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%%%%%%%%%%%%%%蚁群算法求函数极值%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%
clear all; %清除所有变量
close all; %清图
clc; %清屏
m = 20; %蚂蚁个数
G = 500; %最大迭代次数
Rho = 0.9; %信息素蒸发系数
P0 = 0.2; %转移概率常数
XMAX = 5; %搜索变量 x 最大值
XMIN = -5; %搜索变量 x 最小值
YMAX = 5; %搜索变量 y 最大值
YMIN = -5; %搜索变量 y 最小值
%%%%%%%%%%%%%随机设置蚂蚁初始位置%%%%%%%%%%%%%%%%
for i = 1:m
X(i,1) = (XMIN+(XMAX-XMIN)*rand);
X(i,2) = (YMIN+(YMAX-YMIN)*rand);
Tau(i) = func(X(i,1),X(i,2));
end
step = 0.1; %局部搜索步长
for NC = 1:G
lamda = 1/NC;
[Tau_best,BestIndex] = min(Tau);
%%%%%%%%%%%%%计算状态转移概率%%%%%%%%%%%%%%%
for i = 1:m
P(NC,i) = (Tau(BestIndex)-Tau(i))/Tau(BestIndex);
end
%%%%%%%%%%%%%%%%位置更新%%%%%%%%%%%%%%%%%
for i = 1:m
%%%%%%%%%%%%局部搜索%%%%%%%%%%%%%%%%%
if P(NC,i) < P0
temp1 = X(i,1)+(2*rand-1)*step*lamda;
temp2 = X(i,2)+(2*rand-1)*step*lamda;
else
%%%%%%%%%%%%全局搜索%%%%%%%%%%%%%%%%
temp1 = X(i,1)+(XMAX-XMIN)*(rand-0.5);
temp2 = X(i,2)+(YMAX-YMIN)*(rand-0.5);
end
%%%%%%%%%%%%%%%%边界处理%%%%%%%%%%%%%%%
if temp1 < XMIN
temp1 = XMIN;
end
if temp1 > XMAX
temp1 = XMAX;
end
if temp2 < YMIN
temp2 = YMIN;
end
if temp2 > YMAX
temp2 = YMAX;
end
%%%%%%%%%%%%%%%判断蚂蚁是否移动%%%%%%%%%%%
if func(temp1,temp2) < func(X(i,1),X(i,2))
X(i,1) = temp1;
X(i,2) = temp2;
end
end
%%%%%%%%%%%%%%%%%更新信息素%%%%%%%%%%%%%%%
for i = 1:m
Tau(i) = (1-Rho)*Tau(i)+func(X(i,1),X(i,2));
end
[value,index] = min(Tau);
trace(NC) = func(X(index,1),X(index,2));
end
[min_value,min_index] = min(Tau);
minX = X(min_index,1); %最优变量
minY = X(min_index,2); %最优变量
minValue = func(X(min_index,1),X(min_index,2)); %最优值
figure
plot(trace)
xlabel('搜索次数');
ylabel('适应度值');
title('适应度进化曲线')
%%%%%%%%%%%%%%%%%适应度函数%%%%%%%%%%%%%%%%
function value = func(x,y)
value = 20*(x^2-y^2)^2-(1-y)^2-3*(1+y)^2+0.3;
end