Challenge

Week 4.1 - Genetic Algorithm

GGeorge Mathew16 Mar 2022

a code in MATLAB to optimise the stalagmite function and find the global maxima of the function.

clear all
close all
clc
%defining our spaace
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
% creating a 2D mesh
[xx yy] = meshgrid(x,y);
figure(12)

%Evaling 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 fval] =ga(@stalagmite,2);
hold on
%study1 ststical behaviour
num_cases=50

tic
for i=1:num_cases
    [inputs,fopt(i)]=ga(@stalagmite,2);
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
end
study1_time=toc
figure(1)
subplot(2,1,1);
hold on
surfc(x,y,F)
shading interp
plot3(xopt,yopt,fopt,'marker','o','MarkerSize',7,'MarkerFaceColor','r')
title('Unbounded inputs')

subplot(2,1,2 )
plot(fopt)
xlabel('iteration')
ylabel('function min.')
tic
% study 2 - statistical behaviour with upper and lower bounds

for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[1;1]);
    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 input')
subplot(2,1,2)
plot(fopt)
xlabel('iterations')
ylabel('function minimum')


%study 3 increasing the ga iterations
tic
options = optimoptions('ga');
options = optimoptions (options,'populationSize',270);
for i=1:num_cases
    [inputs,fopt(i)] = ga(@stalagmite,2, [],[],[],[],[0;0],[1;1],[],[],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('bounded inputs')
subplot (2,1,2)
plot(fopt)
xlabel('iterations')
ylabel('function minimum')

the function of the pgm to execute the values

function[F]=stalagmite(input_vector)
x=input_vector(1);
y=input_vector(2);
X1=[sin(5.1*pi*x+0.5)]^6;
Y1=[sin(5.1*pi*y+0.5)]^6;
X2=exp(-4*log(2)*(((x-0.0667)^2)/(0.64)));
Y2=exp(-4*log(2)*(((y-0.0667)^2)/(0.64)));
F=-(X1*Y1*X2*Y2);
end

We pgm outputs x and y the function call for it and it is formulated to find out F and returned to the pgm.