写一段matlab程序,利用蚁群算法求解高铁列车停站方案
时间: 2023-08-04 19:10:24 浏览: 58
以下是一个简单的matlab程序,利用蚁群算法求解高铁列车停站方案:
```
% 蚁群算法求解高铁列车停站方案
% 定义问题
stations = ["北京", "天津", "石家庄", "济南", "合肥", "南京", "上海"];
distances = [0, 117, 276, 376, 733, 944, 1318;
117, 0, 236, 355, 612, 823, 1206;
276, 236, 0, 274, 531, 742, 1115;
376, 355, 274, 0, 257, 468, 851;
733, 612, 531, 257, 0, 211, 584;
944, 823, 742, 468, 211, 0, 373;
1318, 1206, 1115, 851, 584, 373, 0]; % 距离矩阵
ants = 100; % 蚂蚁数量
alpha = 1; % 信息启发因子
beta = 2; % 期望启发因子
rho = 0.5; % 信息素挥发因子
Q = 1; % 常数因子
iterations = 50; % 迭代次数
% 初始化信息素矩阵
pheromones = ones(length(stations), length(stations));
% 迭代
for i = 1:iterations
% 初始化每只蚂蚁
for j = 1:ants
current_station = randi(length(stations));
visited_stations = [current_station];
while length(visited_stations) < length(stations)
% 计算下一个站点的概率
probabilities = zeros(length(stations), 1);
for k = 1:length(stations)
if ~any(visited_stations == k)
probabilities(k) = pheromones(current_station, k)^alpha * (1 / distances(current_station, k))^beta;
end
end
probabilities = probabilities / sum(probabilities);
% 选择下一个站点
r = rand;
c = cumsum(probabilities);
next_station = find(r <= c, 1);
visited_stations = [visited_stations, next_station];
current_station = next_station;
end
% 计算路线长度
route_length = 0;
for k = 1:length(stations)-1
route_length = route_length + distances(visited_stations(k), visited_stations(k+1));
end
% 更新信息素矩阵
for k = 1:length(stations)-1
pheromones(visited_stations(k), visited_stations(k+1)) = (1 - rho) * pheromones(visited_stations(k), visited_stations(k+1)) + rho * Q / route_length;
pheromones(visited_stations(k+1), visited_stations(k)) = (1 - rho) * pheromones(visited_stations(k+1), visited_stations(k)) + rho * Q / route_length;
end
end
end
% 找到最优路线
best_route = zeros(1, length(stations));
current_station = randi(length(stations));
visited_stations = [current_station];
while length(visited_stations) < length(stations)
% 计算下一个站点的概率
probabilities = zeros(length(stations), 1);
for k = 1:length(stations)
if ~any(visited_stations == k)
probabilities(k) = pheromones(current_station, k)^alpha * (1 / distances(current_station, k))^beta;
end
end
probabilities = probabilities / sum(probabilities);
% 选择下一个站点
[~, next_station] = max(probabilities);
visited_stations = [visited_stations, next_station];
best_route(length(visited_stations)) = next_station;
current_station = next_station;
end
% 输出结果
disp("最优路线:");
for i = 1:length(best_route)
disp(stations(best_route(i)));
end
```
该程序定义了问题、蚂蚁数量、启发因子、信息素挥发因子、常数因子和迭代次数等参数。然后初始化信息素矩阵,并在每次迭代中更新信息素矩阵。在每次迭代中,每只蚂蚁都会从一个随机站点出发,按照一定的概率选择下一个站点,直到经过所有站点。最后,程序找到最优路线,并输出结果。