遗传算法---实数编码方式
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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 3.1415926int 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
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