蚁群算法matlab代码
时间: 2023-11-25 18:10:14 浏览: 46
以下是蚁群算法的 Matlab 代码示例:
```
function [best_path, best_dist] = ant_colony_optimization(distances, num_ants, num_iterations, evaporation_rate, alpha, beta)
% 初始化信息素矩阵和距离矩阵
num_cities = size(distances, 1);
pheromones = ones(num_cities, num_cities);
distances(distances == 0) = realmax;
% 迭代过程
for iteration = 1:num_iterations
% 初始化蚂蚁的位置和路径
ant_paths = zeros(num_ants, num_cities);
ant_paths(:, 1) = randi(num_cities, [num_ants, 1]);
% 计算每只蚂蚁的路径
for ant = 1:num_ants
for city = 2:num_cities
current_city = ant_paths(ant, city-1);
unvisited_cities = setdiff(1:num_cities, ant_paths(ant, 1:city-1));
probabilities = pheromones(current_city, unvisited_cities).^alpha .* distances(current_city, unvisited_cities).^(-beta);
probabilities = probabilities / sum(probabilities);
next_city = unvisited_cities(find(rand <= cumsum(probabilities), 1));
ant_paths(ant, city) = next_city;
end
end
% 计算每只蚂蚁的路径长度
ant_distances = zeros(num_ants, 1);
for ant = 1:num_ants
for city = 1:num_cities-1
ant_distances(ant) = ant_distances(ant) + distances(ant_paths(ant, city), ant_paths(ant, city+1));
end
ant_distances(ant) = ant_distances(ant) + distances(ant_paths(ant, end), ant_paths(ant, 1));
end
% 更新信息素矩阵
delta_pheromones = zeros(num_cities, num_cities);
for ant = 1:num_ants
for city = 1:num_cities-1
delta_pheromones(ant_paths(ant, city), ant_paths(ant, city+1)) = delta_pheromones(ant_paths(ant, city), ant_paths(ant, city+1)) + 1/ant_distances(ant);
delta_pheromones(ant_paths(ant, city+1), ant_paths(ant, city)) = delta_pheromones(ant_paths(ant, city+1), ant_paths(ant, city)) + 1/ant_distances(ant);
end
delta_pheromones(ant_paths(ant, end), ant_paths(ant, 1)) = delta_pheromones(ant_paths(ant, end), ant_paths(ant, 1)) + 1/ant_distances(ant);
delta_pheromones(ant_paths(ant, 1), ant_paths(ant, end)) = delta_pheromones(ant_paths(ant, 1), ant_paths(ant, end)) + 1/ant_distances(ant);
end
pheromones = (1-evaporation_rate) * pheromones + delta_pheromones;
end
% 找到最短路径和距离
best_dist = realmax;
for ant = 1:num_ants
path_dist = 0;
for city = 1:num_cities-1
path_dist = path_dist + distances(ant_paths(ant, city), ant_paths(ant, city+1));
end
path_dist = path_dist + distances(ant_paths(ant, end), ant_paths(ant, 1));
if path_dist < best_dist
best_path = ant_paths(ant, :);
best_dist = path_dist;
end
end
end
```
在这个代码中,我们定义了一个函数 `ant_colony_optimization`,它接受以下参数:
- `distances`:一个 `n x n` 的矩阵,其中 `n` 是城市的数量,矩阵中的每个元素表示从一个城市到另一个城市的距离。
- `num_ants`:蚂蚁的数量。
- `num_iterations`:算法要运行的迭代次数。
- `evaporation_rate`:信息素挥发速率。
- `alpha` 和 `beta`:控制信息素和距离的相对重要性的参数。
函数返回两个值:最优路径和最优路径的总距离。