Week 4.1 - Genetic Algorithm

Objective
Program a Stalagmite function using the Genetic Algorithm Theory and find the Global Maxima for the gi*
Mathematical Formula.

Theory of Genetic Algorithm:
Genetic Algorithm is the evolution theory proposed by Charles Darwin.
The genetic algorithm is a random-based classical evolutionary algorithm. By random here we mec
order to find a solution using the GA, random changes applied to the current solutions to generate r
'GA' solves any function to find the optimum values (min/max) based on the requirement of the fun
• Matlab provides an inbuilt function that actually helps to do GA quite comfortably.
Optimization
• Optimization in a genetic algorithm is finding out the best solution. In our problem statement, we are
find out the best value of Global Maxima (Global Optima).
• In the simplest case, an optimization problem consists of maximizing & minimizing a real function by
systematically choosing input values from within an allowed set and computing the value of the funcTION
 PROGRAM:
function [f]= stalagmite(input_vector);

x= input_vector(1);
y= input_vector(2);

f1x= (sin (5.1*pi*x)+0.5)) ^6;
f1y= (sin(5.1*pi*y)+0.5)) ^6;
f2x= exp (-4*10g(2) * ( (x-0.0667) ^2) /0.64) ;
f2y= exp(-4*10g(2)* ((y-0.0667) ^2) /0.64) ;


f = -(f1x*f2x*f1y*f2y);
end

% clear all
% close all
% clc

% defining our reasearch space
 x = linspace(0,0.6,150);
 y = linspace(0,0.6,150);
  

 % creating a 2D mesh
 [xx,yy] = meshgrid (x,y);
 
 % evaluate 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

 % surf(xx,yy,f)
 shading intrupt

 [x,fval] = ga(@stalagmite, 2)