Week 4.1 - Genetic Algorithm

close all
clear all
clc

x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_spaces=50;
[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   
% study 1 for unbounded
tic
for i=1:num_spaces
 [results,fopt(i)]=ga(@stalagmite,2)   
  xopt(i)=results(1);
  yopt(i)=results(2);
end
study_time1=toc
figure(1)
surf(x,y,-f)
shading interp
hold on 
plot(xopt,yopt,-fopt,'marker','o')
plot(-fopt)
xlabel('iteration')
ylabel('maximum function')

%study2 for boumded
tic
for i=1:num_cases
[results,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6]);
xopt(i)=results(1)
yopt(i)=results(2)
end
study_time2=toc
figure(2)
surf(x,y,-f)
shadind interp
hold on
plot(xopt,yopt,-fopt,'marker','o')
plot(-fopt)
xlabel('iteration')
ylabel('maximum function')
%study3 increased population
tic
options=optiomoptions('ga')
options=optiomoptions(options,'populationsize',250);
for i=1:num_spaces
  [results,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options)
  xopt(i)=results(1)
  yopt(i)=results(2)
end
study_time3=toc
figure(3)
surf(x,y,-f)
shadind interp
hold on
plot(xopt,yopt,-fopt,'marker','o')
plot(-fopt)
xlabel('iteration')
ylabel('maximum function')

First we have given the values of x and y by taking the limits 0 to 0.6 with 150 values between them.Also considered the number of iterations is 50.Inorder to plot 3D surface,we have taken the 2D array of x and y by using mesh grid command.Then we create another function file for stalagmite function,the output of the function was taken as -f because the ga only minimises the function.

for the first study case of unbounded region,the results were stored in xopt,yopt.The plot3 command was used to plot xopt,yopt,-f.The tic toc commands were used to record the time taken to complete the cycle.

For the study2 of bounded region the lower and upper bounds of x and y were specified.Also the results were stored in xopt,yopt.The plotting was done by using plot3 command.

Also for the study3 we have done the same with increased population and specified bounds.