【路径规划-TSP问题】基于蚁群算法求解31城市旅行商问题含Matlab源码.zip

%%%%%%%%%%%%%%%%%%%%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_max=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_max,n); %各代最佳路线 L_best=inf.*ones(G_max,1); %各代最佳路线的长度 figure(1);%优化解 while NC<=G_max %%%%%%%%%%%%%%%%%%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')