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%                  Ant Colony System Code                          % 
%                      Date 5/27/2006                              % 
%                       Theobald.Zou                               % 
%                      Original  Code                              % 
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clc; 
clear all; 
tic; 
%初始化各参数 
Ant=50;%蚂蚁规模 
ECHO=50;%迭代次数 
%F=(X1.-1)^2+(X2.-2.2)^2+1;%待优化函数 
step=0.1*rand(1);%局部搜索时的步长 
temp=[0,0]; 
%各子区间长度 
start1=0; 
end1=2; 
start2=1; 
end2=3; 
Len1=(end1-start1)/Ant; 
Len2=(end2-start2)/Ant; 
%P = 0.2; 
%初始化蚂蚁位置 
subplot(2,2,1); 
for i=1:Ant 
X(i,1)=(start1+(end1-start1)*rand(1)); 
X(i,2)=(start2+(end2-start2)*rand(1)); 
T0(i)=exp(-((X(i,1)-1)^2+(X(i,2)-2.2)^2+1));%初始信息素,随函数值大,信息素浓度小,反之亦然 
plot(X(i,1),X(i,2),'k.') 
hold on; 
title('(a)'); 
xlabel('X1'); 
ylabel('X2'); 
grid on; 
end; 
%至此初始化完成 
for Echo=1:ECHO    %开始寻优     
%P0函数定义,P0为全局转移选择因子 
a1=0.9; 
b1=(1/ECHO)*2*log(1/2); 
f1=a1*exp(b1*Echo); 
a2=0.225; 
b2=(1/ECHO)*2*log(2); 
f2=a2*exp(b2*Echo); 
if  Echo<=(ECHO/2) 
    P0=f1; 
else 
    P0=f2; 
end; 
%P函数定义，P为信息素蒸发系数 
a3=0.1; 
b3=(1/ECHO).*log(9); 
P=a3*exp(b3*Echo); 
lamda=0.10+(0.14-0.1)*rand(1);%全局转移步长参数 
Wmax=1.0+(1.4-1.0)*rand(1);%步长更新参数上限 
Wmin=0.2+(0.8-0.2)*rand(1);%步长更新参数下限 
%寻找初始最优值 
   T_Best=T0(1); 
    for j=1:Ant 
       if  T0(j)>=T_Best 
           T_Best=T0(j); 
           BestIndex=j; 
       end;     
    end;    
    W=Wmax-(Wmax-Wmin)*(Echo/ECHO);  %局部搜索步长更新参数 
    for j_g=1:Ant  %全局转移概率求取,当该蚂蚁随在位置不是bestindex时 
        if j_g~=BestIndex 
            r=T0(BestIndex)-T0(j_g); 
            Prob(j_g)=exp(r)/exp(T0(BestIndex)); 
        else   %当j_g=BestIndex的时候进行局部搜索 
            if rand(1)<0.5 
                temp(1,1)=X(BestIndex,1)+W*step; 
                temp(1,2)=X(BestIndex,2)+W*step; 
            else 
                temp(1,1)=X(BestIndex,1)-W*step; 
                temp(1,2)=X(BestIndex,2)-W*step; 
            end; 
            Prob(j_g)=0;%bestindex的蚂蚁不进行全局转移 
        end; 
            X1_T=temp(1,1); 
            X2_T=temp(1,2); 
            X1_B=X(BestIndex,1); 
            X2_B=X(BestIndex,2); 
            F1_T=(X1_T-1).^2+(X2_T-2.2).^2+1; 
            F1_B=(X1_B-1).^2+(X2_B-2.2).^2+1; 
            if exp(-F1_T)>exp(-F1_B) 
               X(BestIndex,1)=temp(1,1); 
               X(BestIndex,2)=temp(1,2); 
            end; 
    end;   
    for j_g_tr=1:Ant 
        if Prob(j_g_tr)= 2 
    if min_local(Echo)