多旅行商问题matlab代码

A：以下是一个使用动态规划解决多旅行商问题的 MATLAB 代码示例：

% 输入城市坐标
cities = [0 0; 1 1; 2 1; 1 2; 2 2];

% 求解旅行商路径
path = solveTSP(cities);

% 输出路径
disp(path);

% 动态规划算法求解 TSP
function path = solveTSP(cities)
    n = size(cities, 1);
    dist = distMat(cities);
    dp = zeros(2^n, n);
    path = zeros(1, n);
    
    % 初始化，从任意一点开始，记为第 1 个点
    for i = 2 : n
        dp(bitset(0, i-1), i) = dist(1, i);
    end

    % 动态规划求解
    for s = 3 : n
        C = combnk(2:n, s-1);
        for i = 1 : size(C, 1)
            S = C(i, :);
            M = zeros(1, n);
            for j = 1 : length(S)
                state = bitset(0, S(j)-1);
                for k = 1 : length(S)
                    if j ~= k
                        state = bitset(state, S(k)-1);
                    end
                end
                for k = 1 : n
                    if bitget(state, k-1) == 1
                        M(k) = M(k) + dist(k, S(j)) + dp(bitset(state, j-1), S(j));
                    end
                end
            end
            for j = 1 : length(S)
                state = bitset(0, S(j)-1);
                for k = 1 : length(S)
                    if j ~= k
                        state = bitset(state, S(k)-1);
                    end
                end
                for k = 1 : n
                    if bitget(state, k-1) == 1
                        dp(bitset(state, j-1), k) = min(dp(bitset(state, j-1), k), M(k) - dist(k, S(j)) - dp(bitset(state, j-1), S(j)) + dist(S(j), k));
                    end
                end
            end
        end
    end
    
    % 回到起点
    state = 2^n-1;
    [~, idx] = min(dp(state, :));
    path(n) = idx;
    for i = n-1 : -1: 1
        state = bitset(state, path(i+1)-1, 0);
        [~, idx] = min(dp(state, path(i+1)));
        path(i) = idx;
    end
end

% 计算城市距离矩阵
function dist = distMat(cities)
    n = size(cities, 1);
    dist = zeros(n, n);
    for i = 1 : n
        for j = i+1 : n
            dist(i, j) = norm(cities(i, :) - cities(j, :));
            dist(j, i) = dist(i, j);
        end
    end
end

此代码实现了一个使用了动态规划算法的多旅行商问题求解器。该算法通过计算所有子问题的最短路径长度，然后组合得出最终的旅行商路径解。