蚁群算法matlab代码

这里提供一个简单的蚁群算法的 MATLAB 代码：

% 蚁群算法
% 问题：TSP（旅行商问题）

%% 初始化
clear;clc;

% 城市坐标
city = [0.4 0.4439;
        0.2439 0.1463;
        0.1707 0.2293;
        0.2293 0.761;
        0.5171 0.9414;
        0.8732 0.6536;
        0.6878 0.5219;
        0.8488 0.3609;
        0.6683 0.2536;
        0.6195 0.2634;
        0.672 0.5802;
        0.5878 0.5293;
        0.3683 0.1988;
        0.2695 0.1878;
        0.145 0.4057;
        0.1963 0.5707;
        0.0634 0.6878;
        0.4719 0.8732;
        0.6049 0.9384;
        0.6988 0.9384];

% 城市数量
nCity = size(city, 1);

% 蚂蚁数量
nAnt = 20;

% 迭代次数
nIter = 500;

% α、β、γ 参数
alpha = 1;
beta = 2;
gamma = 5;

% 信息素初始值
tau0 = 1 / (nCity * mean(pdist(city, 'euclidean')));

% 信息素矩阵
tau = tau0 * ones(nCity);

% 距离矩阵
dist = pdist2(city, city);

% 最优解
minPath = Inf;
minPathRecord = zeros(nCity+1, 1);

%% 迭代
for iter = 1:nIter
    % 初始化蚂蚁
    ant = struct('path', zeros(1, nCity+1), 'visited', false(1, nCity), 'L', 0);
    ants = repmat(ant, nAnt, 1);
    
    % 开始搜索
    for k = 1:nAnt
        % 选择起点
        start = randi(nCity);
        ants(k).path(1) = start;
        ants(k).visited(start) = true;

        % 搜寻路径
        for i = 2:nCity
            % 计算转移概率
            current = ants(k).path(i-1);
            unvisited = ~ants(k).visited;
            t = tau(current, unvisited);
            d = dist(current, unvisited);
            p = (t.^alpha) .* ((1./d).^beta);
            p = p / sum(p);

            % 轮盘选择下一个城市
            next = randsample(nCity, 1, true, p);
            ants(k).path(i) = next;
            ants(k).visited(next) = true;
            ants(k).L = ants(k).L + dist(current, next);
        end

        % 回到起点
        ants(k).path(nCity+1) = start;
        ants(k).L = ants(k).L + dist(ants(k).path(nCity), start);

        % 更新最优解
        if ants(k).L < minPath
            minPath = ants(k).L;
            minPathRecord = ants(k).path;
        end
    end

    % 更新信息素矩阵
    delta_tau = zeros(nCity);
    for k = 1:nAnt
        for i = 1:nCity
            j = ants(k).path(i+1);
            delta_tau(ants(k).path(i), j) = delta_tau(ants(k).path(i), j) + gamma / ants(k).L;
        end
    end
    tau = (1 - 0.01) * tau + delta_tau;
end

%% 结果展示
disp('最短路径：');
disp(minPathRecord);
disp(['最短距离：', num2str(minPath)]);

% 绘图
figure;
plot(city(:,1), city(:,2), 'ko', 'MarkerSize', 8, 'LineWidth', 1.5);
hold on;
plot(city(minPathRecord, 1), city(minPathRecord, 2), 'r-', 'LineWidth', 2);
text(city(:,1)+0.01, city(:,2)+0.01, num2str([1:nCity]'));
title(['TSP（旅行商问题）蚁群算法最优解（距离：', num2str(minPath), '）']);
xlabel('x');
ylabel('y');
axis equal;