蚁群算法代码(求函数最值)

function[F]=F(x1,x2)%目标函数F=-(x1.^2+2*x2.^2-0.3*cos(3*pi*x1)-0.4*cos(4*pi*x2)+0.7);Endfunction[maxx,maxy,maxvalue]=antcolony%蚁群算法求函数最大值的程序ant=200;%蚂蚁数量times=50;%蚂蚁移动次数rou=0.8;%信息素挥发系数p0=0.2;%转移概率常数lower_1=-1;%设置搜索范围upper_1=1;%lower_2=-1;%upper_2=1;%fori=1:antX(i,1)=(lower_1+(upper_1-lower_1)*rand);%随机设置蚂蚁的初值位置X(i,2)=(lower_2+(upper_2-lower_2)*rand);tau(i)=F(X(i,1),X(i,2));%第i只蚂蚁的信息量end%随机初始每只蚂蚁的位置step=0.05;%网格划分单位f='-(x.^2+2*y.^2-0.3*cos(3*pi*x)-0.4*cos(4*pi*y)+0.7)';[x,y]=meshgrid(lower_1:step:upper_1,lower_2:step:upper_2);z=eval(f);%eval函数，将字符串内的内容执行再赋给对象figure(1);mesh(x,y,z);%网格图holdon;plot3(X(:,1),X(:,2),tau,'k*')%蚂蚁初始位置holdon;text(0.1,0.8,-0.1,'蚂蚁的初始分部位置')xlabel('x');ylabel('y');zlabel('f(x,y)');fort=1:times%第t次移动lamda=1/t;%步长系数，随移动次数增大而减少[tau_best(t),bestindex]=max(tau);%第t次移动的最优值及其位置fori=1:ant%第i只蚂蚁p(t,i)=(tau(bestindex)-tau(i))/tau(bestindex);%最优值与第i只蚂蚁的值的差比%计算状态转移概率endfori=1:antifp(t,i)p0%局部搜索小于转移概率常数temp1=X(i,1)+(2*rand-1)*lamda;%移动距离temp2=X(i,2)+(2*rand-1)*lamda;else%全局搜索temp1=X(i,1)+(upper_1-lower_1)*(rand-0.5);temp2=X(i,2)+(upper_2-lower_2)*(rand-0.5);end%%%%%%%%%%%%%%%%%%%%%%越界处理iftemp1lower_1temp1=lower_1;endiftemp1upper_1temp1=upper_1;endiftemp2lower_2temp2=lower_2;endiftemp2upper_2temp2=upper_2;end%%%%%%%%%%%%%%%%%%%%%%%ifF(temp1,temp2)F(X(i,1),X(i,2))%判断蚂蚁是否移动X(i,1)=temp1;X(i,2)=temp2;endendfori=1:anttau(i)=(1-rou)*tau(i)+F(X(i,1),X(i,2));%更新信息量endendfigure(2);mesh(x,y,z);holdon;x=X(:,1);y=X(:,2);plot3(x,y,eval(f),'k*')holdon;text(0.1,0.8,-0.1,'蚂蚁的最终分布位置')xlabel('x');ylabel('y'),zlabel('f(x,y)');[max_value,max_index]=max(tau);maxx=X(max_index,1);maxy=X(max_index,2);maxvalue=F(X(max_index,1),X(max_index,2));endfunction[F1]=F1(x)%目标函数F1=x.^2-2*x+1;End%蚁群算法求解一元函数F1=x^2-2*x+1closeclearclcant=10;times=40;rou=0.8;p0=0.2;lb=-2;ub=2;step=0.05;x=lb:0.05:ub;fori=1:antX(i)=lb+(ub-lb)*rand;tau(i)=F1(X(i));endfigure(1);plot(x,F1(x));holdonplot(X,tau,'r*');forkk=1:10fort=1:timeslamda=1/t;%转移次数的倒数[tau_best(t),bestindex]=min(tau);fori=1:antp(t,i)=(tau(bestindex)-tau(i))/tau(bestindex);%转移概率（最优-蚂蚁i）/最优%此种概率选择易陷入局部最优解endfori=1:antifp(t,i)p0temp=X(i)+(2*rand-1)*lamda;%蚂蚁移动elsetemp=X(i)+(ub-lb)*(rand-0.5);endiftemplbtemp=lb;endiftempubtemp=ub;endifF1(temp)F1(X(i))X(i)=temp;endendfori=1:anttau(i)=(1-rou)*tau(i)+F1(X(i));endendendfigure(2);plot(x,F1(x));holdonx=X(i);y=tau(i);plot(x,y,'g*');x1=X(length(X))y1=tau(length(tau))