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
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- 社区专家-Monster-XH 2023-10-24 08:53关注
% 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);
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