Week 4 - Genetic Algorithm

clc 
close all
clear all
% 
x = linspace(0,.6,150);
y = linspace(0,.6,150);
n_cases = 50

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

%% generate stalagmite function values

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

%% STUDY1
  tic
 for i =  1:n_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(x,y,f)
 %shading interp
 
 plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','b')
 
 title('unbounded inputs')
 subplot(2,1,2)
 plot(fopt)
 xlabel('iterations')
 ylabel('fun minimum')
 
 
 %% STUDY 2
 tic
 
 for i =  1:n_cases
     [inputs, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.4;0.4]);
     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',4,'markerfacecolor','r')
 
 title('bounded inputs')
 subplot(2,1,2)
 plot(fopt)
 xlabel('iterations')
 ylabel('fun minimum')
 
 options = optimoptions('ga');
 options = optimoptions(options,'populationsize',170)
 
 
  %% STUDY 3
 tic
 for i =  1:n_cases
     [inputs, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.4;0.4],[],[],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',3,'markerfacecolor','m')
 
 title('bounded inputs')
 subplot(2,1,2)
 plot(fopt)
 xlabel('iterations')
 ylabel('fun minimum')

stalagmite code:
function f = stalagmite(input_vector)
x =  input_vector(1)
y =  input_vector(2)


f1 = (sin(5.1*pi*x+0.5))^6;
f2 = (sin(5.1*pi*y+0.5))^6;
f3 = exp((-4*log(2)*(x-.0667)^2)/0.64);
f4 = exp((-4*log(2)*(y-.0667)^2)/0.64);
f = -(f1*f1*f3*f4);
end