATE  0.5    //变异率(mutation rate)取值范围一般为0.4~0.99
#define MUT_RATE     0.09      //变异率(mutation rate)取值范围一般为0.0001~0.1
#define ITER_NUM     1000      //迭代次数(iteration number)
#define POP_NUM      30        //初始化种群的个数
#define GENE_NUM     32        //基因的位数个数
#define FUN_EXP(x)   ((x) + 10*sin(5*(x)) + 7*cos(4*(x))) //函数表达式
 
typedef unsigned int UINT;
 
//染色体的数据结构
typedef struct{                        
    char geneBit[GENE_NUM]; //基因位(gene bit)表示方式
    double fitValue;          //适应值(fittness value)(衡量个体的优劣)
}Chromosome;
                                        
void randCreatePop(Chromosome *);  //随机创建初始群体
void selection(Chromosome *);  //选择(Selection):根据适应度选择优良个体(最优解)
void crossover(Chromosome *);  //交叉(Crossover):染色体的片断(基因)进行交换
void mutation(Chromosome *);  //变异(Mutation) :随机改变染色体片断(基因)的值
void updatePop(Chromosome *, Chromosome *);//更新种群
void printResult(Chromosome *);  //打印结果(当x为何值时,f(x)最大)
double calcFitValue(double);          //计算染色体的适应度值
double binToDouble(Chromosome);      //将类似二进制的基因位转化为十进制
void test(Chromosome *);  //测试函数
 
 
int main(int argc, char *argv[])                                  
{
int count;                    // 记录迭代次数
Chromosome curPop[POP_NUM];   // 初始种群
Chromosome nextPop[POP_NUM];  // 更新后种群
 
//随机创建初始群体
randCreatePop(curPop);
 
//开始迭代 
for(count=1; count<(ITER_NUM+1); count++)
    {
       updatePop(curPop, nextPop); // 更新种群 
       selection(nextPop);    // 挑选优秀个体 
       crossover(nextPop);    // 交叉得到新个体 
       mutation(nextPop);    // 变异得到新个体 
       updatePop(nextPop, curPop); // 种群更替
   
   printf("\n第%d代迭代的结果:\n", count); // 输出当前迭代次数,即种群的代数
   test(curPop);    //输出结果
}//迭代结束 
  
printResult(curPop); //打印结果(当x为何值时,f(x)最大)

return 0;
 
}//end of main                                              
 
 
//创建初始群体                               
void randCreatePop(Chromosome *pop)
{
UINT i,j;
UINT randValue;
UINT value;

srand((unsigned)time(NULL));   //如果所有的函数都要使用到rand函数,只需要在先运行的函数使用一次srand即可
for(i=0; i {
for(j=0; j {
randValue         = rand()%2;      // 随机产生0或者1                       
pop[i].geneBit[j] = randValue+'0'; // 将随机数(0,1)赋给基因位
}   

value           = binToDouble(pop[i]);    // 计算染色体基因对应的值
pop[i].fitValue = calcFitValue(value); // 计算染色体的适应度值
}                                                                        
   
#if (TEST==1) && (TEST_FLAG==1) //测试
printf("\n随机分配的种群如下:\n");
test(pop);
#endif

}//end of createPop
 
//选择(Selection):根据适应度选择优良个体(最优解) 
void selection(Chromosome *pop) 
{
UINT   i,j;
UINT  sumFitValue;        //总适应值
UINT  avrFitValue;        //平均适应值
float choicePro[POP_NUM]; //选择机会
Chromosome tempPop;       //临时种群变量
 
#if (TEST==1) && (TEST_FLAG==2) //测试
printf("\n没有选择前的种群如下:\n");
test(pop);
#endif
 
// 根据个体适应度来排序(冒泡法) 降序
for(i=POP_NUM; i>0; i--)                           
{
for(j=0; j<(i-1); j++)
 {
 if(pop[j+1].fitValue > pop[j].fitValue)
   {
 tempPop  = pop[j+1];
 pop[j+1] = pop[j];
 pop[j]   = tempPop;
   }   
 }                
}
 
//计算出总适应值
sumFitValue = 0;
for(i=0; i {
sumFitValue += pop[i].fitValue;
}

//计算出平均适应值(四舍五入,保留到小数点后1位)
avrFitValue = (UINT)(((float)sumFitValue/POP_NUM)+0.5);

//计算出每个群体选择机会
for(i=0; i {  //平均概率     = 平均适应值/总适应值
 //群体选择机会 = (群体的概率/平均概率)
choicePro[i] = ((float)pop[i].fitValue/sumFitValue)/((float)avrFitValue/sumFitValue); 
choicePro[i] = (float)((int)(choicePro[i]*100+0.5)/100.0);//保留到小数点后2位,四舍五入
}  
 
//根据选择概率来繁殖(copy)优良个体、淘汰较差个体
//如果choicePro[i]==0淘汰复制一次最优的群体
for(i=0; i {
if(((int)(choicePro[i]+0.55)) == 0)
pop[POP_NUM-1] = pop[0];
}

