Week 5 - Genetic Algorithm

PROGRAM:

clear all 
close all
clc 


x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
[xx,yy] = meshgrid(x,y);
num_cases = 50;
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)=stalagmite(input_vector);
    end
end



% Study 1 - Satistical behavior
for i = 1:num_cases
    [inputs, fopt(i)] = ga(@stalagmite,2);

    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end

figure(1)
subplot(2,1,1)
hold on
surfc(x ,y, -f)
shading interp
plot3(xopt,yopt,-fopt,'Marker','o','markerSize',5,'MarkerFaceColor','r')
title('Unbounded inputs')
subplot(2, 1, 2)
plot(-fopt)
xlabel('Iteration')
ylabel('Function minimum')

tic
% Study 2 - Satistical behavior - with upper and lower bounds
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)
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('Iteration')
ylabel('Function minimum')

% Study 3 increasing GA iterations
options = optimoptions('ga');
options = optimoptions(options,'PopulationSize',170);

tic
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',5,'MarkerFaceColor','r')
title('Bounded inputs')
subplot(2, 1, 2)
plot(-fopt)
xlabel('Iteration')
ylabel('Function minimum')

function [f] = stalagmite(input_vector)
fx = (sin(5.1*pi*input_vector(1)+0.5))^6;

fy = (sin(5.1*pi*input_vector(2)+0.5))^6 ;

fxx = exp((-4*log(2)*(((input_vector(1)-0.0667)^2)/0.64)));

fyy = exp((-4*log(2)*(((input_vector(2)-0.0667)^2)/0.64)));

f = -(fx*fy*fxx*fyy);
end

EXPLANATION:

STEP1

In step 1 i can enter the x and y values and also written the for loop program

(i.e)

STEP 2

In this step 2 to written the Satistical behavior and their plots.

ERRORS:

I had no errors faced in this program.

Genetic algorithm:

Generates a population of points at each iteration. The best point in the population approaches an optimal solution.Selects the next population by computation which uses random number generators.It is to find the maximum and minimum value.