Search code examples
matlabplotparticle-swarm

Find maxima on a surf plot using Particle Swarm Optimization

I'm new to Particle swarm optimization.

I have a surf plot of a 2D image as shown below: enter image description here

And is it possible to fire up the particles randomly and make them find the maxima (global)?

If yes, Can anyone please provide an algorithm or a sample code.

Thank you.

EDIT: Did some coding and got the answer, for a small number of iterations like 10-15 the particles swarm at the maxima but if the iterations are made more than 15 like 50 etc, the particles move away from the maxima.

Can someone give a solution for it, I've included the matlab code and a sample image:

img = imread('gray_scale_img.jpg');
%img is grayscale

a=10; b=0.2; %a is convergence and b is convergence rate
% range=[xmin xmax ymin ymax zmin zmax];
range=[0 440 0 228 0 255]; %<<<---size of the image

Num_iterations = 15;%<<<----problem exists if more iterations
n = 30; % number of particles
best=zeros(Num_iterations,3);

% ----- Start Particle Swarm Optimization -----------
% generating the initial locations of n particles
xrange=range(2)-range(1);
yrange=range(4)-range(3);
zrange=range(6)-range(5);
xn=(rand(1,n)*xrange+range(1));
yn=(rand(1,n)*yrange+range(3));

% Start iterations
for k=1:Num_iterations,
% Show the contour of the function
surfc(double(img)); hold on;
% Find the current best location (xo,yo)

for d = 1:n
xn = ceil(xn);
yn = ceil(yn);
zn(d)=img(yn(d),xn(d));
end

zn_min=max(max(zn));
xo=max(max(xn(zn==zn_min)));
yo=max(max(yn(zn==zn_min)));
zo=max(max(zn(zn==zn_min)));

% Trace the paths of all roaming particles
% Display these roaming particles
plot3(xn,yn,zn,'.',xo,yo,zo,'rp'); axis(range);

% Move all the particles to new locations
nn=size(yn,2);  %a=alpha, b=beta
xn=xn.*(1-b)+xo.*b+a.*(rand(1,nn)-0.5);
yn=yn.*(1-b)+yo.*b+a.*(rand(1,nn)-0.5);
%zn=zn.*(1-b)+zo.*b+a.*(rand(1,nn)-0.5);

%To make sure the particles are well within the range
nn=length(yn);
for l=1:nn,
  if xn(l)<=range(1), xn(l)=range(1); end
  if xn(l)>=range(2), xn(l)=range(2); end
  if yn(l)<=range(3), yn(l)=range(3); end
  if yn(l)>=range(4), yn(l)=range(4); end
  %if zn(l)<=range(5), yn(l)=range(5); end
  %if zn(l)>=range(6), yn(l)=range(6); end
end
drawnow;
hold off;
best(k,1)=xo; best(k,2)=yo; best(k,3)=zo;pause(0.2);
end   %%%%% end of iterations

x_best = best(k,1);
y_best = best(k,2);
z_best = best(k,3);
global_maxima_coordinate =[x_best,y_best]

figure(3);
imshow(A,[]);
hold on
plot(x_best, y_best, 'bx') 
% Draw circle of required radius around the global maxima
theta = 0:pi/50:2*pi;
radius_1 = 15;
xunit_circle_1 = radius_1 * cos(theta) + x_best;
yunit_circle_1 = radius_1 * sin(theta) + y_best;
h_1 = plot(xunit_circle_1, yunit_circle_1,'r');
hold off
title('Global maxima');
Solution

  • Did some coding and got the answer, for a small number of iterations like 10-15 the particles swarm at the maxima but if the iterations are made more than 15 like 50 etc, the particles move away from the maxima.

    Can someone give a solution for it, I've included the matlab code and a sample image:

    img = imread('gray_scale_img.jpg');
%img is grayscale

a=10; b=0.2; %a is convergence and b is convergence rate
% range=[xmin xmax ymin ymax zmin zmax];
range=[0 440 0 228 0 255]; %<<<---size of the image

Num_iterations = 15;%<<<----problem exists if more iterations
n = 30; % number of particles
best=zeros(Num_iterations,3);

% ----- Start Particle Swarm Optimization -----------
% generating the initial locations of n particles
xrange=range(2)-range(1);
yrange=range(4)-range(3);
zrange=range(6)-range(5);
xn=(rand(1,n)*xrange+range(1));
yn=(rand(1,n)*yrange+range(3));

% Start iterations
for k=1:Num_iterations,
% Show the contour of the function
surfc(double(img)); hold on;
% Find the current best location (xo,yo)

for d = 1:n
xn = ceil(xn);
yn = ceil(yn);
zn(d)=img(yn(d),xn(d));
end

zn_min=max(max(zn));
xo=max(max(xn(zn==zn_min)));
yo=max(max(yn(zn==zn_min)));
zo=max(max(zn(zn==zn_min)));

% Trace the paths of all roaming particles
% Display these roaming particles
plot3(xn,yn,zn,'.',xo,yo,zo,'rp'); axis(range);

% Move all the particles to new locations
nn=size(yn,2);  %a=alpha, b=beta
xn=xn.*(1-b)+xo.*b+a.*(rand(1,nn)-0.5);
yn=yn.*(1-b)+yo.*b+a.*(rand(1,nn)-0.5);
%zn=zn.*(1-b)+zo.*b+a.*(rand(1,nn)-0.5);

%To make sure the particles are well within the range
nn=length(yn);
for l=1:nn,
  if xn(l)<=range(1), xn(l)=range(1); end
  if xn(l)>=range(2), xn(l)=range(2); end
  if yn(l)<=range(3), yn(l)=range(3); end
  if yn(l)>=range(4), yn(l)=range(4); end
  %if zn(l)<=range(5), yn(l)=range(5); end
  %if zn(l)>=range(6), yn(l)=range(6); end
end
drawnow;
hold off;
best(k,1)=xo; best(k,2)=yo; best(k,3)=zo;pause(0.2);
end   %%%%% end of iterations

x_best = best(k,1);
y_best = best(k,2);
z_best = best(k,3);
global_maxima_coordinate =[x_best,y_best]

figure(3);
imshow(A,[]);
hold on
plot(x_best, y_best, 'bx') 
% Draw circle of required radius around the global maxima
theta = 0:pi/50:2*pi;
radius_1 = 15;
xunit_circle_1 = radius_1 * cos(theta) + x_best;
yunit_circle_1 = radius_1 * sin(theta) + y_best;
h_1 = plot(xunit_circle_1, yunit_circle_1,'r');
hold off
title('Global maxima');

    And here is a sample image:

    enter image description here