蚁群算法求解TSP问题MATLAB程序

%% 蚁群算法¨
clear
close
clc
n = 10; % 城市数量
m = 100; % 蚂蚁数量
alfa = 1.5;
beta = 2.5;
rho = 0.1;
Q = 1000;
maxgen = 50;
x = [2 14 9 6 3 2 4 8 12 5]';
y = [8 9 12 4 1 2 5 8 1 15]';
% x =
[37,49,52,20,40,21,17,31,52,51,42,31,5,12,36,52,27,17,13,57,62,42,16,8,7,27,30, 43,58,58,37,38,46,61,62,63,32,45,59,5,10,21,5,30,39,32,25,25,48,56,30]';
% y =
[52,49,64,26,30,47,63,62,33,21,41,32,25,42,16,41,23,33,13,58,42,57,57,52,38,68, 48,67,48,27,69,46,10,33,63,69,22,35,15,6,17,10,64,15,10,39,32,55,28,37,40]';
City = [x,y]; % 城市坐标
%% 城市之间的距离
for i = 1:n
D(i,:) = ((City(i,1) - City(:,1)).^2 + (City(i,2) - City(:,2)).^2).^0.5 + eps; end
eta = 1./D; % 启发因子
tau = ones(n); % 信息素矩阵
path = zeros(m,n); % 记录路径
for iter = 1: maxgen
%% 放置蚂蚁
path(:,1) = randi([1 n],m,1);
for i = 2 : n
for j = 1 : m
visited = path(j,1:i-1);
leftcity = setdiff(1:n,visited);
%% 计算剩下城市的概率
P = zeros(1,length(leftcity));
for k = 1:length(leftcity)
P(k) =
tau(visited(end),leftcity(k))^alfa*eta(visited(end),leftcity(k))^beta;%判断是否有重复城市
end
P1 = sum(P);
Pk = P / P1;
P = cumsum(Pk);
r = rand;
index = find(P >= r);
nextcity = leftcity(index(1));
path(j,i) = nextcity;
end
end
for flag = 1:m
if length(unique(path(flag,:))) ~= n %
keyboard;
end
end
if iter >= 2
path(1,:) = Pathbest(iter-1,:);
end
for i = 1 : m
node = path(i,:);
d = 0;
for j = 1 : n - 1
d = d + D(node(j),node(j + 1));
end
L(i) = d;
end
[shortroute,antindex] = min(L);
Lbest(iter) = shortroute;
Pathbest(iter,:) = path(antindex,:);
detatau = zeros(n);
for i = 1 : m
for j = 1 : n-1
detatau(path(i,j),path(i,j + 1)) = detatau(path(i,j),path(i,j + 1)) + Q/L(i);
detatau(path(i,j + 1),path(i,j))=detatau(path(i,j),path(i,j + 1));
end
detatau(path(i,n),path(i,1)) = detatau(path(i,n),path(i,1)) + Q/L(i);
detatau(path(i,1),path(i,n))=detatau(path(i,n),path(i,1));
end
tau = (1 - rho)*tau + detatau;
path = zeros(m,n);
end
index = find(Lbest == min(Lbest));
shortestpath = Pathbest(index(1),:);
shortestdistance = Lbest(index(1))
subplot(1,2,1)
plot(x,y,'o')
hold on
for i = 1 : n - 1
firstcity = shortestpath(i);
nextcity = shortestpath(i + 1);
plot([x(firstcity),x(nextcity)],[y(firstcity),y(nextcity)],'b');
end
firstcity = shortestpath(n);
nextcity = shortestpath(1);
plot([x(firstcity),x(nextcity)],[y(firstcity),y(nextcity)],'b');
axis equal
axis([0 18 0 18])
subplot(1,2,2)
plot(Lbest)
hold on
title('×î¶Ì¾àÀë')。