You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: TSEMO_V1.m
    path of file: ./repos/TS-EMO/Old_versions
    
    the code of the file until where you have to start completion: function [Xpareto,Ypareto,X,Y] = TSEMO_V1(f,X,Y,lb,ub,Opt)
%  Copyright (c) by Eric Bradford, Artur M. Schweidtmann and Alexei Lapkin, 2017-13-12.
%  Version 1.0 by Eric Bradford (eric.bradford@ntnu.no), Artur M.
%  Schweidtmann (Artur.Schweidtman
    
function [index,hv_imp] = hypervolume_improvement_index(Ynew,Sample_nadir,Sample_pareto,Opt)
% Copyright (c) by Eric Bradford, Artur M. Schweidtmann and Alexei Lapkin, 2017-13-12.

r = Sample_nadir;
index = [];

for i = 1 : Opt.NoOfBachSequential
    
    Yfront = Ynew(paretofront(Ynew),:);
    
    if size(Ynew,2) == 2
        hvY = hypervolume_2D(Yfront,r);
         
        for k = 1:size(Sample_pareto,1)
            A = [Ynew;Sample_pareto(k,:)];
            Afront = A(paretofront(A),:);
            hv = hypervolume_2D(Afront,r);
            hv_improvement(k) = hv-hvY;
        end