问题：求f(x)=x+10*sin(5x)+7*cos(4x)最大值， 0<=x<=9
新建输入文件gadata.txt，内容为：
0, 9
表示变量x的下界和上界。
新建日志文件galog.txt，用于记录计算过程及输出结果。
// GA.cpp : Defines the entry point for the console application. //
/* 这是一个非常简单的遗传算法源代码，是由Denis Cormier (North Carolina State University)开发的， Sita S.Raghavan (University of North Carolina at Charlotte)修正。 代码保证尽可能少，实际上也不必查错。 对一特定的应用修正此代码，用户只需改变常数的定义并且定义“评价函数”即可。 注意代码的设计是求最大值，其中的目标函数只能取正值；且函数值和个体的适应值之间没有区别。 该系统使用比率选择、精华模型、单点杂交和均匀变异。如果用 Gaussian变异替换均匀变异，可能得到更好的效果。 代码没有任何图形，甚至也没有屏幕输出，主要是保证在平台之间的高可移植性。 读者可以从ftp.uncc.edu, 目录 coe/evol中的文件prog.c中获得。 要求输入的文件应该命名为‘gadata.txt’；系统产生的输出文件为‘galog.txt’。 输入的文件由几行组成：数目对应于变量数。 且每一行提供次序——对应于变量的上下界。 如第一行为第一个变量提供上下界，第二行为第二个变量提供上下界，等等。 */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
/* Change any of these parameters to match your needs */ //请根据你的需要来修改以下参数
#define POPSIZE 50 /* population size 种群大小*/
#define MAXGENS 1000 /* max. number of generations 最大基因个数*/
const int NVARS = 1; /* no. of problem variables 问题变量的个数*/
#define PXOVER 0.8 /* probability of crossover 杂交概率*/
#define PMUTATION 0.15 /* probability of mutation 变异概率*/
#define TRUE 1
#define FALSE 0
#define PI 3.1415926
int generation; /* current generation no. 当前基因个数*/
int cur_best; /* best individual 最优个体*/
FILE *galog; /* an output file 输出文件指针*/
struct genotype /* genotype (GT), a member of the population 种群的一个基因的结构体类型*/
{
double gene[NVARS]; /* a string of variables 变量*/
double fitness; /* GT's fitness 基因的适应度*/
double upper[NVARS]; /* GT's variables upper bound 基因变量的上界*/
double lower[NVARS]; /* GT's variables lower bound 基因变量的下界*/
double rfitness; /* relative fitness 比较适应度*/
double cfitness; /* cumulative fitness 积累适应度*/
};
struct genotype population[POPSIZE+1]; /* population 种群*/
struct genotype newpopulation[POPSIZE+1]; /* new population; 新种群*/ /* replaces the old generation */ //取代旧的基因
/* Declaration of procedures used by this genetic algorithm */
//以下是一些函数声明
void initialize(void); //种群基因结构体初始化
double randval(double, double); //随机数产生函数
void evaluate(void); //评价函数，可以由用户自定义，该函数取得每个基因的适应度
void keep_the_best(void); //保存每次遗传后的最佳基因
void elitist(void); //搜寻杰出个体函数：找出最好和最坏的个体。如果某代的最好个体比前一代的最好个体要坏，那么后者将会取代当前种群的最坏个体
void select(void); //选择函数：用于最大化合并杰出模型的标准比例选择，保证最优秀的个体得以生存
void crossover(void); //杂交函数：选择两个个体来杂交，这里用单点杂交
void Xover(int,int); //交叉
void swap(double *, double *); //交换
void mutate(void); //变异函数：被该函数选中后会使得某一变量被一个随机的值所取代
void report(void); //报告模拟进展情况
/***************************************************************/
/* Initialization function: Initializes the values of genes */
/* within the variables bounds. It also initializes (to zero) */
/* all fitness values for each member of the population. It */
/* reads upper and lower bounds of each variable from the */
/* input file `gadata.txt'. It randomly generates values */
/* between these bounds for each gene of each genotype in the */
/* population. The format of the input file `gadata.txt' is */
/* var1_lower_bound var1_upper bound */
/* var2_lower_bound var2_upper bound ... */
/***************************************************************/
void initialize(void)
{
FILE *infile;
int i, j;
double lbound, ubound;
if ((infile = fopen("gadata.txt","r"))==NULL)
{
fprintf(galog,"\nCannot open input file!\n");
exit(1);
}
/* initialize variables within the bounds */
//把输入文件的变量界限输入到基因结构体中
for (i = 0; i < NVARS; i++)
{
fscanf(infile, "%lf",&lbound);
fscanf(infile, "%lf",&ubound);
for (j = 0; j < POPSIZE; j++)
{
population[j].fitness = 0; //基因的适应度
population[j].rfitness = 0; //比较适应度
population[j].cfitness = 0; //积累适应度
population[j].lower[i] = lbound; //基因变量的上界
population[j].upper[i]= ubound; //基因变量的下界
population[j].gene[i] = randval(population[j].lower[i], population[j].upper[i]); //变量
}
}
fclose(infile);
}
/***********************************************************/
/* Random value generator: Generates a value within bounds */
/***********************************************************/
//随机数产生函数
double randval(double low, double high)
{
double val;
val = ((double)(rand()%1000)/1000.0)*(high - low) + low;
return(val);
}
/*************************************************************/
/* Evaluation function: This takes a user defined function. */
/* Each time this is changed, the code has to be recompiled. */
/* The current function is: x[1] + 10 * sin(5 * x[1]) + 7 * cos(4 * x[1]) */
/*************************************************************/
