采用粒子群算法求解旅行商问题 matlab源码

粒子群算法（PSO）是一种基于群体智能的优化算法，常用于求解旅行商问题。在Matlab中，我们可以使用以下源码实现。

function [best_path, best_distance] = tsp_pso(points, swarm_size, max_iterations)
    num_points = size(points, 1);
    c1 = 2;
    c2 = 2;
    inertia_weight = 1;
    max_velocity = 0.1;

    % 初始化粒子位置和速度
    positions = rand(swarm_size, num_points);
    velocities = rand(swarm_size, num_points) * max_velocity;
    personal_best = positions;
    global_best = inf;
    global_best_position = zeros(1, num_points);

    for i=1:max_iterations
        for j=1:swarm_size
            distance = calculate_distance(points, positions(j, :));
            if distance < calculate_distance(points, personal_best(j, :))
                personal_best(j, :) = positions(j, :);
            end
            if distance < global_best
                global_best = distance;
                global_best_position = positions(j, :);
            end
        end

        r1 = rand(swarm_size, num_points);
        r2 = rand(swarm_size, num_points);
        velocities = inertia_weight * velocities + c1 * r1 .* (personal_best - positions) + c2 * r2 .* (global_best_position - positions);
        velocities(velocities > max_velocity) = max_velocity;
        velocities(velocities < -max_velocity) = -max_velocity;
        positions = positions + velocities;
    end
    best_path = global_best_position;
    best_distance = global_best;
end

function distance = calculate_distance(points, path)
    distance = 0;
    num_points = size(points, 1);
    for i=1:num_points-1
        distance = distance + norm(points(path(i), :) - points(path(i+1), :));
    end
    distance = distance + norm(points(path(end), :) - points(path(1), :));
end

在这个源码中，我们首先定义了一个tsp_pso函数来实现粒子群算法。该函数接受旅行商问题的点集、粒子群大小和最大迭代次数作为输入，并输出最佳路径和最短距离。我们使用随机初始化粒子位置和速度，并在每次迭代中更新粒子的位置和速度，直到达到最大迭代次数。粒子的个体最优和全局最优都被更新并用来指导粒子搜索的方向。最后我们定义了一个辅助函数calculate_distance来计算路径的总长度。

以上就是使用粒子群算法求解旅行商问题的Matlab源码。