Week 4.1 - Genetic Algorithm

% Challenge 8 - Genetic Algotihm - Function Code
syms x y
function[p] = gene_alg(input_vector)
x = input_vector(1);
y = input_vector(2);
f1x = (sin(5.1*pi*x + 0.5)).^6;
f1y = (sin(5.1*pi*y + 0.5)).^6;
t1 = ((x-0.0667).^2/(0.64));
t2 = ((y-0.0667).^2/(0.64));
f2x = exp(-4.*log(2)*t1);
f2y = exp(-4.*log(2)*t2);
p = -(f1x.*f2x.*f1y.*f2y);
end

% Challenge 8 - Genetic Algorithm
% Search space for the function
x = linspace(0,0.5,350);
y = linspace(0,0.5,350);
[X,Y] = meshgrid(x,y);
% Number of iterations performed by the function to evaluate the fitness
num_case = 150;
% Surface plot for gene_alg function
for i = 1:length(X)
    for j = 1:length(Y)
        input_vector(1) = X(i,j);
        input_vector(2) = Y(i,j);
        p(i,j) = gene_alg(input_vector);
    end
end
% Generate the surface for the plot
    surfc(X,Y,-p);
% Remove the lines produced by mesh grid    
    shading interp
% Initiate timer for calculating survey time
tic
for i=1:num_case
    % Calculate the optimized value of the function
    [inputs,popt(i)] = ga(@gene_alg,2);
    % Optimized value at each iteration
    xopt(i) = inputs(1);
    yopt(i) = inputs(2);
end
% Display time taken to complete the survey
survey1_time = toc
% Plot the graph wit the obtained optimized data
figure(1)
subplot(3,1,1)
surfc(X,Y,-p);
hold on
shading interp
plot3(xopt,yopt,popt,'marker','o','markersize',5,'markerfacecolor','g')
title('Unbounded Inputs')
xlabel('X');
ylabel('Y');
grid on
subplot(3,1,3)
plot(-popt);
xlabel('iterations')
ylabel('function min value')
% Initiate timer for calculating survey time
tic
for j=1:num_case
    % Calculate the optimized value of the function
    [inputs,popt(j)] = ga(@gene_alg,2,[],[],[],[],[0;],[1;1]);
    % Optimized value at each iteration with the boundaary conditions
    xopt(j) = inputs(1);
    yopt(j) = inputs(2);
end
% Display time taken to complete the survey
survey2_time = toc
% Plot the graph with the obtained optimized data
figure(2)
subplot(3,1,1)
hold on
surfc(X,Y,-p)
shading interp
plot3(xopt,yopt,-popt,'marker','o','markersize',5,'markerfacecolor','g')
title('Bounded Inputs')
xlabel('X')
ylabel('Y')
grid on
subplot(3,1,3)
plot(-popt);
xlabel('iterations')
ylabel('functions min value')
% Increase the population by usinf the 'optimoptions' command
options = optimoptions('ga','populationsize',300)
% Initiate timer for calculating survey time
tic
for k=1:num_case
    % Calculate the optimized value of the function
     [inputs,popt(k)] = ga(@gene_alg,2,[],[],[],[],[0;0],[1;1],[],[],options);
    % Optimized value at each iteration 
     xopt(k) = inputs(1);
     yopt(k) = inputs(2);
end
% Display time taken to complete the survey
survey3_time = toc
% Plot the graph with the obtained optimized data
figure(3)
subplot(3,1,1)
hold on
surfc(X,Y,-p)
shading interp
plot3(xopt,yopt,-popt,'marker','o','markersize',5,'markerfacecolor','g')
title('Statistical Study with increase in population')
xlabel('X')
ylabel('Y')
grid on
subplot(3,1,3)
plot(-popt);
xlabel('iterations')
ylabel('function min value')

% Challenge 8 - Genetic Algorithm - Optimum Maximum Value
x = linspace(0,0.5,350);
y = linspace(0,0.5,350);
[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);
        p(i,j) = stalagmite(input_vector);
    end
end
options = optimoptions('ga','PlotFcn',@gaplotbestf,'populationsize',300);
[x,fval] = ga(@stalagmite,2,[],[],[],[],[0;0],[1;1],[],[],options);
xopt = x(1);
yopt = x(2);
figure(4)
surf(xx,yy,-p);
shading interp
hold on
plot3(xopt,yopt,-fval,'ro','markersize',5,'markerfacecolor','r')

TASK 1 :- CODING THE GENETIC ALGORITHM FUNCTION

1. Initiate the 'function' command by namieng it as 'gene_alg' and give the variables required.
2. Define the variables given in the 'gene_alg' function.
3. Give the equation carried by the function.
4. Define each term in the equation by expanding them to thier respective expressions.
5. Type the 'end' command to complete the function.
6. Save the program as 'gene_alg.m'

TASK 2 :- CODING THE GENETIC ALGORITHM PLOTS

1. Define the search space for the function and iteration performed to define the fintess of the plots.
2. Generate the surface plot for the Genetic Algorithm function.
3. Initiate the timer to calculate time taken to complete each survey.
4. Obtain the optimized values for each iteration.
5. By using the 'plot' command and giving the marker size, marker type and marker face color, make a plot with the oobtained values for unbounded method.
6. Use the 'ga' command and 'gene_alg' function and the boundaries required for obtining the optimized values.
7. Use the optimized values and make a plot for bounded method using 'plot' command, giving the marker size, marker type and marker face color.
8. By utilizing the 'optimoptions' function, increase the population size for the function to 300.
9. Obtain the optimized values by using 'ga' command and the 'gene_alg' function.
10. Make a plot for the obtained values by using the 'plot' command, giving the marker size, marker type and marker face color.

TASK 3 :- OBTAINING THE OPTIMUM MAXIMUM VALUE

1. Define the search space for the function.
2. Give the input conditions and declare the input variables.
3. Use the 'optimoptions' command and 'gaplotbestf' function to increase the population size for obtaining the optimim maximum value of the function and the plot of the function.
4. Input the 'ga' command and 'gene_alg' functionand boundaries required to obtain the values.
5. Plot the obtained values by using 'plot' command, giving the marker size, marker type and marker face color.

ERRORS ENCOUNTERED :- None

RESULTS :-