ASM.zip_ASM matlab_ASM matlab_matlab 蚂蚁算法_蚂蚁算法_蚂蚁系统

function [R_best,L_best,L_ave,Shortest_Route,Shortest_Length]=ACATSP(C,NC_max,m,Alpha,Beta,Rho,Q) %%========================================================================= % ACATSP.m %%------------------------------------------------------------------------- %% 主要符号说明 %% C n个城市的坐标，n×2的矩阵 %% NC_max 最大迭代次数 %% m 蚂蚁个数 %% Alpha 表征信息素重要程度的参数 %% Beta 表征启发式因子重要程度的参数 %% Rho 信息素蒸发系数 %% Rho_d 信息素蒸发系数的衰减度 %% Q 信息素增加强度系数 %% R_best 各代最佳路线 %% L_best 各代最佳路线的长度 %%========================================================================= %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%第一步：变量初始化 % 设置初始参数如下： m=30;Alpha=1;Beta=5;Rho=0.5;NC_max=100;Q=100;Rho_d=0 % 10城市坐标为：（C为n*2的矩阵） load oliver30 -ascii; C=oliver30;%这里使用load载入坐标 n=size(C,1);%表示问题的规模（城市个数）,n为第一维的长度 D=zeros(n,n);%D表示完全图的赋权邻接矩阵，D为n*n全零矩阵 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;%应该是0，但是下面要取倒数，故用eps end % D(j,i)=D(i,j);%这句是多余的！ end end Eta=1./D;%Eta为启发因子，这里设为距离的倒数，注意这是阵列的右除，即Eta(i,j)=1/D(i,j) 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(NC_max,n);%各代最佳路线 L_best=inf.*ones(NC_max,1);%各代最佳路线的长度,这一句不懂是什么意思！！为啥乘以无穷大 L_ave=zeros(NC_max,1);%各代路线的平均长度 while NC<=NC_max%停止条件之一：达到最大迭代次数 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%第二步：将m只蚂蚁放到n个城市上 Randpos=[]; for i=1:(ceil(m/n))%ceil函数返回>=A的最近的整数 %Randpos=[Randpos,randperm(n)];%这一句不好理解，可以改成下面的表达方式 Randpos=cat(2,Randpos,randperm(n));%注意是沿着第二维-列来加长的，所以是2 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 %这里产生一只蚂蚁需要遍历的所有城市，但还没有选择 if length(find(visited==k))==0 %于是，J就填满了所有等待访问的城市 J(Jc)=k; % Jc=Jc+1; % end %注意！这是if对应的end! end %下面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);%注意启发因子Eta是个矩阵！这是改进点之一！ 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 %到此为止，m只蚂蚁完全走完了各自的路径 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)); %以上计算出了每只蚂蚁的周游路径长度 end L_best(NC)=min(L); %这里得到所有路径里最短的一条 pos=find(L==L_best(NC)); %找出最短路径所在的行 R_best(NC,:)=Tabu(pos(1),:);%得到第NC次迭代的最优路径 L_ave(NC)=mean(L); %到此为止，第NC次迭代就完成了！ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%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);%这显然是一个蚁周系统，注意L（i）! Delta_Tau(Tabu(i,j),Tabu(i,j+1))=Delta_Tau(Tabu(i,j),Tabu(i,j+1))+Q;%蚁密系统 %Delta_Tau(Tabu(i,j),Tabu(i,j+1))=Delta_Tau(Tabu(i,j),Tabu(i,j+1))+Q/D(i,j); %Delta_Tau(Tabu(i,j),Tabu(i,j+1))=Delta_Tau(Tabu(i,j),Tabu(i,j+1))+Q/L_best(NC);%Maxmin系统 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 这是保留区，可以改进为蚂蚁量系统或蚂蚁密系统，也可以加入混合算法！ % % % % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end Delta_Tau(Tabu(i,n),Tabu(i,1))=Delta_Tau(Tabu(i,n),Tabu(i,1))+Q; end Tau=(1-Rho).*Tau+Delta_Tau; %这就是蚁群算法的改进点之二，信息素的刷新就在这里 Rd(NC)=Rho;%把每一代的信息素挥发系数存进Rd中 Rdd(NC)=Rho_d; NC=NC+1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%第六步：禁忌表清零 Tabu=zeros(m,n); end %注意这是while循环的end！是总的循环控制 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%第七步：输出结果 Pos=find(L_best==min(L_best)); %找出最短的路径所在矩阵的坐标 Shortest_Route=R_best(Pos(1),:); Shortest_Length=L_best(Pos(1)); figure('Name','蚁密系统') subplot(2,2,1) DrawRoute(C,Shortest_Route); title(['最短路径示意图','(\alpha=',num2str(Alpha),',\beta=',num2str(Beta),',\rho=',num2str(Rho),')']); xlabel('城市的X坐标'); ylabel('城市的Y坐标'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% subplot(2,2,2) plot(L_best,'b') hold on plot(L_ave,'r'); legend('\it每代最短路径长度','\it每代平均路径长度'); title(['进行',int2str(NC_max),'次迭代的演化图','(\alpha=',num2str(Alpha),',\beta=',num2str(Beta),',\rho=',num2str(Rho),')']); xlabel('迭代次数'); ylabel('路径长度'); gtext(['\rightarrow 最优结果=', num2str(Shortest_Length) ]); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% subplot(2,2,3) %bar(Rd); plot(Rd,'rx'); grid on xlabel('迭代次数'); ylabel('信息素蒸发系数'); title(['信息素蒸发系数演化图','(\alpha=',num2str(Alpha),',\beta=',num2str(Beta),',\rho=',num2str(Rho),')']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% subplot(2,2,4) plot(Rdd); grid on xlabel('迭代次数'); ylabel('信息素蒸发系数的衰减度'); title(['信息素蒸发系数衰减度演化图','(\alpha=',num2str(Alpha),',\beta=',num2str(Beta),',\rho=',num2str(Rho),')']); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function DrawRoute(C,R) %%==================================================================== %% DrawRoute.m %% 画路线图的子函数 %%-------------------------------------------------------------------- %% C Coordinate 节点坐标，由一个N×2的矩阵存储 %% R Route 路线 %%==================================================================== N=length(R); scatter(C(:,1),C(:,2)); hold on plot([