Notes

% Particle Swarm Optimization - PSO
% Haupt & Haupt
% 2003
clear
ff = ‘testfunction’; % Objective Function
% Initializing variables
popsize = 10; % Size of the swarm
226 MATLAB CODEnpar = 2; % Dimension of the problem
maxit = 100; % Maximum number of iterations
c1 = 1; % cognitive parameter
c2 = 4-c1; % social parameter
C=1; % constriction factor
% Initializing swarm and velocities
par=rand(popsize,npar); % random population of
% continuous values
vel = rand(popsize,npar); % random velocities
% Evaluate initial population
cost=feval(ff,par); % calculates population cost using
% ff
minc(1)=min(cost); % min cost
meanc(1)=mean(cost); % mean cost
globalmin=minc(1); % initialize global minimum
% Initialize local minimum for each particle
localpar = par; % location of local minima
localcost = cost; % cost of local minima
% Finding best particle in initial population
[globalcost,indx] = min(cost);
globalpar=par(indx,:);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Start iterations
iter = 0; % counter
while iter < maxit
iter = iter + 1;
% update velocity = vel
w=(maxit-iter)/maxit; %inertia weiindxht
r1 = rand(popsize,npar); % random numbers
r2 = rand(popsize,npar); % random numbers
vel = C*(w*vel + c1 *r1.*(localpar-par) +
c2*r2.*(ones(popsize,1)*globalpar-par));
% update particle positions
par = par + vel; % updates particle position
overlimit=par<=1;
PROGRAM 7: PARTICLE SWARM OPTIMIZATION 227underlimit=par>=0;
par=par.*overlimit+not(overlimit);
par=par.*underlimit;
% Evaluate the new swarm
cost = feval(ff,par); % evaluates cost of swarm
% Updating the best local position for each particle
bettercost = cost < localcost;
localcost = localcost.*not(bettercost) +
cost.*bettercost;
localpar(find(bettercost),:) =
par(find(bettercost),:);
% Updating index g
[temp, t] = min(localcost);
if temp<globalcost
globalpar=par(t,:); indx=t; globalcost=temp;
end
[iter globalpar globalcost] % print output each
% iteration
minc(iter+1)=min(cost); % min for this
% iteration
globalmin(iter+1)=globalcost; % best min so far
meanc(iter+1)=mean(cost); % avg. cost for
% this iteration
end% while
figure(24)
iters=0:length(minc)-1;
plot(iters,minc,iters,meanc,’–’,iters,globalmin,’:’);
xlabel(‘generation’);ylabel(‘cost’);
text(0,minc(1),’best’);text(1,minc(2),’population
average’)