Week 5 - Genetic Algorithm

% Function code genetic algorithm 

function [f] = stalagmite_fun(input_vector)

fx = (sin(5.1*pi*input_vector(1)+0.5))^6;
fy = (sin(5.1*pi*input_vector(2)+0.5))^6;
fxx = exp((-4*log(2)*(((input_vector(1)-0.0667)^2)/0.64)));
fyy = exp((-4*log(2)*(((input_vector(2)-0.0667)^2)/0.64)));

f = -(fx.*fy.*fxx.*fyy);

end

% Genetic Algorithm
% Main Code 
clear all
close all 
clc

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

num_cases = 50;

% Creating 2D Mesh 
[xx,yy] = meshgrid(x,y);

% Using For Loop
for i = 1:length(xx) % 150 times
    for j = 1:length(yy)
        input_vector(1) = xx(i,j);
        input_vector(2) = yy(i,j);
        f(i,j) = stalagmite_fun(input_vector);
    end
end

% Creates three dimensional surface 
figure(1)
surfc(x,y,-f)
shading interp % It makes the surface more smoother 
colorbar
xlabel('value of x')
ylabel('value of y')
title('Stalagmite Function')

% 1st case 
tic

% Using For Loop
for i = 1:num_cases
    [inputs,fopt(i)] = ga(@stalagmite_fun,2);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end

% fopt = -fopt;
time_study1 = toc

% Plotting
figure(2)
subplot(2,1,1)
hold on 
surfc(x,y,-f)
title('Unbounded Inputs')
xlabel('Value of x')
ylabel('Value of y')
shading interp 
hold on 
plot3(xopt,yopt,-fopt,'Marker','o','markersize',5,'markerfacecolor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('Iteration')
ylabel('Function Maximum')

% 2nd case 
tic 

% Using For Loop 
for i = 1:num_cases
    [inputs2,fopt2(i)] = ga(@stalagmite_fun,2,[],[],[],[],[0,0],[0.6,0.6]);
    xopt2(i) = inputs2(1);
    yopt2(i) = inputs2(2);
end

% fopt = -fopt;
time_study2 = toc

% Plotting 
figure(3)
subplot(2,1,1)
surfc(x,y,-f)
shading interp
title('Bounded Inputs')
xlabel('Value of x')
ylabel('Value of y')
hold on 
plot3(xopt2,yopt2,-fopt2,'marker','o','markersize',5,'markerfacecolor','g')
subplot(2,1,2)
plot(-fopt2)
xlabel('Iteration')
ylabel('Function Maximum')