GENETIC ALGORITHM

AIM:

To calculate global maxima of a stalagmite function

INTRODUCTION

A genetic algorithm is a heuristic search method used in artificial intelligence and computing. It is used for finding optimized solutions to search for problems based on the theory of natural selection and evolutionary biology. Genetic algorithms are excellent for searching through large and complex data sets

FIVE STEPS IN GENETIC ALGORITHM:

The process of natural selection starts with the selection of fittest individuals from a population. They produce offspring which inherit the characteristics of the parents and will be added to the next generation. If parents have better fitness, their offspring will be better than parents and have a better chance of surviving. This process keeps on iterating and at the end, a generation with the fittest individuals will be found.

HOW Genetic ALGORITHM WORKS?

a)Initial Population: The algorithm begins by creating a random initial population.

b)The algorithm then creates a sequence of new populations. At each step, the algorithm uses the individuals in the current generation to create the next population. To create a new population, the algorithm performs the following steps:

c) The algorithm stops when one of the stopping criteria is met

CODE:

In Matlab, GA is used to find the minima of a function. But here maxima is found by using negative of the function.

Steps :

• x,y is defined between 0 to 150 spacing 0.6
• mesh grid command is used to make a 2D grid xx yy
• For loop to solve GA for every element in mesh grid
• input declared for each value in mesh grid
• the output is stored inside the stalgamitneg function
• ga code is entered for unbounded statistical study.
• For the minimum value of the function is obtained, further its x and y values are stored.
• further figure is plotted.
• surfc used for plotting contour.
• shading intrep to smoothen the plots.
• plotting maxima of the function.

clc
clear all
close all

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


%forming mesh grid
[xx yy]=meshgrid(x,y);


%evaluating the function

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

options=optimoptions(\'ga\')
options=optimoptions(options,\'PopulationSize\',300);
tic

for i=1:100
    [min ,fval(i)]=ga(@stalagmiteneg,2,[],[],[],[],[0;0],[1;1],[],[],options);
    xopt(i)=min(1);
    yopt(i)=min(2);
end

%plotting
figure(1);
subplot(2,1,1);
surfc(xx,yy,f);
shading interp;
hold on
plot3(xopt,yopt,fval,\'marker\',\'o\',\'markersize\',5,\'markerfacecolor\',\'r\');
label(\'x-values\');
label(\'y-values\');

subplot(2,1,2);
plot(fval);

FUNCTION:

• Function declared and inputs specified.
• Equations are written.
• Further the we take -ve to obtain the maxima.

function [f] = stalagmiteneg(input_vector)
x= input_vector(1);
y=input_vector(2);
term_1=(sin(16.02*x +0.5))^6;
term_2=(sin(16.02*x +0.5))^6;
term_3=exp((-4*log(2)*(x-0.0667)^2)/(0.64));
term_4=exp((-4*log(2)*(x-0.0667)^2)/(0.64));
f=-1*term_1*term_2*term_3*term_4;
end

PLOTS: