Genetic Algorithm (using MATLAB)
Aim: To write a code in MATLAB to optimise the stalagmite function and to compute the global maxima of the function.
Software used: Octave
Introduction:
Genetic Algorithms (GAs) fall into the category of evolutionary algorithms with working principle based on the mechanics of natural genetics. It is a method fo solving both constrained and unconstrained optimization problems which are based on a natural selection process that mimics biological evolution.
CODES:
Stalagmite function;
function[f]=stalagmite(input_vector)
x=input_vector(1);
y=input_vector(2);
a=(sin((5.1*pi*x)+0.5))^6;
b=(sin((5.1*pi*y)+0.5))^6;
c=exp((-4*log(2)*((x-0.0667)^2))/(0.64));
d=exp((-4*log(2)*((y-0.0667)^2))/(0.64));
f=-(a*b*c*d);
endMain program:
clear all
close all
clc
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
numcase=50;
f =stalagmite(x,y);
%creating a 2-D mesh
[xx,yy]=meshgrid(x,y);
%Evaluating a stalagmite funcion
for i=1:length(xx)
for j=length(yy)
input_vector(1)=xx(i,j);
input_vector(2)=yy(i,j);
f(i,j)=stalagmite(input_vector);
end
end
%Study 1- Statistical Behavior
tic
for i=1:numcase
[inputs,fopt(i)]=ga(@stalagmite,2);
xopt(i)=inputs(1);
yopt(i)=inputs(2);
end
study1_time=toc;
%Plotting
figure(1)
subplot(2,1,1)
hold on
surfc(xx,yy,-f)
shading interp
ylabel('Y Values')
xlabel('X Values')
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Unbounded Inputs')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function Maximum')
saveas(figure(1),'ga1.jpg')
%Study 2-Statistical Behavior with upper and lower bounds
tic
for i=1:numcase
[inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[1;1]);
xopt(i)=inputs(1);
yopt(i)=inputs(2);
end
study2_time=toc;
%Plotting
figure(2)
subplot(2,1,1)
hold on
surfc(xx,yy,-f)
shading interp
ylabel('Y Values')
xlabel('X Values')
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Statistical Behavior with upper and lower bounds')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function Maximum')
saveas(figure(2),'ga2.jpg')
%Study 3-Increasing GA Iterations
options=optimoptions(@ga);
options=optimoptions(options,'populationsize',300);
tic
for i=1:numcase
[inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[1;1],[],[],options);
xopt(i)=inputs(1);
yopt(i)=inputs(2);
end
study3_time=toc;
%Plotting
figure(3)
subplot(2,1,1)
hold on
surfc(xx,yy,-f)
shading interp
ylabel('Y Values')
xlabel('X Values')
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Statistical Behavior with increasing GA iterations')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function Maximum')
saveas(figure(3),'ga3.jpg')RESULT:
The genetic algorithm program is executed and hence the output is achieved.