Week 4.1 - Genetic Algorithm

CASE 1 FINDING GLOBAL MAXIMA 
close all
clear all
clc
%input
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_spaces=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)=stagalmite(input_vector);
end
end
surf(xx,yy,-f)
shading interp
[inputs,fval]=ga(@stagalmite,2);

STUDY 1 

close all
clear all
clc
%input
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_spaces=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)=stagalmite(input_vector);
end
end
%study 1-unbounded
tic
for i=1:num_spaces
[results,fopt(i)]=ga(@stagalmite,2)
xopt(i)=results(1)
yopt(i)=results(2)
end
study_time1=toc
figure(1)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o')
subplot(2,1,2)
plot(-fopt)
xlabel('iteration')
ylabel('function maximum')

STUDY 2 

close all
clear all
clc
%input
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_spaces=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)=stagalmite(input_vector);
end
end
tic
for i=1:num_spaces
[results,fopt(i)]=ga(@stagalmite,2,[],[],[],[],[0;0],[0.6;0.6])
xopt(i)=results(1)
yopt(i)=results(2)
end
study_time2=toc
figure(2)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o')
subplot(2,1,2)
plot(-fopt)
xlabel('iteration')
ylabel('function maximum')

STUDY 3 

close all
clear all
clc
%input
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_spaces=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)=stagalmite(input_vector);
end
end
tic
options=optimoptions('ga')
options=optimoptions(options,'populationsize',250)
for i=1:num_spaces
[results,fopt(i)]=ga(@stagalmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options)
xopt(i)=results(1)
yopt(i)=results(2)
end
study_time3=toc
figure(3)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o')
subplot(2,1,2)
plot(-fopt)
xlabel('iteration')
ylabel('function maximum')


STALAGMITE FUNCTION 

function A= stagalmite(input_vector)
x=input_vector(1);
y=input_vector(2);
f1.x=(sin(5.1*pi*x+0.5)).^6;
f2.x=exp((-4*log(2)*((x-0.0667).^2))/(0.64));
f1.y=(sin(5.1*pi*y+0.5)).^6;
f2.y=exp((-4*log(2)*((y-0.0667).^2))/(0.64));
A=(-f1.x*f2.x*f1.y*f2.y)
end

CODE EXPLANATION AND GRAPH OUTPUT IS GIVEN IN PPT