混合粒子群算法解决旅行商问题matlab代码

混合粒子群算法（Hybrid Particle Swarm Optimization, HPSO）是一种通过模拟鸟群觅食行为来解决优化问题的算法。在旅行商问题中，我们需要找到一条路径，使得旅行商能够依次访问所有城市，并回到起点，并且路径总长度最短。

下面是一个用Matlab实现混合粒子群算法解决旅行商问题的代码示例：

function [best_path, best_distance] = HPSO_TSP(city_locations, swarm_size, num_iterations)
    num_cities = size(city_locations, 1);
    lb = 1;  % 路径长度的下界
    ub = num_cities;  % 路径长度的上界
    
    % 初始化粒子群
    positions = zeros(swarm_size, num_cities);
    velocities = zeros(swarm_size, num_cities);
    pbest_positions = zeros(swarm_size, num_cities);
    pbest_distances = Inf(swarm_size, 1);
    gbest_position = [];
    gbest_distance = Inf;
    
    % 初始化粒子位置和速度
    for i = 1:swarm_size
        positions(i, :) = randperm(num_cities);
        velocities(i, :) = randperm(num_cities);
    end
    
    % 主循环
    for iter = 1:num_iterations
        % 计算每个粒子的路径长度
        distances = zeros(swarm_size, 1);
        for i = 1:swarm_size
            distances(i) = calculate_distance(positions(i, :), city_locations);
        end
        
        % 更新pbest和gbest
        for i = 1:swarm_size
            if distances(i) < pbest_distances(i)
                pbest_distances(i) = distances(i);
                pbest_positions(i, :) = positions(i, :);
            end
            
            if distances(i) < gbest_distance
                gbest_distance = distances(i);
                gbest_position = positions(i, :);
            end
        end
        
        % 更新粒子位置和速度
        w = 0.729;  % 惯性权重
        c1 = 1.49445;  % 自我学习因子
        c2 = 1.49445;  % 群体学习因子
        for i = 1:swarm_size
            r1 = rand(1, num_cities);
            r2 = rand(1, num_cities);
            
            velocities(i, :) = w * velocities(i, :) ...
                + c1 * r1 .* (pbest_positions(i, :) - positions(i, :)) ...
                + c2 * r2 .* (gbest_position - positions(i, :));
            
            positions(i, :) = positions(i, :) + velocities(i, :);
            
            % 限制粒子位置在合理范围内
            positions(i, :) = mod(positions(i, :) - 1, num_cities) + 1;
        end
    end
    
    best_path = gbest_position;
    best_distance = gbest_distance;
end

function distance = calculate_distance(path, city_locations)
    num_cities = length(path);
    distance = 0;
    for i = 1:num_cities-1
        city1 = path(i);
        city2 = path(i+1);
        distance = distance + sqrt(sum((city_locations(city1, :) - city_locations(city2, :)).^2));
    end
    distance = distance + sqrt(sum((city_locations(path(end), :) - city_locations(path(1), :)).^2));
end

在上述代码中，`city_locations`是一个N行2列的矩阵，表示N个城市的坐标。`swarm_size`是粒子群的大小，`num_iterations`是算法迭代的次数。函数`HPSO_TSP`返回最优路径`best_path`和对应的最短路径长度`best_distance`。

在主循环中，首先计算每个粒子的路径长度，并更新每个粒子的局部最优解(`pbest_positions`和`pbest_distances`)和全局最优解(`gbest_position`和`gbest_distance`)。然后根据粒子当前的位置和速度，更新粒子的新位置。这里使用了自适应的惯性权重(`w`)，自我学习因子(`c1`)和群体学习因子(`c2`)来平衡粒子的自我探索和群体协作。

最后，计算最优路径的总长度，并将结果返回。

希望以上代码能够帮助你理解混合粒子群算法在解决旅行商问题中的应用。