Week 4.1 - Genetic Algorithm

% Genetic Algorithm
clear all
close all
clc

%Defining our search space
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);

%Creating a 2Dimensional mesh
[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
surfc(xx,yy,f)
xlabel('x value')
ylabel('y value')
shading interp

[inputs,f] = ga(@stalagmite,2)

%Stalagmite Function
function [f]=stalagmite(input_vector)
x=input_vector(1);
y=input_vector(2);
f1_x=(sin(5.1*pi*x+0.5)).^6;
f1_y=(sin(5.1*pi*y+0.5)).^6;
f2_x=exp(-4*log(2)*((x-0.0667)^2/0.64));
f2_y=exp(-4*log(2)*((y-0.0667)^2/0.64));
f= -f1_x* f1_y* f2_x *f2_y;
end

Optimization

clear all
close all
clc

x = linspace(0,0.6,150)
y = linspace(0,0.6,150)
num_cases = 50
%Creating a 2Dimensional mesh
[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 - statical behaviour
for i =1:num_cases
[input,fopt(i)] = ga(@stalagmite,2)
xopt(i) = input(1)
yopt(i) = input(2)
end

figure(1)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('unbounded inputs')
shading interp
hold off
subplot(2,1,2)
plot(fopt)
xlabel('Iterations')
ylabel('Function minimum')

%study 2- Statistical behaviour - with uppper and lowerbounds
tic
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('Iterations')
ylabel('Function minimum')

%study 3 increasing GA iterations
options=optimoptions('ga')
options=optimoptions(options,'PopulationSize',400);

for i = 1:num_cases
[inputs,fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0,0],[0.2,0.2],[],[],options);
xopt(i) = inputs(1);
yopt(i) = inputs(2);
end
study2_time = tic
figure(3)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('Iterations')
ylabel('Function minimum')