遗传算法流程图?遗传算法的基本原理?遗传算法 交叉和变异?简单遗传算法MATLAB实现(3)

遗传算法计算流程图如下图所示

1.6 MATLAB程序实现

初始化：

%初始化种群 %pop_size: 种群大小 %chromo_size: 染色体长度 function initilize(pop_size, chromo_size) global pop; for i=1:pop_size for j=1:chromo_size pop(i,j) = round(rand); end end clear i; clear j;

计算适应度：（该函数应该根据具体问题进行修改，这里优化的函数是前述的一维函数）

%计算种群个体适应度，对不同的优化目标，此处需要改写 %pop_size: 种群大小 %chromo_size: 染色体长度 function fitness(pop_size, chromo_size) global fitness_value; global pop; global G; for i=1:pop_size fitness_value(i) = 0.; end for i=1:pop_size for j=1:chromo_size if pop(i,j) == 1 fitness_value(i) = fitness_value(i)+2^(j-1); end end fitness_value(i) = -1+fitness_value(i)*(3.-(-1.))/(2^chromo_size-1); fitness_value(i) = -(fitness_value(i)-1).^2+4; end clear i; clear j;

对个体按照适应度大小进行排序：

%对个体按适应度大小进行排序，并且保存最佳个体 %pop_size: 种群大小 %chromo_size: 染色体长度 function rank(pop_size, chromo_size) global fitness_value; global fitness_table; global fitness_avg; global best_fitness; global best_individual; global best_generation; global pop; global G; for i=1:pop_size fitness_table(i) = 0.; end min = 1; temp = 1; temp1(chromo_size)=0; for i=1:pop_size min = i; for j = i+1:pop_size if fitness_value(j)<fitness_value(min); min = j; min~=i temp = fitness_value(i); fitness_value(i) = fitness_value(min); fitness_value(min) = temp; for k = 1:chromo_size temp1(k) = pop(i,k); pop(i,k) = pop(min,k); pop(min,k) = temp1(k); i=1:pop_size if i==1 fitness_table(i) = fitness_table(i) + fitness_value(i); else fitness_table(i) = fitness_table(i-1) + fitness_value(i); end end fitness_table fitness_avg(G) = fitness_table(pop_size)/pop_size; if fitness_value(pop_size) > best_fitness best_fitness = fitness_value(pop_size); best_generation = G; for j=1:chromo_size best_individual(j) = pop(pop_size,j); end end clear i; clear j; clear k; clear min; clear temp; clear temp1;

选择操作：

%赌选择操作 %pop_size: 种群大小 %chromo_size: 染色体长度 %cross_rate: 是否精英选择 function selection(pop_size, chromo_size, elitism) global pop; global fitness_table; for i=1:pop_size r = rand * fitness_table(pop_size); first = 1; last = pop_size; mid = round((last+first)/2); idx = -1; while (first <= last) && (idx == -1) if r > fitness_table(mid) first = mid; elseif r < fitness_table(mid) last = mid; else idx = mid; break; end mid = round((last+first)/2); if (last - first) == 1 idx = last; break; j=1:chromo_size pop_new(i,j)=pop(idx,j); elitism p = pop_size-1; else p = pop_size; end for i=1:p for j=1:chromo_size pop(i,j) = pop_new(i,j); end end clear i; clear j; clear pop_new; clear first; clear last; clear idx; clear mid;

交叉操作：

%单点交叉操作 %pop_size: 种群大小 %chromo_size: 染色体长度 %cross_rate: 交叉概率 function crossover(pop_size, chromo_size, cross_rate) global pop; for i=1:2:pop_size if(rand < cross_rate) cross_pos = round(rand * chromo_size); if or (cross_pos == 0, cross_pos == 1) continue; end for j=cross_pos:chromo_size temp = pop(i,j); pop(i,j) = pop(i+1,j); pop(i+1,j) = temp; clear i; clear j; clear temp; clear cross_pos;

变异操作：

%单点变异操作 %pop_size: 种群大小 %chromo_size: 染色体长度 %cross_rate: 变异概率 function mutation(pop_size, chromo_size, mutate_rate) global pop; for i=1:pop_size if rand < mutate_rate mutate_pos = round(rand*chromo_size); if mutate_pos == 0 continue; end pop(i,mutate_pos) = 1 - pop(i, mutate_pos); end end clear i; clear mutate_pos;

打印算法迭代过程：

%打印算法迭代过程 %generation_size: 迭代次数 function plotGA(generation_size) global fitness_avg; x = 1:1:generation_size; y = fitness_avg; plot(x,y)

算法主函数：

%遗传算法主函数 %pop_size: 输入种群大小 %chromo_size: 输入染色体长度 %generation_size: 输入迭代次数 %cross_rate: 输入交叉概率 %cross_rate: 输入变异概率 %elitism: 输入是否精英选择 %m: 输出最佳个体 %n: 输出最佳适应度 %p: 输出最佳个体出现代 %q: 输出最佳个体自变量值 function [m,n,p,q] = GeneticAlgorithm(pop_size, chromo_size, generation_size, cross_rate, mutate_rate, elitism) global G ; %当前代 global fitness_value;%当前代适应度矩阵 global best_fitness;%历代最佳适应值 global fitness_avg;%历代平均适应值矩阵 global best_individual;%历代最佳个体 global best_generation;%最佳个体出现代 fitness_avg = zeros(generation_size,1); disp "hhee" fitness_value(pop_size) = 0.; best_fitness = 0.; best_generation = 0; initilize(pop_size, chromo_size);%初始化 for G=1:generation_size fitness(pop_size, chromo_size); %计算适应度 rank(pop_size, chromo_size); %对个体按适应度大小进行排序 selection(pop_size, chromo_size, elitism);%选择操作 crossover(pop_size, chromo_size, cross_rate);%交叉操作 mutation(pop_size, chromo_size, mutate_rate);%变异操作 end plotGA(generation_size);%打印算法迭代过程 m = best_individual;%获得最佳个体 n = best_fitness;%获得最佳适应度 p = best_generation;%获得最佳个体出现代 %获得最佳个体变量值，对不同的优化目标，此处需要改写 q = 0.; for j=1:chromo_size if best_individual(j) == 1 q = q+2^(j-1); end end q = -1+q*(3.-(-1.))/(2^chromo_size-1); clear i; clear j;

2. 案例研究

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