Week 4.1 - Genetic Algorithm

Aim: To optimize the stalagmite function and find the Global maxima.

About Genetic Algorithm (GA).

The Genetic Algorithm (GA) is an optimization technique used to solve both constrained and unconstrained

problem that is based on natural selection.

It is based on the process that drives biological evolution.

GA repeatedly modifies a population of individual solutions.

Error faced:

in for loop i had written for i=length (x) which resulted in incorrect plot being generated.

Correction done: wrote for i=1:length(x).

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)=stalagmite(input_vector);
    end
end

%study 1-unbounded

tic
for i=1:num_spaces
    [results,fopt(i)]=ga(@stalagmite,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- bounded
tic
for i=1:num_spaces
    [results,fopt(i)]=ga(@stalagmite,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')

%study3- increased initial population

tic
options=optimoptions('ga')
options=optimoptions(options,'populationsize',250)
for i=1:num_spaces
[results,fopt(i)]=ga(@stalagmite,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')