粒子群算法（PSO）关于参数w的一些改进方法

(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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%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

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%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

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

%%%%%%%%%%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

%%%%%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

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

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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%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

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。