Genetic algorithm using octave

Aim:

To Write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function Clearly expalin the concept of genetic algorithm in your own words and also explain the syntax for 'ga' function in MATLAB

genetic algorithm:

A genetic algorithm is a search heuristic that is inspired by Charles Darwin’s theory of natural evolution. This algorithm reflects the process of natural selection where the fittest individuals are selected for reproduction in order to produce offspring of the next generation.

Program:

clear all
close all
clc

% defining search space
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
num_cases = 40;   % number of times ga runs

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



% evaluating 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


% study 1 : statistical behaviour

tic
for i = 1:num_cases
[inputs, fopt(i)] = ga(@stalagmite,2);
xopt(i) = inputs(1);
yopt(i) = inputs(2);
end
study1_time = toc

figure(1)
subplot(2,1,1)
hold on
surfc(xx, yy, -f)
shading interp
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Unbounded inputs')
xlabel('X values')
ylabel('Y values')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function Maximum')


% study 2 : statistical behaviour with upper and lower bounds

tic
for i = 1:num_cases
[inputs, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[1;1]);
xopt(i) = inputs(1);
yopt(i) = inputs(2);
end
study2_time = toc

figure(2)
subplot(2,1,1)
hold on
surfc(xx, yy, -f)
shading interp
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Bounded inputs')
xlabel('X values')
ylabel('Y values')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function Maximum')

% study 3 : increasing GA population size

options = optimoptions('ga');
options = optimoptions(options,'PopulationSize',450);

tic
for i = 1:num_cases
[inputs, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[1;1],[],[],options)
xopt(i) = inputs(1);
yopt(i) = inputs(2);
end
study3_time = toc

figure(3)
subplot(2,1,1)
hold on
surfc(xx, yy, -f)
shading interp
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
title('Bounded inputs with different population size')
xlabel('X values')
ylabel('Y values')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function Maximum')

Stalagmite function:

% stalagmite function

function [output] = stalagmite(input_vector)
  a = input_vector(1);
  b = input_vector(2);
  
  f1x = (sin(5.1*pi*a+0.5))^6;
  f1y = (sin(5.1*pi*b+0.5))^6;
  f2x = exp(-4*log(2)*(a-0.0667)^2/0.64);
  f2y = exp(-4*log(2)*(b-0.0667)^2/0.64);
  
  [output] = -(f1x*f2x*f1y*f2y);
end

Result:

thus the genetic algorithm programming is done ad output is obtained