哈密顿回路与蚁群算法如何结合

Question

哈密顿回路与蚁群算法如何结合算出城市（只知道距离）之间的最短路径

Answer 1

% 初始化参数
num_cities = 5; % 城市数量
num_ants = 10; % 蚂蚁数量
num_iterations = 100; % 迭代次数
evaporation_rate = 0.5; % 蒸发率
alpha = 1; % 信息素重要性
beta = 5; % 启发式信息重要性

% 城市之间的距离矩阵
distances = [
    0, 2, 3, 4, 5;
    2, 0, 4, 5, 3;
    3, 4, 0, 2, 1;
    4, 5, 2, 0, 6;
    5, 3, 1, 6, 0
];

% 信息素矩阵
pheromones = ones(num_cities, num_cities);

% 最短路径长度和路径初始化
shortest_path_length = inf;
shortest_path = [];

% 蚁群算法迭代
for iteration = 1:num_iterations
    for ant = 1:num_ants
        current_city = randi(num_cities); % 随机选择起始城市
        cities_visited = current_city;
        total_distance = 0;

        % 创建哈密顿回路
        for i = 1:num_cities-1
            current_pheromones = pheromones(current_city, :);
            current_distances = distances(current_city, :);

            % 计算转移概率
            move_probabilities = (current_pheromones.^alpha) .* ((1./current_distances).^beta);
            move_probabilities(cities_visited) = 0; % 已访问城市的概率设置为0
            move_probabilities = move_probabilities / sum(move_probabilities);

            % 选择下一个城市
            next_city = find(rand < cumsum(move_probabilities), 1);
            cities_visited(end+1) = next_city;
            total_distance = total_distance + distances(current_city, next_city);

            current_city = next_city;
        end

        % 更新最短路径
        if total_distance < shortest_path_length
            shortest_path_length = total_distance;
            shortest_path = cities_visited;
        end

        % 更新信息素
        for i = 1:num_cities-1
            pheromones(cities_visited(i),cities_visited(i+1)) = (1 - evaporation_rate) * pheromones(cities_visited(i),cities_visited(i+1)) + 1/total_distance;
        end
    end
end

% 显示结果
disp('最短路径长度:');
disp(shortest_path_length);
disp('最短路径:');
disp(shortest_path);