ES / AI

ATTACHMENT 1.

%By Katarzyna Chowańska & Mateusz Urbanek

clear all; close all; clc;
data = importdata('AIdata12.dat');

% Setting initial values.
u=100;
lambda = u * 5;
epsilon = 10^(-5);
it_max = 200;

xF=data(:,1);
yF=data(:,2);

n=6;
t1=(1/(sqrt(2*n)));
t2=1/(sqrt(2*sqrt(n)));

bP=1;
bO=0;
it = 0;

time1=cputime;

%Creating first population of the Parents.
for i=1:u
  for j=1:6
    if j<4
      P(i,j) = -10+(20*rand);
     else
      P(i,j) = 10*rand;
    endif
  endfor
endfor

%Entering main loop
while abs(bP-bO)>epsilon

%Creating population of the Offsprings.
  for i=1:lambda
    r=randi(u);
    q=randn*t2;
      for j=1:6
        if j<4
          O(i,j) = P(r,j) + randn*P(r,j+3);
        else
          O(i,j) = P(r,j) * exp(randn*t1)*exp(q);
        endif
      endfor
  endfor

  fitP = zeros(u,1);
  fitO = zeros(lambda,1);

%Calculating MSE for the Parents.
  for i=1:u
    for j=1:101
      fitP(i,1)=fitP(i,1)+power(yF(j)-(P(i,1)*(xF(j)^2-P(i,2)*cos(P(i,3)*pi*xF(j)))),2);
    end
      P(i,7)=fitP(i,1)/101;
   end

%Calculating MSE for the Offsprings.
  for i=1:lambda
    for j=1:101
      fitO(i,1)=fitO(i,1)+power(yF(j)-(O(i,1)*(xF(j)^2-O(i,2)*cos(O(i,3)*pi*xF(j)))),2);
    end
      O(i,7)=fitO(i,1)/101;
   end

%Sorting rows by MSE to find Best Parent and Best Offspring
  P=sortrows(P,7);
  O=sortrows(O,7);
  bP=P(1,7);
  bO=O(1,7);

%Merging set of Offsprings to set of Parents and sorting it by MSE again.
  P=vertcat(P,O);

  P=sortrows(P,7);
%Cutting of members with the worst MSE - creating new population of Parents with "u" members.
  P = P(1:end-(lambda),:);

%Increasing number of iterations and checking if it hasn't exceed maximum set at the beggining.
  it = it+1;
  if it == it_max
    break;
  end
end

%Saving and printing time which was needed to execute algorithm.
time2=cputime-time1;
printf('Execute time: %.2fs\n', cputime-time1);

%Printing fitness of result.
fit=P(1,7);
disp("Fitness:");
disp(fit);
disp("");

%Printing number of iterations needed to obtain result
disp("Iterations: ");
disp(it);

%Printing result (parameters a, b, c)
par_a = P(1,1);
par_b = P(1,2);
par_c = P(1,3);

disp("a: ");
disp(par_a);
disp("b: ");
disp(par_b);
disp("c: ");
disp(par_c);

%Calulating values y for each value x from data file using function with parameters obtained by algorithm.
for i=1:101
y(i)=(P(1,1)*(power(xF(i),2)-P(1,2)*cos(P(1,3)*pi*xF(i))));
end

hold on

%Plotting values x and values y from file.
plot(xF,yF,'r');

%Plotting values x from file with values y calculated by us.
plot(xF,y,'b');