Week 5 - Genetic Algorithm

function f =  stalagmite(input_vector)

x = input_vector(1);
y = input_vector(2);

f1 = ((sin(5.1*pi*x+0.5)))^6;
f2 = ((sin(5.1*pi*y+0.5)))^6;
f3 = exp(-4*log(2)*((x-0.0667)^2/0.64));
f4 = exp(-4*log(2)*((y-0.0667)^2/0.64));

f = (f1*f2*f3*f4);
end

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)


% Logic
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
 tic
% Study 1 - Satistical behaviour
for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite, 2);
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end

study_time = 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('Unbonded inputs')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function minimum')

tic
% Study 2 - Stastical behaviour - with upper & lower bounds
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('Bonded inputs')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function minimum')

% Study 3 increaing GA iterations
options = optimoptions('ga');
options = optimoptions(options,'PopulationSize', 170);


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('Bonded inputs with modified population size')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function minimum')