Week 5 - Genetic Algorithm

Aim:

• Write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function.

Governing equation:

f1_x = (sin(5.1*pi*x + 0.5)).⁶;

f1_y = (sin(5.1*pi*y + 0.5)).⁶;

objective: To find out the global maxima with matlab using stalagmite function.

Genetic algorithm:

genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection.

Code:

clc 
clear all
close all


%% PROVIDING THE SEARCH SPACE FOR THE FUNCTION

x=linspace(0,0.7,150);   

y=linspace(0,0.7,150);

[X,Y]=meshgrid(x,y);

num_cases=500; %Number of itreation for which the function will evaluate the fitness

%% CREATING THE SURFACE PLOT OF STALAGEMITE FUNCTION

for i=1:length(X)

for j=1:length(Y)

input_vector(1)=X(i,j);

input_vector(2)=Y(i,j);

f(i,j)=stalagmite(input_vector); %values of function in given search space

end

end

surfc(X,Y,-f); %generating the surface
xlabel('x value')
ylabel('y value')
shading interp %To remove the lines produced by the mesh grid





function [f] = stalagmite(input_vector)

x = input_vector(1);

y = input_vector(2);

f1_x = (sin(5.1*pi*x + 0.5));

f1_y = (sin(5.1*pi*y + 0.5));

t1 = ((x-0.0667))/(0.64);

f2_x = exp(-4.*log(2)*t1);

t2 = ((y-0.0667))/(0.64);

f2_y = exp(-4.*log(2)*t2);

f = -(f1_x.*f2_x.*f1_y.*f2_y);

end

code Explaination:

providing input space for function using meshgrid.

CREATING THE SURFACE PLOT OF STALAGEMITE FUNCTION

using for loop function.

generating the surface.to line produced by meshgrid.

now using the appropiate formula applying stalagmite function.