Genetic Algorithm

Aim - Use MATLAB to optimise the stalagmite function and find the global maxima of the function.

%Global maxima of the given function.
clear all
close all
clc


x=linspace(0,0.6,150);
y=linspace(0,0.6,150);


[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)=stalgmite(input_vector);
        
    end
    
end

%case1 

iterations=100;

tic
for i=1:iterations
    
    [inputa fval1(i)]=ga(@stalgmite,2);
    x1(i)=inputa(1);
    y1(i)=inputa(2);
    
end
time=toc

%plots
figure(1)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(x1,y1,fval1,'marker','*')
title("Case 1 (Unbounded Values)")
subplot(2,1,2)
plot(fval1)
xlabel('No. of Iterations')
ylabel('Function Minimum')

%case 2

tic
for i=1:iterations
    
    [inputb fval2(i)]=ga(@stalgmite,2,[],[],[],[],[0;0],[1;1]);
    x2(i)=inputb(1);
    y2(i)=inputb(2);
    
end
time2=toc


figure(2)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(x2,y2,fval2,'marker','*')
title("Case 2 (Bounded values)")
subplot(2,1,2)
plot(fval2)
xlabel('No. of Iterations') 
ylabel('Function Minimum')

%case 3

options=optimoptions('ga');
options=optimoptions(options,'populationsize',500)


tic
for i=1:iterations
    
   [inputc fval3(i)]=ga(@stalgmite,2,[],[],[],[],[0;0],[1;1],[],[],options);
   x3(i)=inputc(1);
   y3(i)=inputc(2);
   
end

time3=toc


figure(3)
subplot(2,1,1)
hold on
surfc(x,y,f)
shading interp
plot3(x3,y3,fval3,'marker','*')
title("Case 3 (Increased Population)")
subplot(2,1,2)
plot(fval3)
xlabel('No. of Iterations') 
ylabel('Function Minimum')