Week 5 - Genetic Algorithm

Matlab Main Code:

clear all
close all
clc

x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
% creating a two dimensional mesh
[xx yy]=meshgrid(x,y);
%evaluating the stalagmite 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)=stalagmite(input_vector);
    end
end

num_cases=50 % GA runs for 50 iterations
tic          % Study Time count start
% Study-1 statistical behaviour
for i=1:num_cases
    [inputs,fopt(i)]=ga(@stalagmite,2); % GA function is used to run the stalagmite data and give the optimal solutions.
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
    optf(i)=-fopt(i)     %Ga gives us Minima value.Inverse f_opt is taken for Maxima value
end
study1_time = toc     % Study Time count end 


figure(1)
subplot(2,1,1)
hold on
surfc(xx,yy,-f) %Generation of stalagmite function.
shading interp   % To bring visually smooth curve surface without mesh lines
plot3(xopt,yopt,optf,'marker','o','MarkerSize',5,'MarkerFaceColor','r')  %plotting the optimum values with a red dot marker along the stalagmite 3D curves
title('unbounded inputs')
subplot(2,1,2)
plot(optf)              %plot of opt_f for every iterations
xlabel('iterations')
ylabel('function maximum')

    tic    % Study Time count start
    % Study 2-statistical behaviour with upper and lower bounds
    for i=1:num_cases
        [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[1,1]);  % GA function is used to run the stalagmite data and give the optimal solutions.
        xopt(i)=inputs(1);
        yopt(i)=inputs(2);
        optf(i)=-fopt(i)        %Ga gives us Minima value.Inverse f_opt is taken for Maxima value
    end
    study2_time=toc           % Study Time count end 
    figure(2)
    subplot(2,1,1)
    hold on
    surfc(xx,yy,-f)        %Generation of stalagmite function.
    shading interp         % To bring visually smooth curve surface without mesh lines
    plot3(xopt,yopt,optf,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
    title('bounded inputs')
    subplot(2,1,2)
    plot(optf)             %plot of opt_f for every iterations
    xlabel('iterations')
    ylabel('function maximum')
    
    tic        % Study Time count start

% Study-3 increasing GA iterations
options=optimoptions('ga');   % optimoptions is used to increase population size
options=optimoptions(options,'populationsize',  170);

 tic
    
    for i=1:num_cases
        [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[1,1],[],[],options);  % GA function is used to run the stalagmite data and give the optimal solutions.
        xopt(i)=inputs(1);
        yopt(i)=inputs(2);
        optf(i)=-fopt(i)      %Ga gives us Minima value.Inverse f_opt is taken for Maxima value
    end
    study3_time=toc           % Study Time count end 
    figure(3)
    subplot(2,1,1)
    hold on
    surfc(xx,yy,-f)         %Generation of stalagmite function.
    shading interp          % To bring visually smooth curve surface without mesh lines
    plot3(xopt,yopt,optf,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
    title('bounded inputs with increased population size')
    subplot(2,1,2)
    plot(optf)            %plot of opt_f for every iterations
    xlabel('iterations')
    ylabel('function maximum')
    
    

Matlab Function Code:

function [f]=stalagmite(input_vector)
x=input_vector(1);
y=input_vector(2);
f1x=(sin((5.1*pi*x)+0.5))^6;
f1y=(sin((5.1*pi*y)+0.5))^6;
f2x=exp(-4*log(2)*(((x-0.0667)^2)/0.64));
f2y=exp(-4*log(2)*(((y-0.0667)^2)/0.64));
f=-(f1x*f1y*f2x*f2y);
end

Error Rectification:

• While execution of code error occured because meshgrid not created while coding i.e.

[xx yy]=meshgrid(x,y); this code is missing.

• While plotting the surface negative sign of function is not used due to which there is a mismatch between points and surface. corrected by changing f to -f in surf command .

Output:

STATISTICAL STUDY WITHOUT BOUNDATION:

In this case as we can clearly see the optimized results are not accurate and there are so many data points on the graph.

STATISTICAL STUDY WITH BOUNDATION:

• By providing the upper and the lower limit in the ga the search space is reduced with the upper and lower boundary.
• After providing boundary limits the optimum value variation is reduced to the previous case.

STATISTICAL STUDY WITH INCREASE IN SIZE OF POPULATION:

• Here as we have increased the size of the population ,so that the large numbers will provide better solutions.
• It is observed that the optimum points are rduced and we will be having better solutions compared to previous cases.

4.CONCLUSION:

• We can find out the optimum complex solution by using matlab by giving input data in x and y formats.
• With providing boundary counditions to the function ,it has improved drastically and we were closer to the solution.
• By increasing the iterations we can find out the optimum value of any function .This method can be used to find optimum solution.