%An objective function for the low-autocorrelation problem.
%Author: Ofer M. Shir, 2004; oshir@liacs.nl.
%-----------------------------------------------------------------------
function [f] = merit (pop)
% Given a population of binary sequences, this function calculates 
% the merit function according to the formula specified in the exercise
% description. The input pop is the given matrix.
% The output f is the merit factor calculated (row vector).

n = size(pop,1)
m = size(pop,2)
E = zeros(1,m)
%Calculated efficiently in a matrix-notation; auxilary matrices - Y1,Y2
%- are initialized in every iteration. They are shifted form of the
%original y vectors. The diaganol of the dot-squared Y2*Y1 matrix is
%exactly the inner sum of merit function.
for k=1:n-1
    Y1=pop(1:n-k,:)
    Y2=pop(k+1:n,:)'
    E=E+((diag(Y2*Y1)).^2)'
end

%The output:
f = (n*n*ones(1,m))./(2*E)