粒子群算法（PSO）关于参数w的一些改进方法
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互联网集市收集整理的这篇技术教程文章主要介绍了粒子群算法（PSO）关于参数w的一些改进方法，小编现在分享给大家，供广大互联网技能从业者学习和参考。文章包含5462字，纯文字阅读大概需要8分钟。
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(一)线性递减
function [xm,fv] = PSO_lin(fitness,N,c1,c2,wmax,wmin,M,D)
format long;
% fitness学习函数
% c1学习因子1
% c2学习因子2
% wmax惯性权重最大值
% wmin惯性权重最值小
% M最大迭代次数
% D搜索空间维数
% N初始化群体个体数目
% xm目标函数取最小值时的自变量
% fv目标函数最小值
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%初始化种群的个体%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
????for j=1:D
????????x(i,j)=randn;??
????????v(i,j)=randn;??
????end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%先计算各个粒子的适应度，并初始化Pi和Pg%%%%%%%%%%%%
for i=1:N
????p(i)=fitness(x(i,:));
????y(i,:)=x(i,:);
end
pg = x(N,:);?????????????%Pg为全局最优
for i=1:(N-1)
????if fitness(x(i,:))
????????pg=x(i,:);
????end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%主循环，按照公式依次迭代%%%%%%%%%%%%%%%%%%%%%%%%%%
for t=1:M
????for i=1:N
????????w = wmax - (t-1)*(wmax-wmin)/(M-1);
????????v(i,:)=w*v(i,:)+c1*rand*(y(i,:)-x(i,:))+c2*rand*(pg-x(i,:));
????????x(i,:)=x(i,:)+v(i,:);
????????if fitness(x(i,:))
????????????p(i)=fitness(x(i,:));
????????????y(i,:)=x(i,:);
????????end
????????if p(i)
????????????pg=y(i,:);
????????end
????end
????Pbest(t)=fitness(pg);
end
xm = pg';
fv = fitness(pg);
（二）自适应
function [xm,fv] = PSO_adaptation(fitness,N,c1,c2,wmax,wmin,M,D)
format long;
% fitness学习函数
% c1学习因子1
% c2学习因子2
% w惯性权重
% M最大迭代次数
% D搜索空间维数
% N初始化群体个体数目
% xm目标函数取最小值时的自变量
% fv目标函数最小值
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%初始化种群的个体%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
????for j=1:D
????????x(i,j)=randn;??
????????v(i,j)=randn;?
????end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%先计算各个粒子的适应度%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
????p(i)=fitness(x(i,:));
????y(i,:)=x(i,:);
end
pg=x(N,:);?????????????%Pg表示全局最优
for i=1:(N-1)
????if fitness(x(i,:))
????????pg=x(i,:);
????end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%进入主要循环%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for t=1:M
????for j=1:N
????????fv(j) = fitness(x(j,:));
????end
????fvag = sum(fv)/N;
????fmin = min(fv);
????for i=1:N
????????if fv(i) <= fvag
????????????w = wmin + (fv(i)-fmin)*(wmax-wmin)/(fvag-fmin);
????????else
????????????w = wmax;
????????end
????????v(i,:)=w*v(i,:)+c1*rand*(y(i,:)-x(i,:))+c2*rand*(pg-x(i,:));
????????x(i,:)=x(i,:)+v(i,:);
????????if fitness(x(i,:))
????????????p(i)=fitness(x(i,:));
????????????y(i,:)=x(i,:);
????????end
????????if p(i)
????????????pg=y(i,:);
????????end
????end
end
xm = pg';??????????%目标函数取最小值时的自变量
fv = fitness(pg);??%目标函数最小值
?
（三）增加学习因子
% D搜索空间维数
%%%%%%%%%%%%初始化种群的个体%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
????for j=1:D
????????x(i,j)=randn;??%初始化位置
????????v(i,j)=randn;??%初始化速度
????end
end
%%%%%%%%%%先计算各个粒子的适应度，并初始化Pi和Pg%%%%%%%%%%
for i=1:N
????p(i)=fitness(x(i,:));
????y(i,:)=x(i,:);
end
pg = x(N,:);?????????????%Pg为全局最优
for i=1:(N-1)
????if fitness(x(i,:))
????????pg=x(i,:);
????end
end
%%%%%主循环，按照公式依次迭代%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
T = - fitness(pg)/log(0.2);
for t=1:M
????groupFit = fitness(pg);??
????for i=1:N??????
????????Tfit(i) = exp( - (p(i) - groupFit)/T);????
????end???
????SumTfit = sum(Tfit);????
????Tfit = Tfit/SumTfit;????
????pBet = rand();???
????for i=1:N??????
????????ComFit(i) = sum(Tfit(1:i));???????
????????if pBet <= ComFit(i)
????????????pg_plus = x(i,:);???????????
???????????break;???????????
????????end????????
????end????
????C = c1 + c2;????
????ksi = 2/abs( 2 - C - sqrt(C^2 - 4*C));????
????for i=1:N
????????v(i,:)=ksi*(v(i,:)+c1*rand*(y(i,:)-x(i,:))+c2*rand*(pg_plus-x(i,:)));
????????x(i,:)=x(i,:)+v(i,:);
????????if fitness(x(i,:))
????????????p(i)=fitness(x(i,:));
????????????y(i,:)=x(i,:);
????????end
????????if p(i)
????????????pg=y(i,:);
????????end
????end
????T = T * lamda;?
????Pbest(t)=fitness(pg);
end
xm = pg';
fv = fitness(pg);
?
（四）随机权重
function [xm,fv] = PSO_rand(fitness,N,c1,c2,wmax,wmin,rande,M,D)
format long;
% fitness学习函数
% c1学习因子1
% c2学习因子2
% w惯性权重
% M最大迭代次数
% D搜索空间维数
% N初始化群体个体数目
% xm目标函数取最小值时的自变量
% fv目标函数最小值
% rande随机权重方差
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%初始化种群的个体%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:N
????for j=1:D
????????x(i,j)=randn;??
????????v(i,j)=randn;??
????end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%先计算各个粒子的适应度，并初始化Pi和Pg%%%%%%%%%%%%
for i=1:N
????p(i)=fitness(x(i,:));
????y(i,:)=x(i,:);
end
pg = x(N,:);?????????????%Pg为全局最优
for i=1:(N-1)
????if fitness(x(i,:))
????????pg=x(i,:);
????end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%进入主要循环，按照公式依次迭代%%%%%%%%%%%%%%%%%%%%
for t=1:M
????for i=1:N
????????miu = wmin + (wmax - wmin)*rand();
????????w = miu + rande*randn();
????????v(i,:)=w*v(i,:)+c1*rand*(y(i,:)-x(i,:))+c2*rand*(pg-x(i,:));
????????x(i,:)=x(i,:)+v(i,:);
????????if fitness(x(i,:))
????????????p(i)=fitness(x(i,:));
????????????y(i,:)=x(i,:);
????????end
????????if p(i)
????????????pg=y(i,:);
????????end
????end
????Pbest(t)=fitness(pg);
end
xm = pg';
fv = fitness(pg);
?
以上四种w的改进方法各有千秋；请读者以自身要求去选择相应的方法，除此之外，还有很多其它对于w的改进。不过，现在比较主流的给c1，c2,w建立一个相应的关系，通过c1或者c2的值来控制w的变化。
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