% A SIMPLE IMPLEMENTATION OF THE 
% Particle Swarm Optimization IN MATLAB 
function [xmin, fxmin, iter] = PSO() 
% Initializing variables 
success = 0;                    % Success flag 
PopSize = 30;                   % Size of the swarm 
MaxIt = 100;                   % Maximum number of iterations 
iter = 0;                       % Iterations’counter 
fevals = 0;                     % Function evaluations’ counter 
c1 = 2;                       % PSO parameter C1 
c2 = 2;                       % PSO parameter C2 
w = 0.6;                       % inertia weight 
                 % Objective Function 
f = 'DeJong'; 
dim = 10;                        % Dimension of the problem 
upbnd = 10;                      % Upper bound for init. of the swarm 
lwbnd = -5;                     % Lower bound for init. of the swarm 
GM = 0;                         % Global minimum (used in the stopping criterion) 
ErrGoal = 0.0001;                % Desired accuracy 

% Initializing swarm and velocities 
popul = rand(dim, PopSize)*(upbnd-lwbnd) + lwbnd; 
vel = rand(dim, PopSize); 

for i = 1:PopSize, 
   fpopul(i) = feval(f, popul(:,i)); 
   fevals = fevals + 1; 
end 

bestpos = popul; 
fbestpos = fpopul; 
% Finding best particle in initial population 
[fbestpart,g] = min(fpopul); 
lastbpf = fbestpart; 

while (success == 0) & (iter < MaxIt),     
   iter = iter + 1; 

   % VELOCITY UPDATE 
   for i=1:PopSize, 
       A(:,i) = bestpos(:,g); 
   end 
   R1 = rand(dim, PopSize); 
   R2 = rand(dim, PopSize); 
   vel = w*vel + c1*R1.*(bestpos-popul) + c2*R2.*(A-popul); 

   % SWARMUPDATE 
   popul = popul + vel; 
   % Evaluate the new swarm 
   for i = 1:PopSize, 
       fpopul(i) = feval(f,popul(:, i)); 
       fevals = fevals + 1; 
   end 
   % Updating the best position for each particle 
   changeColumns = fpopul < fbestpos; 
   fbestpos = fbestpos.*( 1-changeColumns) + fpopul.*changeColumns; 
   bestpos(:, find(changeColumns)) = popul(:, find(changeColumns)); 
   % Updating index g 
   [fbestpart, g] = min(fbestpos); 
  % currentTime = etime(clock,startTime); 
   % Checking stopping criterion 
   if abs(fbestpart-GM) <= ErrGoal 
       success = 1; 
   else 
       lastbpf = fbestpart; 
   end 

end 

% Output arguments 
xmin = popul(:,g); 
fxmin = fbestpos(g); 

fprintf(' The best vector is : n'); 
fprintf('---  %g  ',xmin); 
fprintf('n'); 
%========================================== 
function DeJong=DeJong(x) 
DeJong = sum(x.^2);