genetic algorithm

introduction

this assigment was about finding the maxima of the stalagmite function .

i studies about how the genetic algorithm works and to use the globaloptimisation tool box

references

1)matlab website

2)wikipedia

3)nptel letchure

after studying all this i gather some basic knowledge about how the algorithm works

sucha as

selection ,crossover and mutation

how the genes of the parents gets intermixted and the mutation occurs ,the fittest of a generation is passed to the next generation

initially a group of population is chosen randomly within the limit that is set , then the

intermixing-the genes are represented in the form of bits are mixied and offsprings are produced which occupuy a new set of locations than that of the parents and some of the offsprings undergoes mutation which can be postive or negative or it may no effectts in the fittness of the offsprings thus the of iteration occurs until satisifactory result is produced and

the average of every single iteration is taken and plotted in term of graph

as we can see that from the graph for populaton of 50 and 50 iterations, the population is spread in different peaks but when the population is increased to250 all the point converge at global maxima (minima)

since the value of optimisation always gives the minima i inverted the graph by giving '-'sign to the stalagmite function thus we can find the maxima like this

the deflection in population set as 50 is big ,compared to 250 size population this deflection in the maxima is due to random black boxprocess happening within the ga algorithm

thus higher the plopulation greater the accurasy but more the computation time reqired

for 50 plopulation time was 6.7358sec

for 250 it was 17.97sec

almost 3 time greater than 50 population size

in this code ihave used the option of initial population size and setting the limit within which population must be created

main code

close all
clear all
clc
%inputs
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
%creating 2d array
[xx,yy]=meshgrid(x,y);
%stetting options
options=optimoptions('ga');
options=optimoptions(options,'populationsize',50)%intial population size
iteration=50
%input to 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
 tic%starting timer 
 iteration=50
 for i=1:iteration
     [inputs,fval(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.6,0.6],[],[],options);
     x_val(i)=inputs(1);
     y_val(i)=inputs(2);
 end
 timetaken=toc%timer end
 subplot(2,1,1)%spliting the window
 hold on
 surfc(xx,yy,f)
 shading interp
 plot3(x_val,y_val,fval,'marker','o')
 xlabel('xvalue')
 ylabel('yvalue')
 subplot(2,1,2)
 plot(fval)
 xlabel('iteration')
 ylabel('minima')
 

stalagmite function code

%stalgamite function
function F=stalagmite(input_vector)
  f1x=(sin(5.1*pi*input_vector(1)+0.5))^6;
  f1y=(sin(5.1*pi*input_vector(2)+0.5))^6;
  f2x=exp(-4*log(2)*((input_vector(1)-0.0677)^2/0.64));
  f2y=exp(-4*log(2)*((input_vector(2)-0.0667)^2/0.64));
  F=-(f1x*f2x*f1y*f2y);
end

50 population size 250poulation size