用matlab写一段CMA-ES代码

以下是一个简单的CMA-ES（协方差矩阵适应进化策略）的Matlab代码：

function [best, fval] = cmaes(fitnessfcn, x0, sigma0, options)
% 输入:
% fitnessfcn: 目标函数句柄
% x0: 初始解向量
% sigma0: 初始步长
% options: 设置参数的结构体
% 输出:
% best: 最优解向量
% fval: 最优解对应的目标函数值

% 初始化参数
n = length(x0);
lambda = 4 + floor(3*log(n));
mu = floor(lambda/2);
weights = log(mu+1/2)-log(1:mu)';
mu_eff = sum(weights)^2/sum(weights.^2);
cc = (4 + mu_eff/n) / (n+4 + 2*mu_eff/n);
cs = (mu_eff+2) / (n+mu_eff+5);
c1 = 2 / ((n+1.3)^2+mu_eff);
cmu = min(1-c1, 2 * (mu_eff-2+1/mu_eff) / ((n+2)^2+mu_eff));
damps = 1 + 2*max(0, sqrt((mu_eff-1)/(n+1))-1) + cs;

% 初始化种群和协方差矩阵
xmean = x0;
ps = zeros(n, 1);
pc = zeros(n, 1);
C = eye(n);
B = eye(n);
D = ones(n, 1);
sigma = sigma0;
counteval = 0;

% 开始迭代
for i = 1:options.MaxIterations
    % 生成新的种群
    arx = repmat(xmean, 1, lambda) + sigma * (B * diag(D) * randn(n, lambda));
    arfitness = zeros(lambda, 1);
    for j = 1:lambda
        arfitness(j) = fitnessfcn(arx(:, j));
        counteval = counteval + 1;
    end
    
    % 更新最优解
    [arfitness, arindex] = sort(arfitness);
    best = arx(:, arindex(1));
    fval = arfitness(1);
    
    % 更新协方差矩阵
    ps = (1-cs)*ps + sqrt(cs*(2-cs)*mu_eff)*(B*diag(D))*(arx(:, arindex(1:mu))-repmat(xmean, 1, mu)) / sigma;
    hsig = norm(ps) / sqrt(1-(1-cs)^(2*counteval/lambda)) < (1.4 + 2/(n+1));
    pc = (1-cc)*pc + hsig*sqrt(cc*(2-cc)*mu_eff)*(arx(:, arindex(1:mu))*weights) / sigma;
    C = (1-c1-cmu)*C + c1*(pc*pc' + (1-hsig)*cc*(2-cc)*C) + cmu*(arx(:, arindex(1:mu))*diag(weights)*arx(:, arindex(1:mu))');
    
    % 更新步长和均值
    sigma = sigma * exp((cs/damps)*(norm(ps)/sqrt(n))-1);
    if mod(counteval/lambda, n/10) < 1
        C = triu(C) + triu(C,1)';
        [B, D] = eig(C);
        D = sqrt(diag(D));
        xmean = arx(:, arindex(1:mu)) * weights;
    end
    
    % 检查是否收敛
    if fval <= options.FunctionTolerance
        break;
    end
end

end

需要注意的是，这只是一个简单的实现，可能存在性能问题和不够健壮的情况。在实际应用中需要根据具体问题进行调整和优化。