Genetic Algorithm

Genetic Algorithm:

genetic algorithm are based on the principal of biological evolution or survival of fittest.

It starts with the random population of points and generates a random poupulation of points called individual at each iteration(generation)of the algorithm.

Three operators to improve a population and to converge to a final population of solution

• selection
• cross over
• mutation

MATLAB has two function of GA

• ga
• gamultiobj

In the given problem we have to find the maximum value of the function through genetic algorithm which solves for minimum value. therefore function is inverted so the max value becomes the min value and hence can be calculated through ga. function value is bounded in the range of .5 to 1.5

clear all
close all
clc

x = linspace(0,.6,150);
y = linspace(0,.6,150);

[xx yy] = meshgrid(x,y);
input = zeros(2);

for i = 1:length(xx)
    for j = 1:length(yy)
        
        input(1) = xx(i,j);
        input(2) = yy(i,j);
        
       func(i,j) = stalagmite(input);
    end
end

surf(xx,yy,(func))

grid on

hold on
title('abc');
xlabel('x-axis');
ylabel('y-axix');
axis('fill')

shading interp


gcn = @stalagmite;
nvar = 2;

hold on
num = 100;
i =1;

opts = gaoptimset(@ga);
opts.populationsize =5;
opts.generations =100;
tic
for i=1:num
    [x_m,val] = ga(gcn,2,[],[],[],[],[0,0],[.1,.3],[],[],opts);
    fval(i) = val;
    x_min(i) = x_m(1);
    y_min(i) = x_m(2);
    
end
s = toc

plot3(x_min,y_min,fval)

figure(2)
plot(fval)
xlabel('Iterations');
ylabel('function minimum value');
ylim([-0.5,1.5]);

% stalagmite function

function [z] = stalagmite(input)
    a = input(1);
    b = input(2);
    f1 = [sin(5.1*pi*a + .5)]^6;
    f2 = [sin(5.1*pi*b + .5)]^6;
    f3 = exp(-4*log(2)*((a -.0667)^2)/.64);
    f4 = exp(-4*log(2)*((b - .0667)^2)/.64);
    z = 1.5 - (f1*f2*f3*f4);
end

It is seen that function minimum value converges around .5051 at x&y = .068 & .067.

Thus at these points the maximum value of original function will occur.