Week 4.1 - Genetic Algorithm

Report on genetic algorithm

AIM:

• To write a code in MATLAB for optimizing the stalagmite function and to find the global maxima of the function.
• To explain the concept of genetic algorithm and also explain the syntax for ga in MATLAB.

GOVERNING EQUATIONS:

Some of the syntax used in this code are

Formula for creating a Stalagmite function.

inp = -fx1*fx2*fy1*fy2

fx1= ((sin((5.1*pi*x)+0.5))^6);

fy1= ((sin((5.1*pi*y)+0.5))^6);

fx2= exp((-4*log(2))*(((x-0.0667)^2)/0.64));

fy2= exp((-4*log(2))*(((y-0.0667)^2)/0.64));

GA syntax

ga(fun,nvars,A,B,Aeq,Beq,lb,ub,nonlcon,intcon,options)

Syntax for creating a surface plot

surfc(x,y,f)

The syntax for removing the mesh/shading from the surface plot

shading interp

REPORT:

This program was done using MATLAB language.

Supplementary code: (Stalagmite function)

function [inp] = stalagmite(input_vector)
x = input_vector(1);
y = input_vector(2);
fx1= ((sin((5.1*pi*x)+0.5))^6);
fy1= ((sin((5.1*pi*y)+0.5))^6);
fx2= exp((-4*log(2))*(((x-0.0667)^2)/0.64));
fy2= exp((-4*log(2))*(((y-0.0667)^2)/0.64));
inp = -fx1*fx2*fy1*fy2;
end

Main code: (GA)

clear all
close all
clc
% A program for Genetic Algorithm
% Giving the inputs for x and y
x= linspace(0,0.6,150);
y= linspace(0,0.6,150);
%Creating a mesh for x and y
[xx,yy] = meshgrid(x,y);
% Calling the function and defining the called function values to f
for m = 1:150
    for n = 1:150
        f(m,n) = stalagmite ([xx(m,n),yy(m,n)]);
    end
end
% Giving the number of times it has to run
num_cases = 50;
tic
%Study 1 - Statistical behavior [inputs,fopt(i)] = ga(fun,nvars).
for i= 1:num_cases
    [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 (x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','Markersize',5)
title('Unbound inputs')
subplot(2,1,2)
plot(fopt)
xlabel('Iteration')
ylabel('function minimum')

tic
% Study2- Statistical behavior( with upper and lower bounds)
% [inputs,fopt(i)] = ga(fun,nvars,A,B,Aeq,Beq,lb,ub)
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)
% plotting
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',3)
title('bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('Iteration')
ylabel('function minimum')

% Study 3 increases GA iteration
% Giving population
options = optimoptions('ga');
options = optimoptions(options,'populationsize',170);
tic
% [inputs,fopt(i)] = ga(fun,nvars,A,B,Aeq,Beq,lb,ub,nonlcon,intcon,options)
% nonlcon-Nonlinear constraints
% intcon-Integer constraints
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',3)
title('GA iterations')
subplot(2,1,2)
plot(fopt)
xlabel('Iteration')
ylabel('function minimum')

ANSWERS TO THE FOLLOWING QUESTIONS:

• What is GA?

GA known as a Genetic algorithm is an algorithm that helps in optimizing problems.

GA takes a function and gives the global maxima and minima for that function.

CONCLUSION:

Thus a code in MATLAB for optimizing the stalagmite function and to find the global maxima of the function is done.