//评价函数，可以由用户自定义，该函数取得每个基因的适应度
void evaluate(void)
{
int mem;
int i;
double x[NVARS+1];
for (mem = 0; mem < POPSIZE; mem++) //种群中的每个成员
{
for (i = 0; i < NVARS; i++) //问题变量
x[i+1] = population[mem].gene[i];
population[mem].fitness = x[1] + 10 * sin(5 * x[1]) + 7 * cos(4 * x[1]);
}
}
/***************************************************************/
/* Keep_the_best function: This function keeps track of the */
/* best member of the population. Note that the last entry in */
/* the array Population holds a copy of the best individual */
/***************************************************************/
//保存每次遗传后的最佳基因
void keep_the_best()
{
int mem;
int i;
cur_best = 0;
/* stores the index of the best individual */
//保存最佳个体的索引
for (mem = 0; mem < POPSIZE; mem++)
{
if (population[mem].fitness > population[POPSIZE].fitness)
{
cur_best = mem;
population[POPSIZE].fitness = population[mem].fitness;
}
}
/* once the best member in the population is found, copy the genes */
//一旦找到种群的最佳个体，就拷贝他的基因
for (i = 0; i < NVARS; i++)
population[POPSIZE].gene[i] = population[cur_best].gene[i];
}
/****************************************************************/
/* Elitist function: The best member of the previous generation */
/* is stored as the last in the array. If the best member of */
/* the current generation is worse then the best member of the */
/* previous generation, the latter one would replace the worst */
/* member of the current population */
/****************************************************************/
//搜寻杰出个体函数：找出最好和最坏的个体。
//如果某代的最好个体比前一代的最好个体要坏，那么后者将会取代当前种群的最坏个体
void elitist()
{
int i;
double best, worst; /* best and worst fitness values 最好和最坏个体的适应度值*/
int best_mem, worst_mem; /* indexes of the best and worst member 最好和最坏个体的 索引*/
best = population[0].fitness;
worst = population[0].fitness;
for (i = 0; i < POPSIZE - 1; ++i)
{
if(population[i].fitness > population[i+1].fitness)
{
if (population[i].fitness >= best)
{
best = population[i].fitness;
best_mem = i;
}
if (population[i+1].fitness <= worst)
{
worst = population[i+1].fitness;
worst_mem = i + 1;
}
}
else
{
if (population[i].fitness <= worst)
{
worst = population[i].fitness;
worst_mem = i;
}
if (population[i+1].fitness >= best)
{
best = population[i+1].fitness;
best_mem = i + 1;
}
}
}
/* if best individual from the new population is better than */
/* the best individual from the previous population, then */
/* copy the best from the new population; else replace the */
/* worst individual from the current population with the */
/* best one from the previous generation */
//如果新种群中的最好个体比前一代的最好个体要强的话，那么就把新种群的最好个体拷贝出来。
//否则就用前一代的最好个体取代这次的最坏个体
if (best >= population[POPSIZE].fitness)
{
for (i = 0; i < NVARS; i++)
population[POPSIZE].gene[i] = population[best_mem].gene[i];
population[POPSIZE].fitness = population[best_mem].fitness;
}
else
{
for (i = 0; i < NVARS; i++)
population[worst_mem].gene[i] = population[POPSIZE].gene[i];
population[worst_mem].fitness = population[POPSIZE].fitness;
}
}
/**************************************************************/
/* Selection function: Standard proportional selection for */
/* maximization problems incorporating elitist model - makes */
/* sure that the best member survives */
/**************************************************************/
//选择函数：用于最大化合并杰出模型的标准比例选择，保证最优秀的个体得以生存
void select(void)
{
int mem, j, i;
double sum = 0;
double p;
/* find total fitness of the population */
//找出种群的适应度之和
for (mem = 0; mem < POPSIZE; mem++)
{
sum += population[mem].fitness;
}
/* calculate relative fitness */
//计算相对适应度
for (mem = 0; mem < POPSIZE; mem++)
{
population[mem].rfitness = population[mem].fitness/sum;
}
population[0].cfitness = population[0].rfitness;
/* calculate cumulative fitness */
//计算累加适应度
for (mem = 1; mem < POPSIZE; mem++)
{
population[mem].cfitness = population[mem-1].cfitness + population[mem].rfitness;
}
/* finally select survivors using cumulative fitness. */
//用累加适应度作出选择
for (i = 0; i < POPSIZE; i++)
{
p = rand()%1000/1000.0;
if (p < population[0].cfitness)
newpopulation[i] = population[0];
else
{
for (j = 0; j < POPSIZE;j++)
if (p >= population[j].cfitness && p<population[j+1].cfitness)
newpopulation[i] = population[j+1];
}
}
/* once a new population is created, copy it back */
//当一个新种群建立的时候，将其拷贝回去
for (i = 0; i < POPSIZE; i++)
population[i] = newpopulation[i];
}
