MATLAB实现模拟退火算法Simulated Annealing Algorithm【数学建模、科学计算算法】.zip

%%%%%%%%%%%%%%%%%%%%%%模拟退火算法解决函数极值%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all; %清除所有变量 close all; %清图 clc; %清屏 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 %%%%%%%%%%%%%%%%%%%%%%%%%%%冷却表参数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% L = 100; %马可夫链长度 K = 0.99; %衰减参数 S = 0.02; %步长因子 T=100; %初始温度 YZ = 1e-8; %容差 P = 0; %Metropolis过程中总接受点 %%%%%%%%%%%%%%%%%%%%%%%%%%随机选点 初值设定%%%%%%%%%%%%%%%%%%%%%%%%% PreX = rand * (XMAX-XMIN)+XMIN; PreY = rand * (YMAX-YMIN)+YMIN; PreBestX = PreX; PreBestY = PreY; PreX = rand * (XMAX-XMIN)+XMIN; PreY = rand * (YMAX-YMIN)+YMIN; BestX = PreX; BestY = PreY; %%%%%%%%%%%每迭代一次退火一次(降温), 直到满足迭代条件为止%%%%%%%%%%%% deta=abs( func2( BestX,BestY)-func2 (PreBestX, PreBestY)); while (deta > YZ) && (T>0.001) T=K*T; %%%%%%%%%%%%%%%%%%%%%在当前温度T下迭代次数%%%%%%%%%%%%%%%%%%%%%% for i=1:L %%%%%%%%%%%%%%%%%在此点附近随机选下一点%%%%%%%%%%%%%%%%%%%%% p=0; while p==0 NextX = PreX + S* (rand * (XMAX-XMIN)+XMIN); NextY = PreY + S*( rand * (YMAX-YMIN)+YMIN); if (NextX >= XMIN && NextX <= XMAX && NextY >=... YMIN && NextY <= YMAX) p=1; end end %%%%%%%%%%%%%%%%%%%%%%%是否全局最优解%%%%%%%%%%%%%%%%%%%%%% if (func2(BestX,BestY) > func2(NextX,NextY)) %%%%%%%%%%%%%%%%%%保留上一个最优解%%%%%%%%%%%%%%%%%%%%% PreBestX = BestX; PreBestY = BestY; %%%%%%%%%%%%%%%%%%%此为新的最优解%%%%%%%%%%%%%%%%%%%%% BestX=NextX; BestY=NextY; end %%%%%%%%%%%%%%%%%%%%%%%% Metropolis过程%%%%%%%%%%%%%%%%%%% if( func2(PreX,PreY) - func2(NextX,NextY) > 0 ) %%%%%%%%%%%%%%%%%%%%%%%接受新解%%%%%%%%%%%%%%%%%%%%%%%% PreX=NextX; PreY=NextY; P=P+1; else changer = -1*(func2(NextX,NextY)-func2(PreX,PreY))/ T ; p1=exp(changer); %%%%%%%%%%%%%%%%%%%%%%%%接受较差的解%%%%%%%%%%%%%%%%%%%% if p1 > rand PreX=NextX; PreY=NextY; P=P+1; end end trace(P+1)=func2(BestX, BestY); end deta=abs( func2( BestX,BestY)-func2 (PreBestX, PreBestY)); end disp('最小值在点:'); BestX BestY disp( '最小值为:'); func2(BestX, BestY) plot(trace(2:end)) xlabel('迭代次数') ylabel('目标函数值') title('适应度进化曲线')