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')