PSO.rar_PSO_PSO 极值_PSO函数求解

%格式标准化 clear all; clc; format long; %初始化各个因子 c1=1.4962; %学习因子c1 c2=1.4962; %学习因子c2 w=0.7298; %惯性权重w N=20; %粒子群规模 D=6; %搜索空间维数(本程序适合3维及以上，不能求解1,2维) eps=10^(-6); %满足条件限制的误差(在不知道最小值时候不用设置) MaxDT=500; %粒子群繁殖的代数 %初始化粒子的速度和位置，数据结构用矩阵A表示 for i=1:N for j=1:2*D A(i,j)=rand; end end for i=1:N for j=2*D+1:3*D A(i,j)=A(i,j-2*D); end end %计算各个粒子的适应度 for i=1:N A(i,3*D+1)=fitness(A(i,1:D),D); end %对粒子的适应度进行排序 B=sortrows(A,3*D+1); %排序后适应度低的前面一半粒子直接进入下一代 NextGeneration=zeros(N,3*D+1); for i=1:N/2 for j=1:3*D+1 NextGeneration(i,j)=B(i,j); end end %后一半粒子进行遗传选择和交叉操作 for i=1:N/2 for j=1:3*D+1 Cross(i,j)=B(i+N/2,j); end end %产生一个随机的交叉位置 for i=1:N/4 Anumber=randperm(D-1); if Anumber(1)~=1 position=Anumber(1); else position=Anumber(2); end %交叉进行 for j=position:D-1 temp=Cross(i,j); Cross(i,j)=Cross(N/2-i+1,j); Cross(N/2-i+1,j)=temp; end end %交叉结束，进行更新 for i=1:N/2 Cross(i,3*D+1)=fitness(Cross(i,1:D),D); if Cross(i,3*D+1)<B(i+N/2,3*D+1) for j=2*D+1:3*D Cross(i,j)=Cross(i,j-2*D); end else for j=2*D+1:3*D Cross(i,j)=B(i,j); end end end %下面选择最好的粒子N/2个进入下一代 Pool=zeros(N,3*D+1); for i=1:N/2 for j=1:3*D+1 Pool(i,j)=B(i+N/2,j); end end for i=1+N/2:N for j=1:3*D+1 Pool(i,j)=Cross(i-N/2,j); end end %POOLX表示排序后的粒子选择池 PoolX=sortrows(Pool,3*D+1); for i=1+N/2:N for j=1:3*D+1 NextGeneration(i,j)=PoolX(i-N/2,j); end end Pbest=NextGeneration(i,2*D+1:3*D); for i=2:N if NextGeneration(i,3*D+1)<fitness(Pbest,D) Pbest=NextGeneration(i,2*D+1:3*D); end end %根据粒子群公式进行迭代(Stander PSO Step) %速度更新 for i=1:N for j=D+1:2*D A(i,j)=w*NextGeneration(i,j)+c1*rand*(NextGeneration(i,j+D)-NextGeneration(i,j-D))+c2*rand*(Pbest(j-D)-NextGeneration(i,j-D)); end end %位置更新 for i=1:N for j=1:D A(i,j)=NextGeneration(i,j)+A(i,j+D); end A(i,3*D+1)=fitness(A(i,1:D),D); if A(i,3*D+1)<NextGeneration(i,3*D+1) for j=2*D+1:3*D A(i,j)=A(i,j-2*D); end else for j=2*D+1:3*D A(i,j)=NextGeneration(i,j-2*D); end end end %下面进入主要循环，循环到最大次数得到最优解和最小值 %DDTime=1; for time=1:MaxDT B=sortrows(A,3*D+1); NextGeneration=zeros(N,3*D+1); for i=1:N/2 for j=1:3*D+1 NextGeneration(i,j)=B(i,j); end end %遗传选择交叉 for i=1:N/2 for j=1:3*D+1 Cross(i,j)=B(i+N/2,j); end end for i=1:N/4 Anumber=randperm(D-1); if Anumber(1)~=1 position=Anumber(1); else position=Anumber(2); end for j=position:D-1 temp=Cross(i,j); Cross(i,j)=Cross(N/2-i+1,j); Cross(N/2-i+1,j)=temp; end end %交叉结束，进行更新 for i=1:N/2 Cross(i,3*D+1)=fitness(Cross(i,1:D),D); if Cross(i,3*D+1)<B(i+N/2,3*D+1) for j=2*D+1:3*D Cross(i,j)=Cross(i,j-2*D); end else for j=2*D+1:3*D Cross(i,j)=B(i,j); end end end %下面选择最好的粒子N/2个进入下一代 Pool=zeros(N,3*D+1); for i=1:N/2 for j=1:3*D+1 Pool(i,j)=B(i+N/2,j); end end for i=1+N/2:N for j=1:3*D+1 Pool(i,j)=Cross(i-N/2,j); end end PoolX=sortrows(Pool,3*D+1); for i=1+N/2:N for j=1:3*D+1 NextGeneration(i,j)=PoolX(i-N/2,j); end end Pbest=NextGeneration(i,2*D+1:3*D); for i=2:N if NextGeneration(i,3*D+1)<fitness(Pbest,D) Pbest=NextGeneration(i,2*D+1:3*D); end end %根据粒子群公式进行迭代 for i=1:N for j=D+1:2*D A(i,j)=w*NextGeneration(i,j)+c1*rand*(NextGeneration(i,j+D)-NextGeneration(i,j-D))+c2*rand*(Pbest(j-D)-NextGeneration(i,j-D)); end end for i=1:N for j=1:D A(i,j)=NextGeneration(i,j)+A(i,j+D); end A(i,3*D+1)=fitness(A(i,1:D),D); if A(i,3*D+1)<NextGeneration(i,3*D+1) for j=2*D+1:3*D A(i,j)=A(i,j-2*D); end else for j=2*D+1:3*D A(i,j)=NextGeneration(i,j-2*D); end end end Pg(time)=fitness(Pbest,D); %DDTime=DDTime+1; %if fitness(Pbest,D)<eps %break; %end end %算法结束，得到的结果显示如下： disp('****************************************************') disp('最后得到的最优位置为：') X=Pbest' disp('得到的函数最小值为：') Minimize=fitness(Pbest,D) disp('****************************************************') %绘制进化代数和适应度关系曲线图 xx=linspace(1,MaxDT,MaxDT); yy=Pg(xx); plot(xx,yy,'b-') hold on grid on title('带交叉因子的粒子群优化算法进化代数与适应度值关系曲线图') legend('粒子适应度曲线走势') %------算法结束---DreamSun GL & HF-------------------------