Week 4 - Genetic Algorithm
Aim: Code in MATLAB to optimize the stelgamite and find the Global Maxima of the function
Genetic Algorithm : A Gentic Algorithm(GA) is a method for solving both constrained and unconstrained optimization problems based on natural selection process that mimics biological evoluion.
You can apply the GA to solve problems that are not well suited for standard optimization algorthim, including problems in which the objective function is discontinous, nondifferentiable etc
Synatx for GA in MATLAB :
x = ga(fun,nvars)
x = ga(fun,nvars,A,b)
x = ga(fun,nvars,A,b,Aeq,beq)
x = ga(fun,nvars,A,b,Aeq,beq,lb,ub)
x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon)
x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,options)
x = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon)
x = ga(fun,nvars,A,b,[],[],lb,ub,nonlcon,IntCon,options)
x = ga(problem)
[x,fval] = ga(___)
[x,fval,exitflag,output] = ga(___)
[x,fval,exitflag,output,population,scores] = ga(___)
Main Coding :
clear all
close all
clc
% Defining the search space OR range
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
%Total no. of Iterations
n = 50;
[xx,yy]= meshgrid(x,y);
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_func(input_vector);
end
end
%Study 1: statistical behaviour
tic
for i=1:n
[inputs,fopt(i)]=ga(@stalagmite,2);
xopt(i)=inputs(1);
yopt(i)=inputs(2);
end
study_1_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')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function maximum')
%Study 2: statistical behaviour with bounds
for k = 1:n
[inputs2 , fopt2(k)] = ga(@stalagmite_func, 2,[],[],[],[],[0;0],[1;1]);
xopt2(k) = inputs2(1);
yopt2(k) = inputs2(2);
end
figure(3)
subplot(2,1,1)
hold on
surfc(xx,yy,-f)
shading interp
plot3(xopt2,yopt2,-fopt2,'marker','o','markerfacecolor','r')
xlabel('X values')
ylabel('Y values')
title('Statistical Behaviour - with upper and lower bound')
figure(4)
subplot(2,1,2)
plot(-fopt2)
xlabel('Iterations')
ylabel('fopt')
title('Statistical Behaviour - with upper and lower bound')
%Study 3 increasing GA iterations
options= optimoptions('ga');
options= optimoptions(options,'PopulationSize',500);
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 modified population size')
subplot(2,1,2)
plot(-fopt)
xlabel('Iterations')
ylabel('Function maximum')Stalagamite function :
function [f] = stalagmite_func(input_vector)
x = input_vector(1);
y = input_vector(2);
term1 = (sin((5.1*pi*x )+ 0.5))^6;
term2 = (sin((5.1*pi*y) + 0.5))^6;
term3 = exp(-4*log(2)*((x-0.0667)^2)/0.64);
term4 = exp(-4*log(2)*((y-0.0667)^2)/0.64);
f = -(term1*term2*term3*term4);
end