蚁群算法TSP问题.rar

%%%%%%%%%%%%%%%%%%%%%%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; %启发式银子重要程度参数 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 1004;... 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 2367;... 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); %表示问题的规模 D = zeros(n,n); %表示两个城市距离间隔矩阵 Dx = bsxfun(@minus,C(:,1),C(:,1)'); Dy = bsxfun(@minus,C(:,2),C(:,2)'); D = (Dx.^2 + Dy.^2).^0.5; 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，完成各自周游%%%%% for j = 2:n for i = 1:m visited = Tabu(i,1:(j-1)); %已经访问的城市 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 J = setdiff(1:n,visited); %%%%%%%%%%%%%%计算待选城市的概率分布%%%%%%%%%%%%%%%%% P = Tau(visited(end),J).^Alpha .* (Eta(visited(end),J).^Beta); P = P/(sum(P)); %%%%%%%%%按概率原则选取下一个城市%%%%%%%%%%%%%%%%%%%% Pcum = cumsum(P); Select = find(Pcum>=rand); Tabu(i,j) = J(Select(1)); 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:(n-1) L = L + diag(D(Tabu(:,i),Tabu(:,i+1))); end L = L + diag(D(Tabu(:,n),Tabu(:,1))); 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); %%%%%%%%%%%%%%%%%%%历代最优路径%%%%%%%%%%%%%%%%%%%%%% 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('适应度度进化曲线') fprintf('最优变量是：%d\n',Shortest_Route); fprintf('最优值是：%f\n',Shortest_Length);