运行ACO算法求解Shubert函数的最小值xopt yopt fopt = ACO Shubert函数 输入：x和y向量 输出：函数值f function f = Shubertx y基于上述信息编写matlab程序完成求解Shubert函数的最优解

function [xopt, yopt, fopt] = ACO() % ACO算法参数设置 n_ant = 100; % 蚂蚁个数 alpha = 1; % 信息素重要程度 beta = 5; % 启发式因子重要程度 rho = 0.1; % 信息素挥发系数 Q = 1; % 常数因子 max_iter = 100; % 最大迭代次数

% Shubert函数定义 function f = Shubert(x, y) f = 0; for i = 1:5 term1 = 0; term2 = 0; for j = 1:2 term1 = term1 + j*cos((j+1)x(i)+j); term2 = term2 + jcos((j+1)*y(i)+j); end f = f + term1 * term2; end

% 初始化信息素矩阵和最优解 tau = ones(10, 10); xopt = 0; yopt = 0; fopt = Inf;

% ACO算法迭代 for iter = 1:max_iter % 初始化蚂蚁位置和已访问城市 ant_pos = randi([1, 10], n_ant, 2); visited = zeros(n_ant, 10, 10);

% 蚂蚁搜索路径
for k = 1:n_ant
    for i = 1:5
        % 计算可行解
        feasible = zeros(10, 10);
        for j = 1:10
            feasible(j, :) = visited(k, j, :) == 0;
        end
        feasible(visited(k, :, i) == 1, :) = 0;
        feasible(:, visited(k, i, :) == 1) = 0;
        feasible(visited(k, i, i) == 1) = 0;
        [row, col] = find(feasible);
        
        % 计算转移概率
        prob = zeros(length(row), 1);
        for j = 1:length(row)
            prob(j) = tau(row(j), col(j))^alpha * (1/abs(Shubert(row(j), col(j)))^beta);
        end
        prob = prob / sum(prob);
        
        % 选择下一个城市
        next = randi(length(row));
        visited(k, row(next), col(next)) = 1;
    end
end

% 更新信息素
delta_tau = zeros(10, 10);
for k = 1:n_ant
    for i = 1:5
        delta_tau(visited(k, i, 1), visited(k, i, 2)) = delta_tau(visited(k, i, 1), visited(k, i, 2)) + Q / Shubert(visited(k, i, 1), visited(k, i, 2));
    end
end
tau = (1 - rho) * tau + delta_tau;

% 更新最优解
for i = 1:10
    for j = 1:10
        if Shubert(i, j) < fopt
            xopt = i;
            yopt = j;
            fopt = Shubert(i, j);
        end
    end
end

% 输出最优解
fprintf('Iteration %d: fopt = %f\n', iter, fopt);

end

% 输出最终结果 fprintf('xopt = %d, yopt = %d, fopt = %f\n', xopt, yopt, fopt); en