Week 4.1 - Genetic Algorithm

Aim:
To write a Program in MATLAB to optimise the stalagmite function and find the global maxima of the function.

Program:

_% Stalagmite Function

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-0.0667)^2)/0.64);
  f4=exp(-4*log(2)*((y-0.0667)^2)/0.64);

  f=-(f1*f2*f3*f4);

end

% Genetic Algotithm
  clear all
  close all
  clc

% Creating a 1 dimensional array
  x=linspace(0,0.6,150);
  y=linspace(0,0.6,150);

% creating a 2 dimensional array
  [xx,yy]=meshgrid(x,y);

%evaluating a 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
 
% statistical behaviour
  tic
  for i=1:n
      [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
  xlabel('x axis')
  ylabel('y axis')
  title('Statistical behaviour iwht unbound inputs')
  plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
  subplot(2,1,2)
  plot(-fopt)
  xlabel('No. of Iterations') 
  ylabel('Function maximum')


% Statistical beh. with upper and lower bounds
  tic
  for i=1:n
  [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[0;0],[1;1]);
  xopt(i)=inputs(1);
  yopt(i)=inputs(2);
  end
  study2_time=toc;

  figure(2)
  subplot(2,1,1)
  hold on
  surf(xx,yy,-f)
  shading interp
  xlabel('x axis')
  ylabel('y axis')
  title('Statistical behaviour wiht upper and lower bounds')
  plot3(xopt,yopt,-fopt,'markersize',5,'markerfacecolor','r')
  subplot(2,1,2)
  plot(-fopt)
  xlabel('No. of Interations')
  ylabel('Function maximum')

% Statistical Beh. with increasing interations of GA
  options=optimoptions('ga')
  options=optimoptions(options,'populationsize',300);

  tic
  for i=1:n
      [inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[1;1],[],[],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
  xlabel('x axis')
  ylabel('y axis')
  title('Statistical behavior with increasing interations')
  plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
  subplot(2,1,2)
  plot(-fopt)
  xlabel('No of iterations')
  ylabel('function maximum')

Explaination:

• the program starts with clear all, close all, clc.
• defining the x and y using linspace to create 150 equal intervals
• using meshgrid command a 2d mehs of x and y array is created, n=50
• after preparing the inputs for the function , we need to obtain 3 cases of genetic algorithm.
• in first study, the max valuess of xx and yy are defined
• tic and toc command is used before and after the loop, for solving the loop in 50 iterations
• to neglect the gridlines on the surface and to obatin a smooth and clean polt we used shading interp and then plot
• the only difference between study1 and study2 is in the 'ga' syntax, the algorith is provided lower limits and upper limits as[0;0] and [1;1]
• for study 3the number of iterations are increased to 300. so for this we use options=optimoptions('SolverName,'Name','Value"), 'popultaions' 300.

Errors:

• invalid expression. use brackers instead of parenthese.
• [x,fval]=ga(@stlagmite(inputvector), f(i,j)=stalagmite(input_vector).

Results:
Thus, a Program in MATLAB to optimise the stalagmite function and find the global maxima of the function is done and the output is verified