在matlab中编写用蚁群算法求解VRP问题的代码

以下是一个简单的用蚁群算法求解VRP问题的Matlab代码：

% 蚁群算法求解VRP问题

% 定义城市坐标
city_pos = [0 0; 20 20; 30 40; 50 50; 70 80; 90 80; 100 60; 120 80; 130 70; 150 10];

% 定义车辆容量
vehicle_capacity = 20;

% 定义初始信息素值
pheromone = ones(size(city_pos, 1), size(city_pos, 1)) * 0.1;

% 定义迭代次数和蚂蚁数量
max_iter = 100;
ant_num = 10;

% 初始化最优路径和路径长度
best_path = [];
best_distance = Inf;

% 迭代
for iter = 1:max_iter
    % 每只蚂蚁的起始城市为1号城市
    ant_pos = ones(ant_num, 1);
    % 初始化每只蚂蚁的路径和距离
    ant_path = zeros(ant_num, size(city_pos, 1));
    ant_distance = zeros(ant_num, 1);
    % 模拟每只蚂蚁的移动
    for ant = 1:ant_num
        % 选择下一个城市
        next_city = choose_next_city(ant_pos(ant), ant_path(ant,:), pheromone, city_pos, vehicle_capacity);
        % 更新路径和距离
        ant_path(ant, :) = [ant_pos(ant), next_city];
        ant_distance(ant) = ant_distance(ant) + norm(city_pos(ant_pos(ant), :) - city_pos(next_city, :));
        % 更新当前城市
        ant_pos(ant) = next_city;
    end
    % 更新最优路径和距离
    [min_distance, min_index] = min(ant_distance);
    if min_distance < best_distance
        best_path = ant_path(min_index, :);
        best_distance = min_distance;
    end
    % 更新信息素
    pheromone = update_pheromone(pheromone, ant_path, ant_distance);
end

% 显示最优路径和距离
disp(['Best path: ', num2str(best_path)]);
disp(['Best distance: ', num2str(best_distance)]);

% 选择下一个城市的函数
function next_city = choose_next_city(current_city, visited_cities, pheromone, city_pos, vehicle_capacity)
    % 计算当前城市到每个未访问城市的距离和信息素值
    unvisited_cities = setdiff(1:size(city_pos, 1), visited_cities);
    dist = norm(city_pos(current_city, :) - city_pos(unvisited_cities, :), 2, 2);
    pheromone_values = pheromone(current_city, unvisited_cities);
    % 计算每个未访问城市的转移概率
    probabilities = pheromone_values .* (1 ./ dist)';
    % 排除车辆容量不足的城市
    capacities = [0; 10; 5; 20; 15; 10; 5; 10; 15; 5];
    feasible_cities = unvisited_cities(capacities(unvisited_cities) <= vehicle_capacity);
    feasible_probabilities = probabilities(capacities(unvisited_cities) <= vehicle_capacity);
    % 按转移概率选择下一个城市
    if isempty(feasible_cities)
        next_city = visited_cities(end);
    else
        feasible_probabilities = feasible_probabilities / sum(feasible_probabilities);
        next_city = randsample(feasible_cities, 1, true, feasible_probabilities);
    end
end

% 更新信息素的函数
function pheromone = update_pheromone(pheromone, ant_path, ant_distance)
    % 计算每只蚂蚁留下的信息素
    delta_pheromone = zeros(size(pheromone));
    for ant = 1:size(ant_path, 1)
        for i = 1:size(ant_path, 2)-1
            delta_pheromone(ant_path(ant, i), ant_path(ant, i+1)) = delta_pheromone(ant_path(ant, i), ant_path(ant, i+1)) + 1/ant_distance(ant);
        end
    end
    % 更新信息素
    pheromone = pheromone * 0.9 + delta_pheromone * 0.1;
end

这个代码中使用了一些简化的数据和假设，例如每个城市的需求量都为1，车辆容量是固定的，信息素挥发因子为0.9等。实际应用中需要根据具体问题进行调整。