Week 5 - Genetic Algorithm

Error occured in the graph as only xx axis was shown.

it is resolved by checking the code line by line.

another minor error occured while plotting the graph

FUNCTION CODE
%Stalagmite Function
function [f] = stalagmite(input_vector)

 fx = (sin(5.1*pi*input_vector(1)+0.5))^6;
 fy = (sin(5.1*pi*input_vector(2)+0.5))^6;
 fxx = exp((-4*log(2)*(((input_vector(1)-0.0667)^2)/0.64)));
 fyy = exp((-4*log(2)*(((input_vector(2)-0.0667)^2)/0.64)));
 f = -(fx*fy*fxx*fyy);

end

clear
close
clc
%Write a code in MATLAB to optimise the stalagmite function and find the global maxima of the function.
%Input
x = linspace(0,0.6,150);
y = linspace(0,0.6,150);
num_cases = 50;
%2-D Mesh
[xx,yy] = meshgrid(x,y);

%Using for loop to evaluate the stalagmite function
for i = 1:length(x)
    for j = 1:length(y)
        input_vector(1) = xx(i,j);
        input_vector(2) =yy(i,j);
        input_vector = [input_vector(1),input_vector(2)];
        f(i,j) = stalagmite(input_vector);
    end
end

%Case-1: Study of statistical behaviour in unbounded condition
%Using tic-toc command to calculate the iteration time.
tic
for i = 1:num_cases
    [input,fopt(i)] = ga(@stalagmite,2);
     xopt(i) = input(1);
     yopt(i) = input(2);
end
studytime1 = toc;

%Plotting-Case1
figure(1)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'Marker','o','MarkerSize',5,'MarkerFaceColor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('No. of Iterations')
ylabel('Function Maximum')
title('Unbounded Condition')


%Case-2: Study of statistical behaviour in bounded condition
%Using tic-toc command for calculating the itration time
tic                                                      
for i = 1:num_cases
    [input, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6]);
     xopt(i) = input(1);
     yopt(i) = input(2);
end
studytime2 = toc;

%Plotting-Case2
figure(2)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('No. of Iteration')
ylabel('Function Maximum')
title('Bounded Condition')

%Case-3: Study of statistical behaviour in increasing number of population
%Calculating the optimum solution for 'ga'
options = optimoptions('ga');
%increasing the size of population
options = optimoptions(options,'PopulationSize',240);      
%Using tic-toc command for calculating the itration time
tic                                                        
for i = 1:num_cases
    [input, fopt(i)] = ga(@stalagmite,2,[],[],[],[],[0;0],[0.6;0.6],[],[],options);
     xopt(i) = input(1);
     yopt(i) = input(2);
end
studytime3 = toc;

%Plotting-Case3
figure(3)
subplot(2,1,1)
surf(x,y,-f)
shading interp
hold on
plot3(xopt,yopt,-fopt,'marker','o','markersize',5,'markerfacecolor','r')
subplot(2,1,2)
plot(-fopt)
xlabel('No. of Iteration')
ylabel('Function Maximum')
title('increasing number of population')

Step-wise explanation of code

BEGIN
     INITIALIZE Initialise the input terms by using array creation method and no. of terms
                Creating two dimensional mesh by using meshgrid command.               
          CASE1 Study of statistical behaviour in unbounded condition
                Use for loop to evaluate the stalagmite function
                 Function Call
                Use tic-toc command to calculate the iteration time.
          PLOT  Plotting the graphs to No. of Iterations vs Function Maximum for unbounded condition
       ENDCASE1

          CASE2  Study of statistical behaviour in bounded condition
                 Use for loop to evaluate the stalagmite function
                  Function Call
                 Use tic-toc command to calculate the iteration time
          PLOT  Plotting the graphs to No. of Iterations vs Function Maximum for bounded condition
       ENDCASE2

          CASE3 Study of statistical behaviour in increasing number of population
                Use for loop to evaluate the stalagmite function
                 Function Call
                Use tic-toc command to calculate the iteration time
          PLOT  Plotting the graphs to No. of Iterations vs Function Maximum
       ENDCASE3
END

BEGIN
     FUNCTION create a function to reduce the complication and length of the code
              Give the name of the function and save it by using the same name
              Stalagmite Function
              function [f] = stalagmite(input_vector)

              fx = (sin(5.1*pi*input_vector(1)+0.5))^6;
              fy = (sin(5.1*pi*input_vector(2)+0.5))^6;
              fxx = exp((-4*log(2)*(((input_vector(1)-0.0667)^2)/0.64)));
              fyy = exp((-4*log(2)*(((input_vector(2)-0.0667)^2)/0.64)));
              f = -(fx*fy*fxx*fyy);
              
     ENDFUNCTION    
 END