Week 4.1 - Genetic Algorithm

GENETIC ALGORITHEM

AIM:

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

OBJECTIVE:

• Write a code in MATLAB to optimize the stalagmite function and find the global maxima of the function.
• Clearly explain the concept of genetic algorithm in your own words and also explain the syntax for ga in MATLAB in your report.
• Make sure that your code gives the same output, even if it is made to run several times.
• Plot graphs for all 3 studies and for F maximum vs no. of iterations. Title and axes labels are a must, legends could be shown if necessary.

GENETIC ALGORITHEM:

A genetic algorithm is a search heuristic that is inspired by Charles Darwin's theory of natural evolution. This algorithm reflects the process of natural selection where the fittest individuals are selected for reproduction in order to produce offspring of the next generation.

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. 3. For this in Matlab we are using a method called 'Optimization'.

FUNCTION:

MAIN CODE:

clear all

close all

clc

% searc space

x=linspace(0,0.6,150);

y=linspace(0,0.6,150);

no_cases=50;

%meshgrid

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

% Evaluating stalagmite function

for i=1:length(xx)

for j=1:length(yy)

inputs(1)=xx(i,j);

inputs(2)=yy(i,j);

f1(i,j)=stalagmite_fun(inputs);

end

end

surf(x,y,f1);

shading interp

% study-1:statistical behaviour unbounded

tic

for i=1:no_cases

[inputs2,fopt(i)]=ga(@stalagmite_fun,2)

xopt(i)=inputs2(1)

yopt(i)=inputs2(2)

end

time=toc

%ploting

figure(1)

subplot(2,1,1)

surfc(x,y,-f1)

hold on

shading interp

plot3(xopt,yopt,-fopt)

xlabel('x')

ylabel('y')

grid on

subplot(2,1,2)

plot(-fopt)

xlabel('iterations')

ylabel('function main value')

%STUDY-2 statistical behaviour bounded

for j=1:no_cases

[inputs2,fopt(j)]=ga(@stalagmite_fun,2,[],[],[],[],[0;0],[1;1])

xopt(j)=inputs(1)

yopt(j)=inputs(2)

end

time=toc

%ploting

figure(2)

subplot(1,2,1)

surfc(x,y,-f1)

hold on

shading interp

plot3(xopt,yopt,-fopt)

xlabel('x')

ylabel('y')

grid on

subplot(1,2,2)

plot(-fopt)

xlabel('iterations')

ylabel('function main value')

cases2=optimoptions('ga','PopulationSize',300)

%STUDY-3

for k=1:no_cases

[inputs2,fopt(k)]=ga(@stalagmite_fun,2,[],[],[],[],[0;0],[1;1],[],[],cases2)

xopt(k)=inputs(1)

yopt(k)=inputs(2)

end

time=toc

%ploting

figure(3)

subplot(2,1,1)

surfc(x,y,-f1)

hold on

shading interp

plot3(xopt,yopt,-fopt)

xlabel('x')

ylabel('y')

grid on

subplot(2,1,1)

plot(-fopt)

xlabel('iterations')

ylabel('function main value')

OUTPUTS:

figure(1)

figure(2)

FIGURE(3)

LINKS:

https://drive.google.com/drive/folders/1lwInK2MkehftPnTeeECW-qmDcHkIaLMu?usp=sharing