Week 4.1 - Genetic Algorithm

Genetic algoritm:

GA widely used in bussiness, science and engineering.

• optimizational and search problems
• scheduling and timetabling

There are different ways to implement GA, they all met the below conditions

• Uses concept from evolutionary biology
• Genetic representation of a solutions
• A function to generate new solutions
• Fitness functions
• Selection function
• Crossover functions
• Mutation functions

Need of GA

• Fastest search technique
• Multidimensional systems
• Mutaion testing
• Provide optimistaion over large space state

Genetic algorithm appications

• Design of water resource system(Earth Science)
• Portfolio soptimization (Finance mathematics)
• Design of anti-terrorism system(Social science)
• Automated design, research of composite material
• Control engineering
• DNA, RNA prdiction
• Design of particle accelrator beamlines(Physice)

Program Code

clear all
close all
clc


x=linspace(0,0.6,150);
y=linspace(0,0.6,150);

[xx yy]=meshgrid(x,y);

for i=1:length(x)
    for j=1:length(y)
        input_vector(1)=xx(i,j);
        input_vector(2)=yy(i,j);
        f(i,j)=stalagmite(input_vector);   
    end
end

surfc(xx,yy,f)
xlabel(' X Values')
ylabel(' Y Values')
shading interp

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

Function Code

function f = stalagmite(input)

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

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


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

Explantion

1. Linspace is used to get 150 values of X,Y
2. By using mesh grip we get two dimesnional array as XX,YY
3. for loop is used to evaluate stalgmite function
4. Function code named as 'stalagmite' has be written to solve the formual
5. by assigning X, fval as output we execute the GA for the stalmite fucntion
6. X- Solution
7. Y-Objecxtive function value at the solution
8. Surfc and annotation is done.