Week 4.1 - Genetic Algorithm

GENETIC ALGORITHM

a genetic algorithm is a natural selection that belongs to the larger class of evolutionary algorithms. Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems. Genetic algorithms simulate the process of natural selection which means those species who can adapt to changes in their environment are able to survive and reproduce and go to next generation

examples

optimizing decision trees for better performance

solving sudoku puzzles

hyperparameter optimization

clear all

close all

clc

% Inputs

x =linspace (0,0.6,150);

y =linspace (0,0.6,150);

num_cases = 60

% Storing in 2D array 
[xx,yy]=meshgrid(x,y);

% calling the 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) = gafunctioin(input_vector);
    end
end


num_case = 50
%Study 1 behaviour

tic

for i = 1:num_cases

[inputs,fopt(i)] = ga(@func,2);
xoption(i) = inputs(1);
yoption(i)=inputs(2);

end

studytimel=tic
% Unbounded inputs
figure(1) 
subplot(2,1,1)
hold on
surfc(x,y,-f)

shading interp
plot3(xoption, yoption, -fopt, 'Marker', 'o', 'Markersize',5, 'Markerfacecolor', 'r') 
title('Unbounded inputs')
subplot(2,1,2)

plot(-fopt) 
xlabel('iterations') 
ylabel('function maximum')
%Study 2 behaviour

tic

for i = 1:num_cases

[inputs,fopt(i)] = ga(@func,2,[],[],[],[],[0,0],[0.5,0.5]); 
xoption(i)= inputs(1); 
yoption(i)= inputs(2);
end

studytime2 tic

% Bounded inputs:
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 inputs')

subplot(2,1,2)

plot(-fopt)

xlabel('iterations')

ylabel('function maximum')

%Study 3 bheaviour

options=optimoptions('ga'); 
options=optimoptions (options,'Population size',200);

tic

for i=1:num cases 
    [inputs, fopt(i)]=ga(@func,2,[],[],[],[],[0;0],[0.5;0.5],[],[], options);
MAIN  PROGRAMME
xoption(i) = inputs(1); 
yoption(i)=inputs(2);

end

studytime3= toc

Optimization

figure(3)

subplot (2,1,1)
hold on

surfc(x,y,-f)

shading interp

plot3(xoption,yoption,-fopt, 'Marker', 'o', 'Markersize',5, 'Markerfacecolor', 'r')

title('Optimization')

subplot(2,1,2)

plot(-fopt)

xlabel('iterations')

ylabel('function maximum')

FUNCTION PROGRAMME
function [f] = gafunctioin(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)))

e = -(a*b*c*d);

endfunction


EXPLANATION

The code is used to get the value of the function at different grid points on the x-y plane which will be plotted in the z-direction. we have multiplied the -ve sign to convert the function into maxima since the genetic algorithm function can only calcualte the minima value for a function.

GA Syntax

x = ga(fun,nvars)

x= ga(fun,nvars,A,b)

x= ga(fun,nvars A,b,Aeq,beq)

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub)

x= ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon)

x = ga(fun,nvars,A,b,Aeq,beq,lb.ub.nonlcon,options)

x = ga(fun,nvars,A,b,[][],lb,ub,nonlcon,IntCon)

x = ga(fun,nvars,A,b,[],[],lb,ub nonicon,IntCon,options)

x = ga(problem)

errors are mainly occured due to spelling mistakes and forget to use paranthesis