Week 4.1 - Genetic Algorithm

clear all
close all
clc


x = linspace(0,0.6,150)
y = linspace(0,0.6,150)
num_cases = 50
[xx,yy] = meshgrid(x,y);

% evaluating the stalagmite function

for i = 1:length(xx)
for j = 1:length(yy)
    input_vector(1) = xx(i,j);
    input_vector(2) = yy(i,j);
    
    f(i,j) = stalagmite(input_vector);
    
end
end
%study 1-statistikal behavior
  for   i=1:num_cases
        [inputs,fopt(i)] = ga(@stalagmite,2)
        xopt(i) = inputs(1);
        yopt(i) = inputs(2);
  end


figure(1)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('unbounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('iteration')
ylabel('function minimum')

tic

%study 2- statical behavior -with upper and lower ounds

for i = 1:num_cases
[inputs,fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6]);
xopt(i) = inputs(1);
yopt(i) = inputs(2);

end
study2_time = toc

figure(2)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'Marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('Bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('iteration')
ylabel('function minimum')

% study 3 increasing GA iteration

options = optimoptions('ga');
options = optimoptions(options,'Populationsize',200);

tic
for i = 1:num_cases
    [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);


end
study3_time = toc
figure(3)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('Bounded inputs with iteration')
subplot(2,1,2)
plot(fopt)
xlabel('iteration')
ylabel('function minimum')


Stalagmite Function :

function [f] = stalagmite(input_vector)
x = input_vector(1);
y = input_vector(2);

f1x = (sin((5.1*pi*x)+0.5))^6;
f1y = (sin((5.1*pi*y)+0.5))^6;
f2x = exp(-4*log(2)*((x-0.0667)^2)/0.64);
f2y = exp(-4*log(2)*((y-0.0667)^2)/0.64);

f = -(f1x*f1y*f2x*f2y);

end

Stalagmie_Algorithm :

close all
clear all
clc

% interation
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);

%creating a 2D mesh
[xx,yy] = meshgrid(x,y);

% evaluating the stalagmite function

for i = 1:length(xx)
for j = 1:length(yy)
    inputs_vector(1) = xx(i,j);
    inputs_vector(2) = yy(i,j);
    
    f(i,j) = stalagmite(input_vector);
    
end
end
surfc(xx,yy,f)
[x,[fval=ga(@stalagmite(input_vector,2))];
shading interp

xlabel('xvalue')
ylabel('yvalue')