Week 4 - Genetic Algorithm

AIM:

• To write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function.

THEORY:

In CS and op research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algos are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection.

CODING:

MAIN CODE:

clear all
close all
clc
 % definin our search space
 x = linspace(0,0.6,150);
 y = linspace(0,0.6,150);
 num_cases = 50;
 
 % creating a 2D mesh
 [xx yy] = meshgrid(x,y);
 
 % eval tha stalgamite func
  for i = 1:length(xx)
      for j = 1:length(yy)
          input_vector(1) = xx(i,j);
          input_vector(2) = xx(i,j);
          f(i,j) = stalagamite(input_vector);
      end
  end
  
  % stat behaviuor
  
  surfc(xx,yy,-f)
  xlabel('X')
  ylabel('Y')
  shading interp
  
  plot3(x0pt1,yopt1,'marker','o','markersize',5,'markerfacecolor','r');
  title('unbound inputs')
  subplot(2,1,2)
  plot(-fopt1)
  xlabel('iteration')
  ylabel('function_minimum')
 
  % Behaviour
  tic
  for i = 1:num_cases
      [inputs,fopt2(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[1;1]);
      xopt2(i) = inputs(1);
      yopt2(i) = inputs(2);
  end
  study_time2 = toc;
  figure(2)
  subplot(2,1,1)
  hold on 
  surfc(xx,yy,-f)
  xlabel('X')
  ylabel('Y')
  shading interp
  
  plot3(xopt2,yopt2,-fopt2,'marker','o','markersize',5,'markerfacecolor','r')
  subplot(2,1,2)
  plot(-fopt2)
  xlabel('iteration')
  ylabel('function_minimum')
  
  % inc popilation
  options = gaoptimset(@ga);
  options = gaoptimset(options,'populationsize',300);
  tic
  for i = 1:num_cases
      [inputs,fopt3(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[1;1]);
      xopt3(i) = inputs(1);
      yopt3(i) = inputs(2);
  end
  study_time2 = toc;
  figure(2)
  subplot(2,1,1)
  hold on 
  surfc(xx,yy,-f)
  xlabel('X')
  ylabel('Y')
  shading interp
  
  plot3(xopt2,yopt2,-fopt2,'marker','o','markersize',5,'markerfacecolor','r')
  subplot(2,1,2)
  plot(-fopt3)
  xlabel('iteration')
  ylabel('function_minimum')
  
  
 

FUNCTION:

% stalagamite function

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*f2_x*f1_y*f2_y);
end

RESULT:

EXPLANATION:

1. Creating a Stalgamite function as shown in the code.
2. Maximization of stalagamite function using gen. algo.
3. Creating a 2D array using mesh grid command.
4. Assigning values of input(1) and input(2) using 2 for loops.
5. Plotting the values.