Aim of the project:

Optimization of the stalagmite function using the genetic algorithm and to find out the global maxima

%% Description

%

% This is a program to maximize the Stalagmite function by using Genetic Algorithm and conducting its 3 studies.

%

%% Output

%

% Plot of Stalagmite function.

% Plot of all 3 studies.

% Maximized output of stalagmite function.

% Plot of maximum output vs no of iterations.

% Program

%% 1) Defining Range

x = linspace(0,0.6,150);                                                                                                                    % range of x

y = linspace(0,0.6,150);                           % range of y

[xx yy] = meshgrid(x,y);                      % creating 2D array of range

iterations = 40;

%% 2) Solving Stalagmite Function

% nested loop is run for the entire range to input each range value one by one.

for i = 1:length(xx)

    for j= 1:length(yy)

        input_vector(1) = xx(i,j);                 % picking values from xx matrix

        input_vector(2) = yy(i,j);                % picking values from yy matrix

        sol(i,j) = stalagmite(input_vector);      % calling the stalagmite function and proving inputs.

    end

end

%% 2.1) Plotting Stalagmite Function

figure(1)

surfc(xx, yy, -sol);                      % plotting the stalagmite functn using the surfc command

shading interp                            % removing the shadings from the plot

xlabel('xx'); ylabel('yy');

title('Stalagmite Function')

%% 3) First Study (Unbound Inputs)

%

% use the for loop to run the itaerations and call the ga function every time

%

tic;                                               % start the timer for first study

for i = 1:iterations;                               % start the loop

    [sol1 fval1(i)] = ga(@stalagmite, 2);          % calling ga function

                                                     % sol1 is the solution

                                                    % and fval1 is the function value

    sol_x1(i) = sol1(1);                               % storing the value of x seperately

    sol_y1(i) = sol1(2);                              % storing the value of y seperately

    clc                                             % clearing the command window after each iteration.

end

study1_time = toc;                                  % stopping the timer

%% 3.1) Plotting First Study

figure(2)

subplot(2,1,1);                                                  % creating first half of the figure

plot3(-sol_x1, -sol_y1, -fval1,'- .','markersize',10,'color','r')     % plotting the solution of first study

xlabel('x'); ylabel('y'); zlabel('function value');              % labelling the axes

title('Study 1');                                                % title of the plot

hold on                                                          % holding the next plots

surfc(-xx,-yy,-sol);                                                % plotting the stalagmite function

shading interp;                                                  % removing the shading from the plot

legend('Solutions')

subplot(2,1,2);                                                  % creating second half of the figure

plot(fval1,'-o');                                               % plotting the function values

title('Iterations vs Function Value');                           % title of the plot

xlabel('Iterations'); ylabel('Function Value');                  % labelling the axes

legend('function values')

hold off

%% 4) Second Study (Bounded Inputs)

%

% use the for loop to run the iterations and also provide the lower and upper bounds

%

tic;                                                                          

for i = 1:iterations                                                    % starting the timer

    [sol2 fval2(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1]);       % calling the ga function

    sol_x2(i) = sol2(1);

    sol_y2(i) = sol2(2);                                                % storing x and y values seperately

    clc                                                                % clearing command window on each iteration

end

study2_time = toc;                                                      % stooping the study timer

%% 4.1) Plotting Second Study

figure(3)

subplot(2,1,1);                                                         % generating the upper half of the figure

plot3(-sol_x2,-sol_y2,-fval2,'- .','markersize',10,'color','r');             % plotting the solution of the function

title('Study 2');                                                       % title of plot

xlabel('x'); ylabel('y'); zlabel('z');                                 % labelling the axes

hold on

surfc(-xx, -yy, -sol);                                                     % plotting the stalgmite function

shading interp;

legend('Solutions')                                                     % inseting the required legends

subplot(2,1,2);                                                         % generating the lower half of the plot

plot(fval2,'-o');                                                       % plotting the function values

xlabel('Iterations'); ylabel('Function Value');                         % labelling the axes

title('Iterations vs Function Values');                                 % title of the plot

legend('function values')                                               % inserting required legends

hold off

%% 5) Third Study (Bounded Inputs with Population Size')

tic;                                                                           % starting the study timer

options = optimoptions('ga');                                                  % initializing options

options = optimoptions('ga','PopulationSize',500);                             % proving options parameters using optimoptions function

% now ga will maximize the default optimization parameters replaced by values in options

for i = 1:iterations                                                            % starting the loop

    [sol3 fval3(i)] = ga(@stalagmite, 2,[],[],[],[],[0;0],[1;1],[],options);    % solving the stalagmite function

    sol_x3(i) = sol3(1);                                                        % seperating x and y values

    sol_y3(i) = sol3(2); 

    clc                                                                         % clearing command window on each iteration

end

study3_time = toc;                                                              % stopping the timer

%% 5.1) Plotting the third Study

figure(4)

subplot(2,1,1);                                                        % generating the upper half of the plot

plot3(-sol_x3, -sol_y3, -fval3,'- .','markersize',15,'color','r');          % plotting the solution

xlabel('x'); ylabel('y'); zlabel('Function Value');                   % labelling the axes

title('Study 3');                                                      % title of the plot

hold on

surfc(-xx,-yy,-sol);                                                      % plotting th stalagmite function

shading interp;                         

legend('Solution')                                                     % inserting required legends

subplot(2,1,2);                                                        % generating lower half of the plot

plot(fval3,'-o');                                                      % plotting the function values

xlabel('Iterations'); ylabel('Function Value');                        % labelling the axes

title('Iterations vs Function Value');                                 % title of the plot

legend('function values')                                              % inserting legendd

hold off

%% Displaying Soluton Outputs

disp('------------------------------Maximized Stalagmite Function------------------------------')

disp('Solution Values :')                    % displaying value of solution obtained after third study 

disp(' ')

disp(sol_x3)                               % values of x (input_vector(1))

disp(' ')

disp(sol_y3)                               % values of y (input_vector(2))

disp('Function Values :') 

disp(' ')

disp(fval3)                                % displaying function values

disp(' ')

disp('------------------------------Time taken for each study------------------------------')

fprintf('\nTime taken for first study = %f seconds\n\n',study1_time)     % displaying time taken for all three studies

fprintf('Time taken for second study = %f seconds\n\n',study2_time)

fprintf('Time taken for third study = %f seconds\n\n',study3_time)

function [F] = stalagmite(input)

f1x = (sin(5.1*pi*input(1) + 0.5))^6;

f1y = (sin(5.1*pi*input(2) + 0.5))^6;

f2x = exp(-4*log(2)*(((input(1) - 0.0667^2)/(0.64))));

f2y = exp(-4*log(2)*(((input(2) - 0.0667^2)/(0.64))));

F = -(f1x * f1y * f2x * f2y);

end