Week 4.1 - Genetic Algorithm

GENECTIC ALGORITHM CODE

clear all
close all
clc

x = linspace(0,0.6,150);
y = linspace(0,0.6,150);

[xx,yy] = meshgrid(x,y);

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;
tic
%Study1 satistical behaviour
 for i = 1:num_cases
     [inputs ,fopt(i)] = ga(@stalagmite,2);
     xopt(i)=inputs(1);
     yopt(i)=inputs(2);
 end

 study1_time = toc
 
figure(1)
subplot(2,1,1)
hold on 
surfc(xx,yy,f)
shading interp 
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Unbounded inputs');
subplot(2,1,2)
plot(fopt)
xlabel('Iterations');
ylabel('Function Min')



tic
%Study2 satistical behaviour with upper and lower limits
 for i = 1:num_cases
     [inputs ,fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6]);
     xopt(i)=inputs(1);
     yopt(i)=inputs(2);
 end

 study2_time = toc
 
figure(2)
subplot(2,1,1)
hold on 
surfc(xx,yy,f)
shading interp 
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('bounded inputs');
subplot(2,1,2)
plot(fopt)
xlabel('Iterations');
ylabel('Function Min')



tic
%Study2 satistical behaviour with upper and lower limits
 options = optimoptions('ga');
 options = optimoptions(options,'populationsize',180);

for i = 1:num_cases
     [inputs ,fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options);
     xopt(i)=inputs(1);
     yopt(i)=inputs(2);
 end

 study3_time = toc
 
figure(3)
subplot(2,1,1)
hold on 
surfc(xx,yy,f)
shading interp 
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('bounded inputs');
subplot(2,1,2)
plot(fopt)
xlabel('Iterations');
ylabel('Function Min')

     
     

FUNCTION CODE

function z = stalagmite(input)

x = input(1);
y = input(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);

z = -(f1x*f1y*f2x*f2y);  

OUTPUTS