蚂蚁算法matlab实现TSP

最新推荐文章于 2024-04-25 14:58:08 发布

双木linwis

最新推荐文章于 2024-04-25 14:58:08 发布

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文章标签： matlab

本文链接：https://blog.youkuaiyun.com/likesomething1/article/details/108882414

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本文介绍了如何用MATLAB实现解决旅行商问题（TSP）的算法。首先设置城市数量为35，随机生成城市坐标，然后通过矩阵计算城市之间的距离。接着设定蚂蚁数量、参数及挥发系数，初始化信息素和先验效应。通过迭代过程，不断更新蚂蚁路径，寻找最优解。最后，展示最优路径长度随迭代次数的变化。

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clear;
close all;
clc;

n = 35; %城市的数量
x = rand(1,n)*10;
y = rand(1,n)*10;

D = zeros(n,n);
for i = 1:n
for j = 1:n
if i~= j
D(i,j) = sqrt(power(x(i)-x(j),2) + power(y(i)-y(j),2));
else
D(i,j) = eps;
end
end
end

m = 80; %蚂蚁的数量
alpha = 2;
beta = 6;
rho = 0.2; %挥发素
Q = 10;
Heu_F = 1./D; %先验效应
Tau = ones(n,n); % 初始化边的信息素
Table = zeros(m,n);
iter = 1;
iter_max = 500;
Route_best = zeros(iter_max,n); %最优路径
Length_best = zeros(iter_max,1); % 最优路径的长度

%% 迭代
while iter <= iter_max
%% 初始化蚂蚁出发点
start = zeros(m,1);
for i = 1:m
temp = randperm(n);
start(i) = temp(1);
end

%% 更新蚂蚁的运动轨迹
Table(:,1) = start;
city_index = 1:n;
for i = 1:m
    for j = 2:n
       has_visited = Table(i,1:(j-1));
       allow_index = ~ismember(city_index,has_visited);
       allow = city_index(allow_index);
       %%计算蚂蚁转移概率
       P = allow;
       for k = 1:length(allow)
          P(k) = Tau(has_visited(end),allow(k))^alpha *  Heu_F(has_visited(end),allow(k))^ beta;
       end
       P = P / sum(P);
       Pc = cumsum(P); % 轮盘,cumsum是依次求行和
       target_index = find(Pc >= rand);
       target = allow(target_index(1));
       Table(i,j) = target;
    end
end
%% 计算长度
Length = zeros(m,1);
for i  = 1:m
    Route = Table(i,:);
    for j = 1:n-1
    Length(i) = Length(i) + D(Route(j),Route(j+1));
    end
    Length(i) = Length(i) + D(Route(n),Route(1));
end
%% 得到最佳路径和长度
[min_Length,min_index] = min(Length);
if iter >1
    if min_Length > Length_best(iter-1)
        Length_best(iter) = Length_best(iter-1);
        Route_best(iter,:) = Route_best(iter-1,:);
    else
        Length_best(iter) = min_Length;
        Route_best(iter,:) = Table(min_index,:);
    end
else 
    Length_best(iter) = min_Length;
    Route_best(iter,:) = Table(min_index,:);
end
%%更新代数和信息素
iter = iter+1;
Delta_Tau = zeros(n,n);
for i = 1:m
    for j =1:n-1
    Delta_Tau(Table(i,j),Table(i,j+1)) = Delta_Tau(Table(i,j),Table(i,j+1)) + Q/Length(i);
    end
end
Tau = (1-rho)*Tau + Delta_Tau;
Table = zeros(m,n);

end
plot(Length_best);