1. Problem description:
Particle Swarm Optimization (PSO), also known as particle swarm optimization, is an evolutionary computing technology developed by J. Kennedy and RC Eberhart in 1995. It is derived from the simulation of a simplified social model. Among them, the "swarm" originated from the particle swarm conforms to the 5 basic principles of swarm intelligence proposed by MM Millonas when developing the model for artificial life (artificial life). "Particle" is a compromise choice, because it is necessary to describe the members of the group as having no mass or volume, but also to describe its speed and acceleration.
The PSO algorithm was originally designed to graphically simulate the graceful and unpredictable movement of a flock of birds. Through the observation of the social behavior of animals, it is found that the social sharing of information in the group provides an evolutionary advantage, and this is used as the basis for the development of algorithms. The initial version of PSO was formed by adding the speed matching of the nearest neighbors, and considering the multi-dimensional search and the acceleration based on the distance. Later, the inertial weight w was introduced to better control the development (exploitation) and exploration (exploration), forming the standard version.
2. Part of the program:
function main
% this is particle swarm optimization program
% n:dimension of variable; m:number of particle
% x:m*n matrix; v:m*n matrix
% pbx:m*n matrix; gbx:1*n matrix
% pbf:m*1 matrix; gbf:number
clear all;
clc
tic;
E0=0.001; %permitted error
MaxNum=100; %iteration number of every time
%
n=1;
m=50;
c1=2;
c2=2;
w=1;
vmax=0.5;
rand('state',sum(100*clock));
% random m particle
x=-4+8*rand(m,n);
v=2*rand(m,n);
% compute fitness
for i=1:m
for j=1:n
f(i)=fitness(x(i,j));
end
end
% find individual max and global max
pbx=x;
pbf=f;
[gbf i]=min(pbf);
gbx=pbx(i,:);
% start loop
k=1;
while k<=MaxNum
for i=1:m
for j=1:n
f(i)=fitness(x(i,j));
end
if f(i)<pbf(i)
pbf(i)=f(i);
pbx(i,:)=x(i,:);
end
end
[gbf i]=min(pbf);
gbx=pbx(i,:);
for i=1:m
v(i,:)=w*v(i,:)+c1*rand*(pbx(i,:)-x(i,:))+c2*rand*(gbx-x(i,:));
for j=1:n
if v(i,j)>vmax
v(i,j)=vmax;
elseif v(i,j)<-vmax
v(i,j)=-vmax;
end
end
x(i,:)=x(i,:)+v(i,:);
end
if abs(gbf)<E0,break,end
k=k+1;
end
% Display the results
disp('the maximum value is');1/gbf-1
disp('and the corresponding coordinate is');gbx
x=-4:0.01:4;
y=1.1*(1-x+2*x.^2).*exp(-x.^2/2);
plot(x,y);
hold on;
plot(gbx,1/gbf-1,'r*');
hold off
toc
3. Simulation conclusion:
D00001