Week 4.1 - Genetic Algorithm

genitical algoritham is an matametical operation used to determine the maximum values of the functions

there are the inputs are x,y and num-case,

x = lispace(0,0.6,150)

y=linspace(0,0.6,150)

num_case = 50

the linspace commad used to determine the xand y values between 0 to 0.6 thwre are 150 equal interval values

for making 2d array, the meshgrid is (x,y)

i is the length of x and j is the length of y and the j is the sum of vector 1&2

vectors 1&2 is the , input_vector(1)=xx(i,j)

input_vector(2)=yy(i,j)

j=stalagmite (input_vector)

we can studing the first statistical behavior

the fopt of the input is genitic algoritham @stalagmite 2

(input,fopt(i))=ga(@stalagmite, 2)

xopt and yopt are the input of i of 1&2

xopt(i)=input(1)

yopt9i)=input(2)

for making the plot for the figure one

sub plot is (2,1,1)&(2,1,2) and the surf is (x,y,f)

plotin the figure 1 is ,

plot3(xopt,yopt,fopt,'marker','o',markersize',5,markerfacecolor','r')

we can be studing the second statistica behaviour

the plot of the input is genetic algorithm and the xopt and uopt are the inputs of i at 1&2

for giving the tic &toc commad to second study time

for making the plot 2

subplot and surf are same for the figure one

plot command is ,

plot3(xopt,yopt,fopt,'marker',markersize',5,'markerfacecolor','r')

xlabel is interation and ylabel is function is minimum

we can be studying the ga interation with increasng

options=optimoptions(ga)

options=optimoptions(options,'populationsize',250)

that is increasd the population to 250

and providing xopt,yopt and fopt

for making the plot3

all are same to making the plot of figure 1&2

plot39xopt,yopt,fopt,marker','o',markersize,5,markerfacecolor,'r')

providing the x7y labels

clear all
close all
clc 

%input
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
num_case = 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 satistical behaviour
tic
for i = 1:num_case
    [input,fopt(i)] = ga(@stalagmite, 2)
    xopt(i)=input(1);
    yopt(i)=input(2);
end

study_timel = toc

figure(1)
subplot(2,1,1)
surf(x,y,f)
shading interp
hold on
plot3(xopt,yopt,fopt,'Marker','o','MarkerSize',5,'MarkerFaceColor','r')
subplot(2,1,2)
plot(fopt)
xlabel('lterations')
ylabel('Function Minimum')

%study 2_statistical behaviour with upper and lower bomds
tic
for i =1:num_case
    [inputs,fopt(i)] = ga(@stalagmite, 2);
    xopt(i) = input(1);
    yopt(i) = input(2);
end

study_time2=toc

figure(2)
subplot(2,1,1)
surfc(x,y,f)
shading interp
hold on
plot3(xopt,yopt,fopt,'Marker','.','Markersize',5,'MarkerFaceColor','r')
subplot(2,1,2)
plot(fopt)
title('iterations')
xlabel('iterations')
ylabel('function mimimum')

%study 3 increasing ga iterations 
tic
options = optimoptions('ga');
options = optimoptions(options,'populationsize',250);

for i = num_case
    [inputs,fopt(i)]=ga(@stalagmite, 2)
    xopt(i) = input(1);
    yopt(i) = input(2);
end

study_time3=toc

figure(3)
subplot(2,1,1)
surfc(x,y,f)
shading interp
hold on
plot3(xopt,yopt,fopt,'Marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('bouned input wisth')
subplot(2,1,2)
plot(fopt)
xlabel('iteration')
ylabel('Functon Minimum')


FUNCTION OF STALGMITE

function A = stalagmite(input_vector)
x = input_vector(1);
y = input_vector(2);
f1 = (sin(5.1*pi*x+0.5)).^6;
f2 = exp((-4*log(2)*((x-0.06670).^2))/0.64);
f3 = (sin(5.1*pi*y+0.5)).^6;
f4 = exp((-4*log(2)*((y-0.06670).^2))/0.64);

A = (f1*f2*f3*f4)
end