遗传算法matlab程序

以下是一个简单的遗传算法的 MATLAB 程序：

function [best_sol, best_fitness] = genetic_algorithm(pop_size, num_generations, crossover_prob, mutation_prob)

% 初始化种群
population = randi([0, 1], pop_size, 10); 

for i = 1:num_generations
    
    % 计算适应度
    fitness = sum(population, 2);
    
    % 选择父代
    parents = selection(population, fitness);
    
    % 交叉
    offspring = crossover(parents, crossover_prob);
    
    % 变异
    offspring = mutation(offspring, mutation_prob);
    
    % 合并子代和父代
    population = [parents; offspring];
    
    % 保留适应度最高的个体
    [best_fitness, best_index] = max(fitness);
    best_sol = population(best_index, :);
    
end

end

function parents = selection(population, fitness)

% 轮盘赌选择
prob = fitness / sum(fitness);
cum_prob = cumsum(prob);
parents = zeros(size(population));
for i = 1:size(population, 1)
    r = rand();
    for j = 1:size(population, 1)
        if r <= cum_prob(j)
            parents(i, :) = population(j, :);
            break;
        end
    end
end

end

function offspring = crossover(parents, crossover_prob)

% 一点交叉
offspring = zeros(size(parents));
for i = 1:2:size(parents, 1)
    if rand() < crossover_prob
        crossover_point = randi(size(parents, 2));
        offspring(i, :) = [parents(i, 1:crossover_point), parents(i+1, crossover_point+1:end)];
        offspring(i+1, :) = [parents(i+1, 1:crossover_point), parents(i, crossover_point+1:end)];
    else
        offspring(i, :) = parents(i, :);
        offspring(i+1, :) = parents(i+1, :);
    end
end

end

function offspring = mutation(parents, mutation_prob)

% 每个基因独立变异
offspring = parents;
for i = 1:size(parents, 1)
    for j = 1:size(parents, 2)
        if rand() < mutation_prob
            offspring(i, j) = 1 - parents(i, j);
        end
    end
end

end

这个程序实现了一个简单的遗传算法，用于解决一个二进制字符串的最大一的个数问题。其中，种群中每个个体都是一个长度为 10 的二进制字符串，适应度定义为其中 1 的个数。在每一代中，进行选择、交叉和变异操作，得到子代种群，然后将父代和子代合并，并保留适应度最高的个体。程序的输入参数包括种群大小、迭代次数、交叉概率和变异概率。程序的输出是最优解和最优适应度。