guotao.m

用MATLAB编写的粒子群基本算法－PSO算法来求无约束函数的极值问题

%郭涛算法_多父体杂交算法和郭涛算法_精英多父体杂交算法分别20次数值实验,并给出平均时间
function GuoTao()
clear all;
N=50;%初始个体个数
M=8;
n=1;%论域维数,可修改,用循环做
eps=1e-6;%精度
upper=10;lower=-10;%论域范围
drop=upper-lower;
 
%郭涛算法_多父体杂交算法
minP0=zeros(20,n);minQ0=zeros(20,1);
minFrequency0=zeros(20,1);minTimes0=zeros(20,1);
for i=1:20
    [minP0(i,:),minQ0(i),minFrequency0(i),minTimes0(i)]=GT(N,M,n,upper,lower,eps);
end
%对minP、minQ、minFrequency按minQ从小到打排序
tempP=zeros(20,n);tempFrequency=zeros(20,1);
[X,I]=sort(minQ0);
for r=1:20
    tempP(r,:)=minP0(I(r),:);
    tempFrequency(r)=minFrequency0(I(r));
end
minP0=tempP;minQ0=X;minFrequency0=tempFrequency;
averageTime0=sum(minTimes0)/20;
averageFrequency0=sum(minFrequency0)/20;
 
%郭涛算法_精英多父体杂交算法
minP1=zeros(20,n);minQ1=zeros(20,1);
minFrequency1=zeros(20,1);minTimes1=zeros(20,1);
for i=1:20
    [minP1(i,:),minQ1(i),minFrequency1(i),minTimes1(i)]=GT_GYZJ(N,M,n,upper,lower,eps);
end
%对minP、minQ、minFrequency按minQ从小到打排序
tempP=zeros(20,n);tempFrequency=zeros(20,1);
[X,I]=sort(minQ1);
for r=1:20
    tempP(r,:)=minP1(I(r),:);
    tempFrequency(r)=minFrequency1(I(r));
end
minP1=tempP;minQ1=X;minFrequency1=tempFrequency;
averageTime1=sum(minTimes1)/20;
averageFrequency1=sum(minFrequency1)/20;


%郭涛算法_多父体杂交算法
function [P_Best,Best,Frequency,Time]=GT(N,M,n,upper,lower,eps)
if nargin<6
    disp('输入参数错误');
    return;
elseif nargout<4
    disp('输出参数错误');
    return;
end
   
drop=upper-lower;%若各个分量上下界不同，可以用数组来代替
P=zeros(N,n);%存放初始N个个体，每个个体有n个基因位
Q=zeros(N,1);%存放P中个体对应函数值
Frequency =0;%当前比较次数
tic
%生成初始群体P
for s=1:n
    P(:,s)=drop*rand(N,1)+lower;
end
%生成初始群体P对应的函数值
for r=1:N
    Q(r)=f(P(r,:));
end
[Best,BestIndex]=min(Q);[Worst,WorstIndex]=max(Q);
%以下为郭涛算法主体循环部分
A=zeros(1,M);B=zeros(1,M);
while Worst-Best>eps
    Frequency=Frequency +1;
    %从P中选M个个体生成空间V，其下标存放于A中
    A=floor(rand(1,M)*(N-1))+1;
    %生成Xson的各个组合系数(待检测)
    sum=0;minbound=-0.5;maxbound=1.5;
    for r=1:M-1
        B(r)=(maxbound-minbound)*rand(1)+minbound;
        sum=sum+B(r);
        maxbound=min(1.5,1.5-sum);
        minbound=max(-0.5,-0.5-sum);
    end
    B(M)=1-sum;
    %生成Xson
    Xson=zeros(1,n);
    for r=1:M
        Xson=Xson+B(r)*P(A(r),:);
    end
    %越界处理
    for s=1:n
        if Xson(s)<lower
            Xson(s)=lower;
        elseif Xson(s)>upper
            Xson(s)=upper;
        end
    end
    y=f(Xson);
    if y<Worst
        P(WorstIndex,:)=Xson;Q(WorstIndex)=y;
        [Best,BestIndex]=min(Q);
        [Worst,WorstIndex]=max(Q);  
    end           
end
P_Best=P(BestIndex,:);Time=toc;



%郭涛算法_精英多父体杂交算法
function [P_Best,Best,Frequency,Time]=GT_GYZJ(N,M,n,upper,lower,eps)
if nargin<6
    disp('输入参数错误');
    return;
elseif nargout<4
    disp('输出参数错误');
    return;
end
   
drop=upper-lower;%若各个分量上下界不同，可以用数组来代替
P=zeros(N,n);%存放初始N个个体，每个个体有n个基因位
Q=zeros(N,1);%存放P中个体对应函数值
Frequency =0;%当前比较次数
tic
%生成初始群体P
for s=1:n
    P(:,s)=drop*rand(N,1)+lower;
end
%生成初始群体P对应的函数值
for r=1:N
    Q(r)=f(P(r,:));
end
[Best,BestIndex]=min(Q);[Worst,WorstIndex]=max(Q);
%以下为郭涛算法主体循环部分
A=zeros(1,M);B=zeros(1,M);
while Worst-Best>eps
    Frequency=Frequency +1;
   
    [m,A(1)]=min(Q);
    %从P中选M-1个个体生成空间V，其下标存放于A中
    A(2:end)=floor(rand(1,M-1)*(N-1))+1;
    %生成Xson的各个组合系数(待检测)
    sum=0;minbound=-0.5;maxbound=1.5;
    for r=1:M-1
        B(r)=(maxbound-minbound)*rand(1)+minbound;
        sum=sum+B(r);
        maxbound=min(1.5,1.5-sum);
        minbound=max(-0.5,-0.5-sum);
    end
    B(M)=1-sum;
    %生成Xson
    Xson=zeros(1,n);
    for r=1:M
        Xson=Xson+B(r)*P(A(r),:);
    end
    %越界处理
    for s=1:n
        if Xson(s)<lower
            Xson(s)=lower;
        elseif Xson(s)>upper
            Xson(s)=upper;
        end
    end
    y=f(Xson);
    if y<Worst
        P(WorstIndex,:)=Xson;Q(WorstIndex)=y;
        [Best,BestIndex]=min(Q);
        [Worst,WorstIndex]=max(Q);  
    end           
end
P_Best=P(BestIndex,:)
Time=toc


%函数f(x)
function y=f(x)
n=length(x);
y=1;
for i=1:n
    s=0;
    for j=1:5
        s=s+j*cos((j+1)*x(i)+j);
    end
    y=y*s;
end