遗传算法的matlab程序

以下是一个简单的遗传算法的 Matlab 程序，用于最小化函数 f(x) = x^2，其中 x 的范围为 [-10, 10]。

% 遗传算法最小化函数 f(x) = x^2，x 范围为 [-10, 10]

% 初始化参数
pop_size = 50; % 种群大小
chrom_length = 10; % 染色体长度
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率
max_gen = 100; % 最大迭代次数
range = [-10, 10]; % 取值范围

% 随机生成初始种群
pop = rand(pop_size, chrom_length);

for i = 1:max_gen
    % 计算适应度函数值
    fitness = sum(pop.^2, 2);
    
    % 选择
    [sorted_fit, idx] = sort(fitness);
    selected_pop = pop(idx(1:pop_size/2), :);
    
    % 交叉
    cross_pop = zeros(size(selected_pop));
    for j = 1:pop_size/2
        if rand < pc
            k = j + pop_size/2;
            p1 = selected_pop(j, :);
            p2 = selected_pop(k, :);
            c_point = randi(chrom_length-1);
            cross_pop(j, :) = [p1(1:c_point), p2(c_point+1:end)];
            cross_pop(k, :) = [p2(1:c_point), p1(c_point+1:end)];
        else
            cross_pop(j, :) = selected_pop(j, :);
            cross_pop(j+pop_size/2, :) = selected_pop(j+pop_size/2, :);
        end
    end
    
    % 变异
    mut_pop = cross_pop;
    for j = 1:pop_size
        if rand < pm
            m_point = randi(chrom_length);
            mut_pop(j, m_point) = rand*(range(2)-range(1)) + range(1);
        end
    end
    
    % 合并种群
    pop = [selected_pop; mut_pop];
end

% 找到最优解
fitness = sum(pop.^2, 2);
[~, idx] = min(fitness);
x = sum((2.^(0:chrom_length-1)).*pop(idx, :));
x = (range(2)-range(1))*x/(2^chrom_length-1) + range(1);
fprintf('最优解 x = %.4f\n', x);