clc;clear all;close all;
%% initialization
%
swarm_size = 64; % number of the swarm particles
maxIter = 50; % maximum number of iterations
inertia = 1.0;
correction_factor = 2.0;
% set the position of the initial swarm
a = 1:8;
[X,Y] = meshgrid(a,a);
C = cat(2,X',Y');
D = reshape(C,[],2);
swarm(1:swarm_size,1,1:2) = D; % set the position of the particles in 2D
swarm(:,2,:) = 0; % set initial velocity for particles
swarm(:,4,1) = 1000; % set the best value so far
plotObjFcn = 1; % set to zero if you do not need a final plot
%% define the objective funcion here (vectorized form)
objfcn = @(x)(x(:,1) - 20).^2 + (x(:,2) - 25).^2;
tic;
%% The main loop of PSO
for iter = 1:maxIter
swarm(:, 1, 1) = swarm(:, 1, 1) + swarm(:, 2, 1)/1.3; %update x position with the velocity
swarm(:, 1, 2) = swarm(:, 1, 2) + swarm(:, 2, 2)/1.3; %update y position with the velocity
x = swarm(:, 1, 1); % get the updated position
y = swarm(:, 1, 2); % updated position
fval = objfcn([x y]); % evaluate the function using the position of the particle
% compare the function values to find the best ones
for ii = 1:swarm_size
if fval(ii,1) < swarm(ii,4,1)
swarm(ii, 3, 1) = swarm(ii, 1, 1); % update best x position,
swarm(ii, 3, 2) = swarm(ii, 1, 2); % update best y postions
swarm(ii, 4, 1) = fval(ii,1); % update the best value so far
end
end
[~, gbest] = min(swarm(:, 4, 1)); % find the best function value in total
% update the velocity of the particles
swarm(:, 2, 1) = inertia*(rand(swarm_size,1).*swarm(:, 2, 1)) + correction_factor*(rand(swarm_size,1).*(swarm(:, 3, 1) ...
- swarm(:, 1, 1))) + correction_factor*(rand(swarm_size,1).*(swarm(gbest, 3, 1) - swarm(:, 1, 1))); %x velocity component
swarm(:, 2, 2) = inertia*(rand(swarm_size,1).*swarm(:, 2, 2)) + correction_factor*(rand(swarm_size,1).*(swarm(:, 3, 2) ...
- swarm(:, 1, 2))) + correction_factor*(rand(swarm_size,1).*(swarm(gbest, 3, 2) - swarm(:, 1, 2))); %y velocity component
% plot the particles
clf;plot(swarm(:, 1, 1), swarm(:, 1, 2), 'bx'); % drawing swarm movements
axis([-2 40 -2 40]);
pause(.1); % un-comment this line to decrease the animation speed
disp(['iteration: ' num2str(iter)]);
end
toc
%% plot the function
if plotObjFcn
ub = 40;
lb = 0;
npoints = 1000;
x = (ub-lb) .* rand(npoints,2) + lb;
for ii = 1:npoints
f = objfcn([x(ii,1) x(ii,2)]);
plot3(x(ii,1),x(ii,2),f,'.r');hold on
end
plot3(swarm(1,3,1),swarm(1,3,2),swarm(1,4,1),'xb','linewidth',5,'Markersize',5);grid
end