/***************************************************************/
/* Crossover selection: selects two parents that take part in */
/* the crossover. Implements a single point crossover */
/***************************************************************/
//杂交函数：选择两个个体来杂交，这里用单点杂交
void crossover(void)
{
int mem, one;
int first = 0; /* count of the number of members chosen */
double x;
for (mem = 0; mem < POPSIZE; ++mem)
{
x = rand()%1000/1000.0;
if (x < PXOVER)
{
++first;
if (first % 2 == 0)
Xover(one, mem);
else
one = mem;
}
}
}
/**************************************************************/
/* Crossover: performs crossover of the two selected parents. */
/**************************************************************/
//交叉
void Xover(int one, int two)
{
int i;
int point; /* crossover point */
/* select crossover point */
if(NVARS > 1)
{
if(NVARS == 2)
point = 1;
else
point = (rand() % (NVARS - 1)) + 1;
for (i = 0; i < point; i++)
swap(&population[one].gene[i], &population[two].gene[i]);
}
}
/*************************************************************/
/* Swap: A swap procedure that helps in swapping 2 variables */
/*************************************************************/
void swap(double *x, double *y)
{
double temp;
temp = *x;
*x = *y;
*y = temp;
}
/**************************************************************/
/* Mutation: Random uniform mutation. A variable selected for */
/* mutation is replaced by a random value between lower and */
/* upper bounds of this variable */
/**************************************************************/
//变异函数：被该函数选中后会使得某一变量被一个随机的值所取代
void mutate(void)
{
int i, j;
double lbound, hbound;
double x;
for (i = 0; i < POPSIZE; i++)
for (j = 0; j < NVARS; j++)
{
x = rand()%1000/1000.0;
if (x < PMUTATION)
{
/* find the bounds on the variable to be mutated 确定*/
lbound = population[i].lower[j];
hbound = population[i].upper[j];
population[i].gene[j] = randval(lbound, hbound);
}
}
}
/***************************************************************/
/* Report function: Reports progress of the simulation. Data */
/* dumped into the output file are separated by commas */
/***************************************************************/
//报告模拟进展情况。输出文件中的数据用逗号隔开
void report(void)
{
int i;
double best_val; /* best population fitness 最佳种群适应度*/
double avg; /* avg population fitness 平均种群适应度*/
double stddev; /* std. deviation of population fitness 种群适应度偏差 */
double sum_square; /* sum of square for std. calc 各个个体平方之和*/
double square_sum; /* square of sum for std. calc 平均值的平方乘个数*/
double sum; /* total population fitness 所有种群适应度之和*/
sum = 0.0;
sum_square = 0.0;
for (i = 0; i < POPSIZE; i++)
{
sum += population[i].fitness;
sum_square += population[i].fitness * population[i].fitness;
} avg = sum/(double)POPSIZE;
square_sum = avg * avg * POPSIZE;
stddev = sqrt((sum_square - square_sum)/(POPSIZE - 1));
best_val = population[POPSIZE].fitness;
fprintf(galog, "\n generation=%5d, best_val=%6.3f, avg=%6.3f, stddev=%6.3f \n\n", generation, best_val, avg, stddev);
}
/**************************************************************/
/* Main function: Each generation involves selecting the best */
/* members, performing crossover & mutation and then */
/* evaluating the resulting population, until the terminating */
/* condition is satisfied */
/**************************************************************/
void main(void)
{
int i;
if ((galog = fopen("galog.txt","w"))==NULL)
{
exit(1);
}
generation = 0;
fprintf(galog, "\n generation best average standard \n");
fprintf(galog, " number value fitness deviation \n");
initialize();
evaluate(); //评价函数，可以由用户自定义，该函数取得每个基因的适应度
keep_the_best(); //保存每次遗传后的最佳基因
while(generation<MAXGENS)
{
generation++;
select(); //选择函数：用于最大化合并杰出模型的标准比例选择，保证最优秀的个体得以生存
crossover(); //杂交函数：选择两个个体来杂交，这里用单点杂交
mutate(); //变异函数：被该函数选中后会使得某一变量被一个随机的值所取代
report(); //报告模拟进展情况
evaluate(); //评价函数，可以由用户自定义，该函数取得每个基因的适应度
elitist(); //搜寻杰出个体函数：找出最好和最坏的个体。如果某代的最好个体比前一代的最好个体要坏，那么后者将会取代当前种群的最坏个体
}
fprintf(galog,"\n\n Simulation completed\n");
fprintf(galog,"\n Best member: \n");
for (i = 0; i < NVARS; i++)
{
fprintf (galog,"\n var(%d) = %3.3f",i,population[POPSIZE].gene[i]);
}
fprintf(galog,"\n\n Best fitness = %3.3f",population[POPSIZE].fitness);
fclose(galog);
printf("Success\n");
}
/***************************************************************/ 计算结果为：
x=7.857 f(x)=24.855
注：遗传算法用来取得近似最优解，而不是最优解
