Week 4.1 - Genetic Algorithm

function [f]=stalagmite_func(input_vector)
f1x=(sin((5.1*pi).*input_vector(1)+0.5)).^6;
f1y=(sin((5.1*pi).*input_vector(2)+0.5)).^6;

f2x=exp((((input_vector(1)-0.0667).^2)/0.64).*(-4*log(2)));
f2y=exp((((input_vector(2)-0.0667).^2)/0.64).*(-4*log(2)));
f1=f1x*f1y*f2x*f2y;
f=-f1;
end

clear all 
close all
clc
%inputs 
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_case = 50;
%forming 2d array
[xx, yy]=meshgrid(x,y);

for i=1:length(x)
    for j=1:length(y)
        input_vector(1)=xx(i,j);
        input_vector(2)=yy(i,j);
        f(i,j)=stalagmite_func(input_vector);
    end 
end

%study 1 - unbounded
tic
for i=1:num_case
   [input,fopt(i)]=ga(@stalagmite_func,2);
       xopt(i)=input(1);
       yopt(i)=input(2);
end

study_time1=toc
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('Interaction')
ylabel('Function maximum')

%study 2 - statistical study with upper bound and lower bound
tic
for i=1:num_case
   [input,fopt(i)]=ga(@stalagmite_func,2,[],[],[],[],[0;0],[1;1]);
       xopt(i)=input(1);
       yopt(i)=input(2);
end

study_time2=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('unbounded inputs')
subplot(2,1,2)
plot(-fopt)
xlabel('Interaction')
ylabel('Function maximum')

%study 3 - Increasing iterations 
options=optimoptions('ga');
options=optimoptions(options,'Populationsize',150);
tic
for i=1:num_case
   [input,fopt(i)]=ga(@stalagmite_func,2,[],[],[],[],[0;0],[1;1],[],[],options);
       xopt(i)=input(1);
       yopt(i)=input(2);
end

study_time2=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('unbounded inputs')
subplot(2,1,2)
plot(-fopt)
xlabel('Interaction')
ylabel('Function maximum')