Week 4.1 - Genetic Algorithm

1-Selection rules select the individuals, called parents, that contribute to the population at the next generation.

2-Crossover rules combine two parents to form children for the next generation.

3-Mutation rules apply random changes to individual parents to form children.

syntax of ga-

ga(fun,nvars,A,b,Aeq,beq,lb,ub,nonlcon,intcon,options)

ga -genetic algorithm.

fun-objective function.

nvars- no. of variables.

A - Linear inequality constraints

b - Linear inequality constraints

Aeq - Linear equality constraints

beq — Linear equality constraints

lb — Lower bounds

ub — Upper bounds

nonlcon — Nonlinear constraints

intcon — Integer variables

options — Optimization options

global maxima -'ga' finds global minimum as default, to find the global maxima we inver the stalagmite function by equating the value to negetive

programming code for optimise of stalagmite function and find the global maxima-

%defining our search space
x =linspace(0,0.6,150);
y =linspace(0,0.6,150);

%creating a 2Dimensional function
[xx yy] = meshgrid(x,y);

% evaluvating 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



[inputs,fval]= ga(@stalagmite,2);
x_output=inputs(1);
y_input=inputs(2);


% case-1 sampling for 50 itteration
N=50;
%to calculate the time taken to run the itteration we use tic and toc command 
%case 1 for unbounded inputs
tic 

for i=1:N
    [inputs,f1_out(i)]= ga(@stalagmite,2);
    x1_output(i)=inputs(1);
    y1_output(i)=inputs(2);
    
end
study_time=toc


figure(1)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
xlabel('x value')
ylabel('y value')

shading interp
%using plot3 command to draw 3-d plot
plot3(x1_output,y1_output,f1_out,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('unbounded inputs')
subplot(2,1,2)
%plot for itteration vs f maximum
plot(f1_out)
%labeling the plot
xlabel('iteration')
ylabel('f maximum')
zlabel('f maximum')

% case-2 sampling for 50 itteration for bounded inputs
N=50;
%to calculate the time taken to run the itteration we use tic and toc command 
tic 
for i=1:N
    [inputs,f2_out(i)]= ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6]);
    x2_output(i)=inputs(1);
    y2_output(i)=inputs(2);
    
end
study2_time=toc


figure(2)
subplot(2,1,1)
hold on
surfc(xx,yy,f)
%labeling the plot
xlabel('x value')
ylabel('y value')
zlabel('f maximum')

shading interp
%using plot3 command to draw 3-d plot
plot3(x2_output,y2_output,f2_out,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('bounded inpuuts')
subplot(2,1,2)
%plot for itteration vs f maximum
plot(f2_out)
xlabel('iteration')
ylabel('f maximum')


% case-3 sampling for 50 itteration for bounded and controled population
% size 
options=optimoptions('ga','PopulationSize',200)

N=50;
%to calculate the time taken to run the itteration we use tic and toc command 
tic 
for i=1:N
    [inputs,f3_out(i)]= ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options);
    x3_output(i)=inputs(1);
    y3_output(i)=inputs(2);
    
end
study3_time=toc


figure(3)
subplot(2,1,1)
hold on
%labeling the plot
surfc(xx,yy,f)
xlabel('x value')
ylabel('y value')
zlabel('f maximum')

shading interp
%using plot3 command to draw 3-d plot
plot3(x3_output,y3_output,f3_out,'marker','o','MarkerSize',5,'MarkerFaceColor','r')
title('bounded inpuuts for a controlled population size')
subplot(2,1,2)
%plot for itteration vs f maximum
plot(f3_out)
xlabel('iteration')
ylabel('f maximum')

function of stalagmite-

function [f]=stalagmite(input_vector)
x=input_vector(1);
y=input_vector(2);
f1_x=(sin(5.1*pi*x+0.5))^6;
f1_y=(sin(5.1*pi*y+0.5))^6;
f2_x=exp((-4*log(2)*(x-0.0667)^2)/0.46);
f2_y=exp((-4*log(2)*(y-0.0667)^2)/0.46);
f=-f1_x*f2_x*f1_y*f2_y;
end

screenshot