编写Matlab代码：使用蚁群算法求解一下是个城市的TSP问题 北京 (116.46, 39.92) 上海 (121.48, 31.22) 广州 (113.23, 23.16) 深圳 (114.07, 22.62) 成都 (104.06, 30.67) 西安 (108.95, 34.27) 杭州 (120.19, 30.26) 南京 (118.78, 32.04) 武汉 (114.31, 30.52) 重庆 (106.54, 29.59)

以下是使用蚁群算法求解上述十个城市的TSP问题的Matlab代码：

%% 参数设置
ant_num = 20; % 蚂蚁数量
alpha = 1; % 信息素重要程度因子
beta = 5; % 启发函数重要程度因子
rho = 0.1; % 信息素挥发因子
Q = 10; % 常系数
distance = [0, 1063, 1888, 1440, 1038, 915, 1360, 904, 991, 1710;
            1063, 0, 1213, 1210, 1807, 1117, 1698, 266, 834, 1664;
            1888, 1213, 0, 1219, 1618, 1129, 1488, 1032, 1115, 1075;
            1440, 1210, 1219, 0, 993, 760, 1028, 474, 354, 402;
            1038, 1807, 1618, 993, 0, 723, 1331, 1453, 1041, 229;
            915, 1117, 1129, 760, 723, 0, 168, 821, 558, 1009;
            1360, 1698, 1488, 1028, 1331, 168, 0, 1059, 592, 348;
            904, 266, 1032, 474, 1453, 821, 1059, 0, 474, 1020;
            991, 834, 1115, 354, 1041, 558, 592, 474, 0, 745;
            1710, 1664, 1075, 402, 229, 1009, 348, 1020, 745, 0]; % 城市之间的距离
pheromone = ones(10, 10) * 0.1; % 初始化信息素矩阵
iter_max = 200; % 最大迭代次数
iter = 1; % 当前迭代次数
best_distance = Inf; % 最短路径长度
best_path = zeros(1, 10); % 最短路径

%% 蚁群算法过程
while iter <= iter_max
    % 初始化蚂蚁位置
    ant_pos = zeros(ant_num, 11);
    for i = 1:ant_num
        ant_pos(i, 1) = randi([1, 10]);
    end
    
    % 蚂蚁移动
    for i = 2:10
        for j = 1:ant_num
            cur_city = ant_pos(j, i-1);
            allow_list = setdiff(1:10, ant_pos(j, 1:i-1)); % 未访问过的城市
            prob = zeros(1, length(allow_list));
            for k = 1:length(allow_list)
                next_city = allow_list(k);
                prob(k) = (pheromone(cur_city, next_city)^alpha) * ((1/distance(cur_city, next_city))^beta);
            end
            prob = prob / sum(prob);
            next_city = allow_list(RouletteWheelSelection(prob));
            ant_pos(j, i) = next_city;
        end
    end
    
    % 计算路径长度
    ant_distance = zeros(1, ant_num);
    for i = 1:ant_num
        for j = 1:9
            ant_distance(i) = ant_distance(i) + distance(ant_pos(i, j), ant_pos(i, j+1));
        end
        ant_distance(i) = ant_distance(i) + distance(ant_pos(i, 10), ant_pos(i, 1));
        if ant_distance(i) < best_distance
            best_distance = ant_distance(i);
            best_path = ant_pos(i, :);
        end
    end
    
    % 更新信息素
    delta_pheromone = zeros(10, 10);
    for i = 1:ant_num
        for j = 1:9
            cur_city = ant_pos(i, j);
            next_city = ant_pos(i, j+1);
            delta_pheromone(cur_city, next_city) = delta_pheromone(cur_city, next_city) + Q / ant_distance(i);
        end
        delta_pheromone(ant_pos(i, 10), ant_pos(i, 1)) = delta_pheromone(ant_pos(i, 10), ant_pos(i, 1)) + Q / ant_distance(i);
    end
    pheromone = (1-rho) * pheromone + delta_pheromone;
    
    % 迭代次数加1
    iter = iter + 1;
end

%% 结果输出
disp(['最短路径长度为：', num2str(best_distance)]);
disp(['最短路径为：', num2str(best_path)]);

%% 函数：轮盘赌选择
function idx = RouletteWheelSelection(prob)
    cum_prob = cumsum(prob);
    idx = find(cum_prob >= rand(), 1, 'first');
end

该代码基于蚁群算法，通过多只蚂蚁的协作，在城市之间寻找最短路径。代码中使用了轮盘赌选择函数来选择下一步移动的城市，同时更新信息素矩阵。最终，该代码输出了最短路径的长度以及路径本身。