Week 4.1 - Genetic Algorithm

AIM - TO PREPARE THE GLOBAL MAXIMA BY USING OF STALAGMITE FUNCTION

clear all

close all

clc

% Defining our search space

x=linspace(0,0.6,150);

y=linspace(0,0.6,150);

% Creating a 2 dimensional 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

% creating the 3dimensional

surfc(xx,yy,-f)

xlabel('x value')

ylabel('y value')

title ('stalagmite function')

shading interp

[inputs,fval]= ga(@stalagmite,2)

% performing the unbonded conditions

num_cases=50;

for i=1:num_cases

[inputs,fopt(i)]=ga(@stalagmite,2);

xopt(i)= inputs(1);

yopt(i)= inputs(2);

end

tic

study_1=toc

figure(2)

subplot(2,1,1)

hold on

surfc(x,y,-f)

title('Unbounded inputs')

xlabel('x value')

ylabel('y value')

shading interp

hold on

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

subplot(2,1,2)

plot(-fopt)

xlabel('iterations')

ylabel('function maximum')

legend ('function maximum', 'iterations')

% performing the bounded conditions

tic;

for i=1:num_cases

[inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6]);

xopt(i)=inputs(1);

yopt(i)=inputs(2);

end

study_2_time=toc

figure(3)

subplot(2,1,1)

surfc(x,y,-f)

shading interp

title('Bounded inputs')

xlabel('x value')

ylabel('y value')

hold on

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

subplot(2,1,2)

plot(-fopt)

xlabel('iterations')

ylabel('function maximum')

% incresing the population size

options=optimoptions(@ga)

options=optimoptions(@ga,'PopulationSize',500) %increasing the population size

tic

for i=1:num_cases

[inputs,fopt(i)]=ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options);

xopt(i)=inputs(1);

yopt(i)=inputs(2);

end

study_3_time=toc %gives the time taken for study

figure(4)

subplot(2,1,1)

surfc(x,y,-f) %creates a surface to visualise 3D

shading interp

title('bounded inputs with increased population size')

xlabel('x value')

ylabel('y value')

hold on

plot3(xopt,yopt,-fopt,'marker','o','markersize',4,'markerfacecolor','r')

subplot(2,1,2)

plot(-fopt) %plotting -f vs number of iterations

xlabel('iterations')

ylabel('function maximum')

CONCEPT OF GENETIC ALGORITHEM

The Genetic algorithem works on the process of natural selection

It is a method for solving the both constraned and un constraned optimization problems that is based on the natural selection

Some of the population based Algorithems are

1- genetic algorithems

2- differential evalution

3- partical swarn optimization

The process flow from the working of genetic algorithems

The 3 main process are going to behind the GA

1 - selection

2- cross over

3- mutation

These 3 steps are create the next generations by the use of current population

SELECTION

It rules the selet the individuals called parents, that contribute the population at the next generation

MUTATION

It rules apply random changes to individuals parents to form the childrens

CROSS OVER

It rules combine two parents to form childrens for the next generation

SYNTEX FOR GA

SYNTEX for defending GA

The GA syntax in matlab is used to find the minimum of function using genetic algorithm. There are several ways to define the GA function depending on the problem being solved. The syntax used for this study is shown below

x= ga (fun,nvars)

where,

x = optimal solution/variables;

fun = Objective function;

nvars = Number of variables;

x = ga (fun,nvars,A,B,Aeq,BEQ,lb,ub)

where,

A, B = Linear inequality constraints

Aeq, Beq = Linear equality constraints

If there are no linear equalities and inequalities, then A, B, Aeq, Beq are set to '[]'

x= ga (fun,nvars,A,B,Aeq,Beq,lb,ub,non icon,Intcon,options)

where,

nonlcon = Nonlinear constraints

IntCon = Integer Values

options = Optimization options

If there are no nonlinear constraints and integer values, the nonlcon and IntCon are set to '[]'.

ERRORS

The following are the facing errors while write the programme

i am facing above the these errors and it over come by the use of command window and what i am gives incorect values and rectify the correct values and it will be easy to over come easily .

CONCLUTION

1 To find out the GA while using stalagmite function

the eqation of stalagmite fucntion is