Week 4.1 - Genetic Algorithm

AIM:- To study about Genitic Algorithm and to calculate the global maxima of stalagmite function using Genetic Alogarithm in matlab.

OBCTIVE:

1.To study about Genetic Algorithm and stalagmite function.

2. To write a code in matlab to optimse the stalagmite function and fid the global maxima of the function.
3. To plot graph based on the studies done for Genetic Algorithm .

THEORY :A genetic algorithm (GA) is a method for solving both constrained and unconstrained optimization problems based on a natural selection process that mimics biological evolution. The algorithm repeatedly modifies a population of individual solutions. Generates a population of points at each iteration.

Concept of Genetic Algorithm –

1.Genetic Algorithm is a search-based optimization technique based on the principai of genitic and natural selection .it is frequently used to find optimal or near –optimal solution to difficult problems which otherise would take a lifetime to solve.

2. Nature has always been a great source of inspiration to all mankind . Genetic Algorithm arearch based on the concepts ofnatural selection and genetics.
3. Genetic Algorithm are a subset of much larger branch of compulation known as evolutionary Computation.

4. The flow chart of Genetic Alogarithm is given
   

Stalagmite function-A stalagmite function generally refers to the function with which we are generating values over a stalagmite kind of surface for finding out the local and global maxima and minima of that particular given function.

The stalagmite function is given as,

Syntax for genetic algorithm

x = ga(fun,nvars,A,b,Aeq,beq) finds a local minimum x to fun, subject to the linear equalities Aeq*x = beq and A*x ≤ b. (Set A=[] and b=[] if no linear inequalities exist.) ga evaluates the matrix product Aeq*x as if x is transposed (Aeq*x').

x = ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon) subjects the minimization to the constraints defined in nonlcon. The function nonlcon accepts x and returns vectors C and Ceq, representing the nonlinear inequalities and equalities respectively. ga minimizes the fun such that C(x) ≤ 0 and Ceq(x) = 0. (Set lb=[] and ub=[] if no bounds exist.)

MATLAB PROGRAM FOR GA :-

clear all

close all

clc

%Define our search space

x=linspace(0,0.6,150);

y=linspace(0,0.6,150);

n=50;

%Creating a 2D array

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

%Evalueating a 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:n;

[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

xlabel('\bf X-axis')

ylabel('\bf Y-axis')

title('\bf Statistical beheviour with unbounded inputs')

plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')

subplot(2,1,2)

plot(-fopt)

xlabel('\bf No of iterations')

ylabel('\bf function maximum')

%study 2:statistical behaviour with lower and upper

tic

for i=1:n

[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

xlabel('\bf X-axis')

ylabel('\bf Y-axis')

title('\bf statistical behaviour with lower and upper')

plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')

subplot(2,1,2)

plot(-fopt)

xlabel('\bf No of iteration')

ylabel('\bf function maximum')

% Study 3: Statistical behaviour with increasing iterations of GA

options=optimoptions('ga');

options=optimoptions(options,'populationsize',300);

tic

for i=1:n

[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

xlabel('\bf X-axis')

ylabel('\bf Y-axis')

title('\bf Statistical behaviour with increasing iterations of GA')

plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')

subplot(2,1,2)

plot(-fopt)

xlabel('\bf No of iterations ')

ylabel('\bf function maximum')

OUTPUT-

I hope this will make you satisfy.

THANK YOU

SKILL LYNC