蚁群算法优化问题
%%%%%%%%%%%%蚁群算法解决 TSP 问题%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%
clear all; %清除所有变量
close all; %清图
clc; %清屏
m = 50; %蚂蚁个数
Alpha = 1; %信息素重要程度参数
Beta = 5; %启发式因子重要程度参数
Rho = 0.1; %信息素蒸发系数
G = 200; %最大迭代次数
Q = 100; %信息素增加强度系数
C = [1304 2312;3639 1315;4177 2244;3712 1399;3488 1535;3326 1556;...
3238 1229;4196 1044;4312 790;4386 570;3007 1970;2562 1756;...
2788 1491;2381 1676;1332 695;3715 1678;3918 2179;4061 2370;...
3780 2212;3676 2578;4029 2838;4263 2931;3429 1908;3507 2376;...
3394 2643;3439 3201;2935 3240;3140 3550;2545 2357;2778 2826;...
2370 2975]; %31 个省会城市坐标
%%%%%%%%%%%%%%%第一步：变量初始化%%%%%%%%%%%%%%
n = size(C,1); %n 表示问题的规模(城市个数)
D = zeros(n,n); %D 表示两个城市距离间隔矩阵
for i = 1:n
for j = 1:n
if i ~= j
D(i,j) = ((C(i,1)-C(j,1))^2+(C(i,2)-C(j,2))^2)^0.5;
else
D(i,j) = eps;
end
D(j,i) = D(i,j);
end
end
Eta = 1./D; %Eta 为启发因子，这里设为距离的倒数
Tau = ones(n,n); %Tau 为信息素矩阵
Tabu = zeros(m,n); %存储并记录路径的生成
NC = 1; %迭代计数器
R_best = zeros(G,n); %各代最佳路线
L_best = inf.*ones(G,1); %各代最佳路线的长度
figure(1); %优化解
while NC <= G
%%%%%%%%%%第二步：将 m 只蚂蚁放到 n 个城市上%%%%%%%%%%
Randpos = [];
for i = 1:(ceil(m/n))
Randpos = [Randpos,randperm(n)];
end
Tabu(:,1) = (Randpos(1,1:m))';
%%%第三步：m 只蚂蚁按概率函数选择下一座城市，完成各自的周游%%%%
for j = 2:n
for i = 1:m
visited = Tabu(i,1:(j-1)); %已访问的城市
J = zeros(1,(n-j+1)); %待访问的城市
P = J; %待访问城市的选择概率分布
Jc = 1;
for k = 1:n
if length(find(visited==k))==0
J(Jc) = k;
Jc = Jc+1;
end
end
%%%%%%%%%%%计算待选城市的概率分布%%%%%%%%%%%
for k = 1:length(J)
P(k) = (Tau(visited(end),J(k))^Alpha)...
*(Eta(visited(end),J(k))^Beta);
end
P = P/(sum(P));
%%%%%%%%%%%按概率原则选取下一个城市%%%%%%%%%
Pcum = cumsum(P);
Select = find(Pcum >= rand);
to_visit = J(Select(1));
Tabu(i,j) = to_visit;
end
end
if NC >= 2
Tabu(1,:) = R_best(NC-1,:);
end
%%%%%%%%%%%%%第四步：记录本次迭代最佳路线%%%%%%%%%%
L = zeros(m,1);
for i = 1:m
R = Tabu(i,:);
for j = 1:(n-1)
L(i) = L(i)+D(R(j),R(j+1));
end
L(i) = L(i)+D(R(1),R(n));
end
L_best(NC) = min(L);
pos = find(L==L_best(NC));
R_best(NC,:) = Tabu(pos(1),:);
%%%%%%%%%%%%%%%第五步：更新信息素%%%%%%%%%%%%%
Delta_Tau = zeros(n,n);
for i = 1:m
for j = 1:(n-1)
Delta_Tau(Tabu(i,j),Tabu(i,j+1)) = ...
Delta_Tau(Tabu(i,j),Tabu(i,j+1))+Q/L(i);
end
Delta_Tau(Tabu(i,n),Tabu(i,1)) = ...
Delta_Tau(Tabu(i,n),Tabu(i,1))+Q/L(i);
end
Tau = (1-Rho).*Tau+Delta_Tau;
%%%%%%%%%%%%%%%第六步：禁忌表清零%%%%%%%%%%%%%
Tabu = zeros(m,n);
%%%%%%%%%%%%%%%%%历代最优路线%%%%%%%%%%%%%%%
for i = 1:n-1
plot([ C(R_best(NC,i),1), C(R_best(NC,i+1),1)],...
[C(R_best(NC,i),2), C(R_best(NC,i+1),2)],'bo-');
hold on;
end
plot([C(R_best(NC,n),1), C(R_best(NC,1),1)],...
[C(R_best(NC,n),2), C(R_best(NC,1),2)],'ro-');
title(['优化最短距离:',num2str(L_best(NC))]);
hold off;
pause(0.005);
NC = NC+1;
end
%%%%%%%%%%%%%%%%%第七步：输出结果%%%%%%%%%%%%%%
Pos = find(L_best==min(L_best));
Shortest_Route = R_best(Pos(1),:); %最佳路线
Shortest_Length = L_best(Pos(1)); %最佳路线长度
figure(2),
plot(L_best)
xlabel('迭代次数')
ylabel('目标函数值')
title('适应度进化曲线')