%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Ant Colony System Code %
% Date 5/27/2006 %
% Theobald.Zou %
% Original Code %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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)<P0
X(j_g_tr,1)=X(j_g_tr,1)+lamda*(X(BestIndex,1)-X(j_g_tr,1));%Xi=Xi+lamda*(Xbest-Xi)
X(j_g_tr,2)=X(j_g_tr,2)+lamda*(X(BestIndex,2)-X(j_g_tr,2));%Xi=Xi+lamda*(Xbest-Xi)
else
X(j_g_tr,1)=X(j_g_tr,1)+((-1)+2*rand(1))*Len1;%Xi=Xi+rand(-1,1)*Len1
X(j_g_tr,2)=X(j_g_tr,2)+((-1)+2*rand(1))*Len2;%Xi=Xi+rand(-1,1)*Len2
end;
end;
%信息素更新
for t_t=1:Ant
T0(t_t)=(1-P)*T0(t_t)+(exp(-(X(t_t,1)-1).^2+(X(t_t,2)-2.2).^2+1));
end;
if Echo==round(ECHO/3)%迭代经过1/3时用绿色点表示蚂蚁的分布位置
subplot(2,2,2);
for i_draw1=1:Ant
plot(X(i_draw1,1),X(i_draw1,2),'g.')
axis([0 2 1 3]);
hold on;
title('(b)');
xlabel('X1');
ylabel('X2');
end;
grid on;
end;
[c_iter,i_iter]=max(T0); %求取每代全局最优解
minpoint_iter=[X(i_iter,1),X(i_iter,2)];
minvalue_iter=(X(i_iter,1)-1).^2+(X(i_iter,2)-2.2).^2+1;
min_local(Echo)=minvalue_iter;%保存每代局部最优解
%将每代全局最优解存到min_global矩阵中
if Echo >= 2
if min_local(Echo)<min_global(Echo-1)
min_global(Echo)=min_local(Echo);
else
min_global(Echo)=min_global(Echo-1);
end;
else
min_global(Echo)=minvalue_iter;
end;
end;%ECHO循环结束
subplot(2,2,3);
for i_draw3=1:Ant
plot(X(i_draw3,1),X(i_draw3,2),'r.')%迭代结束用红色点表示蚂蚁的分布位置
axis([0 2 1 3]);
hold on;
title('(c)');
xlabel('X1');
ylabel('X2');
end;
grid on;
subplot(2,2,4);
min_global=min_global';
index(:,1)=1:ECHO;
plot(index(:,1), min_global(:,1),'b-')
hold on;
title('(d)');
xlabel('iteration');
ylabel('f(x)');
grid on;
[c_max,i_max]=max(T0);
minpoint=[X(i_max,1),X(i_max,2)]
minvalue=(X(i_max,1)-1).^2+(X(i_max,2)-2.2).^2+1
runtime=toc
