Example5_1.m

% 智能优化算法及其MATLAB实例（第2版）by包子阳 P102 例5.1
% 蚁群算法解决TSP问题
%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%
clear all;
close all;
clc;
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;    %信息素增强强度系数
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 2391; 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) = sqrt((C(i,1)-C(j,1))^2 + (C(i,2)-C(j,2))^2);
        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);        %信息素矩阵
Tabu = zeros(m,n);      %存储并记录路径的生成
NC = 1;                 %迭代记录器
R_best = zeros(G,n);    %各代最佳路线
L_best = inf.*ones(G,1);%各代最佳路线长度

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))   %ceil()朝正无穷大四舍五入
        Randpos = [Randpos,randperm(n)];    %randperm(n) 返回行向量，其中包含从 1 到 n 没有重复元素的整数随机排列。
    end
    Tabu(:,1) = (Randpos(1,1:m))';  %存储每只蚂蚁经过的第一个城市
    %%%%%%%%%%第三步：m只蚂蚁按概率函数选择下一座城市，完成各自周游%%%%%%%%%%%
    for j = 2:n             %要去的第n座城市，或者说对于每只蚂蚁而言第n次选择
        for i = 1:m         %对于每一只蚂蚁
            visited = Tabu(i,1:j-1);    %已经访问过的城市
            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;          %k - 待访问城市的序号
                    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);    %???为什么不是选择概率最大的,我认为下一行代码更合理
%             Select = find(P == max(P));
            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,:);      %第i只蚂蚁走过的路径
        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)); %最后要回到起点
    end
    L_best(NC) = min(L);
    pos = find(L==L_best(NC));  %找到第NC代最优路径的第pos只蚂蚁
    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);
    %%%%%%%%%%%%%%%%%%%绘制当代最优路线%%%%%%%%%%%%%%%%%%%
    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(0.05);
    
    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));
figure(2)
plot(L_best)
xlabel('迭代次数')
ylabel('目标函数值-路程')
title('适应度进化曲线')