Week 4.1 - Genetic Algorithm

clear all
close all
clc 

%stalagmite function
%inputs

%in linspace command 1st value represents starting point of value 2nd point
% refers ending point of value and last point refers no of values in between
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);

%num of iteration to run GA i.e 30
num_cases=30;

%meshgrid transforms vectors into 2d array
[xx,yy]=meshgrid(x,y);

%evaluating the stalagmite function using the for loop
%the loop staring from 1 to maxmimum value of xx
for i=1:length(xx)
    
    %the loop starting from 1 to maxmimum value of yy
    for j=1:length(yy)

        %input_vector (1) is assigned to xx
        input_vector(1)=xx(i,j);

        %input_vector (2) is assigned to yy
        input_vector(2)=yy(i,j);
        
        %calling the function input_vector is the input value for stalagmite function
        f(i,j)=stalagmite_func(input_vector);

    end
end


%study1-statistical behaviour(unbounded) of GA
%tic and toc command is used to calculate the study time
tic

for i=1:num_cases

    %calculating the optimized value of the function
    [inputs, fval(i)]=ga(@stalagmite_func,2);
      
    %inputs1 and 2 are assigned to x_out and y_out
    x_out(i) = inputs(1);
    y_out(i) = inputs(2);

end

% tic toc command to display the timetaken to study
study1_time=toc;

%plotting the graph
figure(1)

%subplot divides the current figure into rectangular panes 
subplot(2,1,1)

% surfc generating the 3D surface plot with contour plot under it 
surfc(xx,yy,-f)

%xlable is used to define xaxis
xlabel('x')

%ylabel is used to define yaxis
ylabel('y')

%title is used for title of plot   
title('case(1)unbounded inputs');

%shading interp varies the color in each line segment 
shading interp

%hold on is used to add plot in existing plot
hold on

%plot is used to create 2D line data 
plot3(x_out,y_out,-fval,'marker','o','markerFaceColor','r')

%subplot divides the current figure into rectangular panes
%plot is used to create 2D plots
subplot(2,1,2)
plot(-fval)

%xlable is used to define xaxis
xlabel('no of iterations');

%ylabel is used to define yaxis
ylabel('function maximum');

% figure1 -from the results as shown its clear that the results are not
% much accurate and giving a lot of variation in optimizing function
%thus further optimization is required .


%STUDY2 - statistical behaviour with boundation of GA with upper and lower bounds
%the difference over here is providing the upper and the lower limit in 
%the GA so that the search space is reduced with the upper and lower boundary

%tic toc command is used calculate the study time 
tic

for i=1:num_cases

    %calculating the optimized value of the function
    %[0;0] is upper and lower limit of x
    %[1;1] is upper and lower limit of y
    [inputs,fval(i)]=ga(@stalagmite_func,2,[],[],[],[],[0;0],[1;1]);
    
    x_out(i)=inputs(1);
    y_out(i)=inputs(2);
end

study2_time=toc;

%plotting the bounded inputs
figure(2)
subplot(2,1,1)
hold on
surfc(xx,yy,-f)
xlabel('x')
ylabel('y')
title('bounded inputs');
shading interp
plot3(x_out,y_out,-fval,'marker','o','markersize',6,'markerFaceColor','r');
subplot(2,1,2)
plot(-fval)
xlabel('no of iterations')
ylabel('function maximum')

%FIGURE2-after providing the boundary limits the variation in value of
%function has reduced comparing study 1

%study3 -statistical study with increasing in populations size(GA)

%optimoptions command is used to increase the size of population
%it will be working on the large set of numbers and which will led to
%increase the possibilities of finding the better fitness of the function
%increasing the size to 170
options=optimoptions('ga');
options=optimoptions(options,'populationsize',170);

%tic toc command is used to calculate the study time
tic

 %[0;0]    is upper and lower limit of x
 %[0.5;0.5] is upper and lower limit of y

for i=1:num_cases
    [inputs,fval(i)]=ga(@stalagmite_func,2,[],[],[],[],[0;0],[0.5;0.5],[],[],options);
    x_out(i)=inputs(1);
    y_out(i)=inputs(2);
end

study3_time=toc;

%plotting bounded inputs increased population size
figure(3)
subplot(2,1,1)
hold on
surfc(xx,yy,-f)
shading interp
xlabel('x');
ylabel('y');
title('bounded inputs with increased population size');
plot3(x_out,y_out,-fval,'marker','o','markersize',6,'markerFaceColor','r')
subplot(2,1,2)
plot(-fval)
xlabel('no of iterations');
ylabel('function maximum');

%FIGURE 3 -now we getting the most accurate result which is between 0.999997 to 0.999998.



%stalagmite function
function[f] = stalagmite_func(input_vector)

f1_x=(sin((5.1*pi).*input_vector(1)+0.5)).^6;
f1_y=(sin((5.1*pi).*input_vector(2)+0.5)).^6;
f2_x=exp((((input_vector(1)-0.0667).^2)/0.64).*(-4*log(2)));
f2_y=exp((((input_vector(2)-0.0667).^2)/0.64).*(-4*log(2)));
f1=f1_x*f1_y*f2_x*f2_y;
f=-f1;
end


%end of program
outputs
inputs =0.0668 ,0.0668
studytime1=2.0927
studytime2=2.0532
studytime3=4.4675​