针对一个类旅行商问题,用matlab建立一个基于模拟退火(SA)和深度优先搜索(DFS)的类旅行商问题(TSP)求解模型
时间: 2023-05-28 07:03:13 浏览: 62
以下是一个基于模拟退火和深度优先搜索的TSP求解模型的MATLAB代码:
% 生成城市坐标
n = 10; % 城市数量
x = rand(n,1); % 生成随机x坐标
y = rand(n,1); % 生成随机y坐标
% 计算距离矩阵
dist = zeros(n,n);
for i = 1:n
for j = 1:n
dist(i,j) = sqrt((x(i)-x(j))^2 + (y(i)-y(j))^2);
end
end
% 初始化模拟退火参数
T0 = 100; % 初始温度
Tf = 1e-5; % 终止温度
alpha = 0.95; % 降温系数
maxIter = 100; % 最大迭代次数
% 初始化DFS参数
visited = zeros(n,1);
route = zeros(n+1,1);
route(1) = 1;
% 开始模拟退火
T = T0;
while T > Tf
% 随机生成新解
newRoute = route;
i = randi(n-1)+1;
j = randi(n-1)+1;
if i == j
continue;
end
temp = newRoute(i);
newRoute(i) = newRoute(j);
newRoute(j) = temp;
newRoute(end) = 1;
% 计算新解的成本
newCost = 0;
for k = 1:n
newCost = newCost + dist(newRoute(k),newRoute(k+1));
end
% 计算成本变化量
deltaCost = newCost - cost;
% 判断是否接受新解
if deltaCost < 0
route = newRoute;
cost = newCost;
elseif exp(-deltaCost/T) > rand()
route = newRoute;
cost = newCost;
end
% 降温
T = alpha*T;
% 每隔一定迭代次数执行一次DFS
if mod(iter,10) == 0
[route,cost] = dfs(visited,route,cost,dist);
end
% 更新迭代次数
iter = iter + 1;
end
% 定义DFS函数
function [route,cost] = dfs(visited,route,cost,dist)
n = length(visited);
if sum(visited) == n
route(end) = route(1);
return;
end
minCost = Inf;
minIndex = 0;
for i = 1:n
if visited(i) == 0
newRoute = route;
newRoute(end) = i;
newCost = cost + dist(route(end),i);
if newCost < minCost
minCost = newCost;
minIndex = i;
end
end
end
route(end+1) = minIndex;
visited(minIndex) = 1;
cost = minCost;
[route,cost] = dfs(visited,route,cost,dist);
end
% 输出结果
route
cost