Week 4.1 - 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

program for minimisation



clear all
close all
clc

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

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

%evaluating the stalgamite 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,fval]=ga(@stalagmite,2)

function [f]=get_stalagmite(x,y)

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


program for maximisation


clear all
close all
clc

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

[x,y]=meshgrid(x,y);

num_cases=50;
f=get_stalagmite(x,y);


tic

%study 1 - statistical behavior
for i=1:num_cases
    [inputs,fopt(i)]=ga(@stalagmite,2);
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
end

study1_time=toc

%plotting1
figure(1)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','g')
title('Unbounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('Iterations')
ylabel('function minimum')

tic

%study 2 -statistical behaviour

for i=1:num_cases
 [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.4;0.4])
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
end

study2_time=toc

%plotting2

figure(2)

subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',3,'markerfacecolor','g')
title('Bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('Iterations')
ylabel('function minimum')

%increrasing ga iteration
options=optimoptions('ga');
options=optimoptions(options,'populationsize',170);

tic

for i=1:num_cases
 [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.4;0.4],[],[],options)
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
end

study3_time=toc

%plotting3

figure(3)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','g')
title('Bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('Iterations')
ylabel('function minimum')