蚁群算法解决三维TSP问题MATLAB代码

以下是使用蚁群算法解决三维TSP问题的MATLAB代码示例：

% 设置参数
num_ants = 50; % 蚂蚁数量
num_iter = 500; % 迭代次数
q0 = 0.9; % 贪心因子
alpha = 1; % 信息启发因子
beta = 5; % 启发式因子
rho = 0.1; % 信息素挥发因子
Q = 1; % 信息素常数
Lnnn = 10000; % 初始最短路径长度

% 初始化三维坐标
n = 10; % 城市数量
x = rand(n, 1);
y = rand(n, 1);
z = rand(n, 1);

% 初始化距离矩阵
d = zeros(n, n);
for i = 1:n
    for j = 1:n
        d(i, j) = sqrt((x(i) - x(j))^2 + (y(i) - y(j))^2 + (z(i) - z(j))^2);
    end
end

% 初始化信息素矩阵
tau = ones(n, n);

% 开始迭代
for iter = 1:num_iter
    % 初始化蚂蚁位置和路径长度
    ant_pos = zeros(num_ants, 1);
    ant_path_len = zeros(num_ants, 1);

    % 对每只蚂蚁进行迭代
    for k = 1:num_ants
        % 初始化蚂蚁位置和已访问城市集合
        ant_pos(k) = randi(n);
        visited_cities = ant_pos(k);

        % 开始访问城市
        for i = 2:n
            curr_city = ant_pos(k);

            % 计算每个未访问城市的概率
            unvisited_cities = setdiff(1:n, visited_cities);
            p = zeros(length(unvisited_cities), 1);
            for j = 1:length(unvisited_cities)
                next_city = unvisited_cities(j);
                p(j) = tau(curr_city, next_city)^alpha * (1 / d(curr_city, next_city))^beta;
            end
            p = p / sum(p);

            % 根据概率选择下一个访问城市
            if rand < q0
                [~, idx] = max(p);
                next_city = unvisited_cities(idx);
            else
                next_city = randsample(unvisited_cities, 1, true, p);
            end

            % 更新蚂蚁位置和已访问城市集合
            ant_pos(k) = next_city;
            visited_cities = [visited_cities next_city];
            ant_path_len(k) = ant_path_len(k) + d(curr_city, next_city);
        end

        % 加上回到起点的路径长度
        ant_path_len(k) = ant_path_len(k) + d(ant_pos(k), ant_pos(1));
    end

    % 更新信息素矩阵
    delta_tau = zeros(n, n);
    for k = 1:num_ants
        for i = 1:n-1
            curr_city = ant_pos(k, i);
            next_city = ant_pos(k, i+1);
            delta_tau(curr_city, next_city) = delta_tau(curr_city, next_city) + Q / ant_path_len(k);
        end
        delta_tau(ant_pos(k, n), ant_pos(k, 1)) = delta_tau(ant_pos(k, n), ant_pos(k, 1)) + Q / ant_path_len(k);
    end
    tau = (1 - rho) * tau + delta_tau;

    % 更新最短路径长度和路径
    [min_path_len, min_path] = min(ant_path_len);
    if min_path_len < Lnnn
        Lnnn = min_path_len;
        best_path = ant_pos(min_path, :);
    end
end

% 输出结果
disp(['最短路径长度：' num2str(Lnnn)])
disp(['最短路径顺序：' num2str(best_path)])

以上代码实现了基本的蚁群算法，如果需要更好的性能，可以尝试使用改进的蚁群算法，如ACO-QP和ACO-ACS。