#if (TEST==1) && (TEST_FLAG==2) //测试
printf("\n经过选择的种群如下:\n");
test(pop);
#endif
 
}//end of selection
 
//交叉(Crossover):染色体的片断(基因)进行交换
void crossover(Chromosome *pop)  

char  tmpStr[GENE_NUM]="";
UINT  i;
    UINT  randPos;
  UINT  randValue;

// srand( (unsigned)time( NULL ) );
randValue=rand()%100;   // 随机产生0到49之间的数;
if(randValue >= (int)(CROSS_RATE*100)) // randValue<50的概率只有50%,即变异率为0.5
{
#if (TEST==1) && (TEST_FLAG==3) //测试
printf("\n种群没有进行交叉.\n");
#endif

return ;
}
 
#if (TEST==1) && (TEST_FLAG==3) //测试
printf("\n交叉前,种群如下:\n");
test(pop);
printf("\n交叉的位置依次为:");
#endif
 
//种群中个体染色体两两交叉
for(i=0; i {
//crossover child i and child i+1
randPos = (rand()%(GENE_NUM-1)+1);   // 随机产生交叉点,交叉点控制在1到(GENE_NUM-1)之间
strncpy(tmpStr, pop[i].geneBit+randPos, GENE_NUM-randPos);
strncpy(pop[i].geneBit+randPos, pop[i+1].geneBit+randPos, GENE_NUM-randPos);
strncpy(pop[i+1].geneBit+randPos, tmpStr, GENE_NUM-randPos);
 
#if (TEST==1) && (TEST_FLAG==3) //测试
printf(" %d", randPos);
#endif
}
 
// 为新个体计算适应度值
    for(i=0; i {
       pop[i].fitValue = calcFitValue( binToDouble(pop[i]) );     
}
 
#if (TEST==1) && (TEST_FLAG==3) //测试
printf("\n交叉后,种群如下:\n");
test(pop);
#endif
 
}//end of crossover
 
//变异(Mutation) :随机改变染色体片断(基因)的值
void mutation(Chromosome *pop)   
{
UINT randRow, randCol;  
UINT randValue;
      
// srand( (unsigned)time( NULL ) );    
randValue=rand()%100;   // 随机产生0到99之间的数;
if(randValue >= (int)(MUT_RATE*100)) // randValue<2的概率只有2%,即变异率为0.02
{
#if (TEST==1) && (TEST_FLAG==4) //测试
printf("\n种群中没有基因变异.\n");
#endif

return ;
}
 
randCol = rand()%GENE_NUM;    // 随机产生要变异的基因位号 
randRow = rand()%POP_NUM;     // 随机产生要变异的染色体号

#if (TEST==1) && (TEST_FLAG==4)   //测试
printf("\n变异前,种群如下:\n");
test(pop);
printf("\n变异的位置:染色体号=%d 基因位号=%d\n", randRow+1, randCol);
#endif

pop[randRow].geneBit[randCol] = (pop[randRow].geneBit[randCol]=='0') ? '1':'0'; //1变为0, 0变为1
pop[randRow].fitValue = calcFitValue( binToDouble(pop[randRow]) ); // 计算变异后的适应度值 
 
#if (TEST==1) && (TEST_FLAG==4) //测试
printf("\n变异后,种群如下:\n");
test(pop);
#endif
 
}//end of mutation
 
//更新种群
void updatePop(Chromosome *newPop, Chromosome *oldPop)
{
UINT i;
 
for(i=0; i {
oldPop[i]=newPop[i];    
}
 
}//end of updatePop
 
//打印结果(当x为何值时,f(x)最大)
void printResult(Chromosome *pop)
{  
UINT i;
double x = 0;
double optValue = 0;  // 函数的最优值
 
for(i=0; i {
   if(pop[i].fitValue > optValue)
   {
   optValue = pop[i].fitValue;
   x = binToDouble(pop[i]);
   }
 
}
 
printf("\n当x=%lf时,函数得到最大值为:%lf\n\n", x, optValue);
 
}//end of printResult
 
 
//计算染色体的适应度值
double calcFitValue(double x)
{
     return FUN_EXP(x);  // 
 
}//end of calcFitValue
 
//将类似二进制的基因位转化为十进制
double binToDouble(Chromosome pop)
{
   UINT i;
   UINT radix  = 1;
   UINT TEMP = 0;
   double result = 0;
 
   for(i=0; i   { //printf("%d", pop.geneBit[i]);
TEMP += (pop.geneBit[i]-'0')*radix;
radix  *= 2;
   }
   result = 0 + 9.0 * TEMP / (UINT_MAX);
   return result;
  
}//end of binToDec
 
void test(Chromosome *pop)
{
int i;
int j;

for(i=0; i {
printf("%d: ", i+1);
for(j=0; j printf("%c", pop[i].geneBit[j]);

printf("   %lf", binToDouble(pop[i]));
printf("   fixValue=%lf\n", calcFitValue(binToDouble(pop[i])));
}
}

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