Week 4.1 - Genetic Algorithm

function [f]=stalagmite(input_vector);
% STALAGMITE FUNCTION 
%formulae 
%global maxima=f=(f1x*f1y*f2x*f2y)
x=input_vector(1);
y=input_vector(2);
f1_x=[sin(5.1*pi*x+0.5)]^6;
f1_y=[sin(5.1*pi*y+0.5)]^6;
f2_x=exp(-4*log(2)*(((x-0.0667)^2)/(0.64)));
f2_y=exp(-4*log(2)*(((y-0.0667)^2)/(0.64)));
f=-(f1_x*f1_y*f2_x*f2_y);
end




% solving genetic algorithm

% defining two input values
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);

% creating 2d mesh
[xx yy]=meshgrid(x,y);
% generating stalgamite 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
figure(1)
surfc(xx,yy,f)
shading interp
%creating genetic algorithm function with 2 input variables
[inputs,fval]=ga(@stalagmite,2)
%study 1 statistical behaviour with 2 inputs USING COMMAND tic toc to
%calculate time required.
num_case=70
tic
for i=1:num_case
    %optimizing function
    [inputs,fopt(i)]= ga(@stalagmite,2)
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
end

study_time_1=toc
figure(2)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','g')
title('unbounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('number of iteration')
ylabel('function maximum')

%study2 bounded inputs x1,y1=0,0; x2,y2=0.6,0.6
tic
for i=1:num_case
    [inputs,fopt(i)]= ga(@stalagmite,2,[],[],[],[],[0,0],[0.6,0.6])
    xopt(i)=inputs(1);
    yopt(i)=inputs(2);
end

study_time_1=toc
figure(3)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','g')
title('bounded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('number of iteration')
ylabel('function maximum')

tic
%study3 incrasing ga iteration 400 populationsize

options=optimoptions('ga')
options=optimoptions(options,'populationsize',400)

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

study_time_1=toc
figure(4)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(xopt,yopt,fopt,'marker','o','markersize',5,'markerfacecolor','g')
title('unbonded inputs')
subplot(2,1,2)
plot(fopt)
xlabel('number of iteration')
ylabel('function maximum')