写一份matlab遗传算法

好的，以下是一个简单的 Matlab 遗传算法的实现：

% 遗传算法实现
% 目标函数：f(x) = x^2 + 2x + 1
% 求解区间：[-10, 10]
% 种群大小：50
% 交叉概率：0.8
% 变异概率：0.01
% 迭代次数：100

pop_size = 50; % 种群大小
chrom_length = 16; % 染色体长度
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率
max_gen = 100; % 迭代次数

% 初始化种群
pop = round(rand(pop_size, chrom_length));

for i = 1:max_gen
    % 计算适应度
    x = bin2dec(num2str(pop));    fitness = x.^2 + 2*x + 1;
    
    % 轮盘赌选择
    p_fit = fitness / sum(fitness);
    cum_fit = cumsum(p_fit);
    new_pop = zeros(size(pop));
    for j = 1:pop_size
        idx = find(cum_fit >= rand, 1);
        new_pop(j,:) = pop(idx,:);
    end
    
    % 交叉操作
    for j = 1:2:pop_size
        if rand < pc
            cpoint = randi([1, chrom_length-1]);
            temp1 = [new_pop(j,1:cpoint), new_pop(j+1,cpoint+1:end)];
            temp2 = [new_pop(j+1,1:cpoint), new_pop(j,cpoint+1:end)];
            new_pop(j,:) = temp1;
            new_pop(j+1,:) = temp2;
        end
    end
    
    % 变异操作
    for j = 1:pop_size
        for k = 1:chrom_length
            if rand < pm
                new_pop(j,k) = 1 - new_pop(j,k);
            end
        end
    end
    
    % 更新种群
    pop = new_pop;
end

% 输出最优解
x = bin2dec(num2str(pop(1,:)));
y = x^2 + 2*x + 1;
fprintf('最优解：x=%d, y=%d\n', x, y);