Week 4.1 - Genetic Algorithm

AIM:To write a code in matlab to optimise the stalagmite function and find the global maxima of the fuction

GENETIC ALGORITHAM

The genetic algoritham is a method for solving both constrained optimization problems that is based on natural selection the process that drives biological evolution the genetic algoritham repeatedly modifies a population of individual solutions

PROGRAM;

close all
clear all
clc
%input
x=linspace(0,0.6,150);
y=linspace(0,0.6,150);
num_spaces=50;
%forming 2d array
[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)=stagalmite(input_vector);
    end
end
%study 1-unbounded
tic
for i=1:num_spaces
    [results,fopt(i)]=ga(@stagalmite,2)
    xopt(i)=results(1)
    yopt(i)=results(2)
end
study_time1=toc
figure(1)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o')
subplot(2,1,2)
plot(-fopt)
xlabel('iteration')
ylabel('function maximum')
%study 2-bounded
tic
for i=1:num_spaces
    [results,fopt(i)]=ga(@stagalmite,2,[],[],[],[],[0;0],[0.6;0.6])
    xopt(i)=results(1)
    yopt(i)=results(2)
end
study_time2=toc
figure(2)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o')
subplot(2,1,2)
plot(-fopt)
xlabel('iteration')
ylabel('fuction maximum')
%study3- increased initial population
tic
options=optimoptions('ga')
options=optimoptions(options,'populationsize',250)
for i=1:num_spaces
    [results,fopt(i)]=ga(@stagalmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options)
    xopt(i)=results(1)
    yopt(i)=results(2)
end
study_time3=toc
figure(3)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o')
subplot(2,1,2)
plot(-fopt)
xlabel('iteration')
ylabel('function maximum')

STALAGMITE FUNCTION CODE:

function A = stagalmite(input_vector)
x=input_vector(1);
y=input_vector(2);
f1=(sin(5.1*pi*x+0.5)).^6;
f2=exp((-4*log(2)*((x-0.0667).^2))/0.64);
f3=(sin(5.1*pi*y+0.5)).^6;
f4=exp((-4*log(2))*((y-0.0667).^2)/0.64);
A = -(f1*f2*f3*f4);
end

PROGRAM EXPLANATION:

*First we initialise the values of x and y taking 150 values between the intervel 0 and 0.6

we consider no of iterations num_spaces=50

*since we need to plot a 3D surface plot we take the 2nd array of x and y using meshgrid command and store them in input_vector array so that it can be used as an argument to call the function stalagmite

we create another function file for the stalagmite function.here we take the output as -f is considered it automatically gives us maxima

*we take no of iterations=num_spaces and we use the genetic algorithm function.we store the outputs into results which contain maximas and fopt which contain the value at which the maxima is obtained

*now we store the result into xopt,yopt now we need to plot the surface of x,y,-f to get the 3D plot

*we use the plot3 command to make a plot of xopt,yopt and -fopt to plot the optimum maximas

*fopt function so that we can visualise the optimum values at each iteration

*to get the time taken to complete cycle we used the tic toc command to record the time

*we use the plot3 command to make a plot of xopt,yopt and -fopt to plot the optimum maximas

*plot the fopt function so that we can visualise the optimum values at each iteration

*to get the time taken to complete cycle we used the tic toc command to record the tim