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An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems

  • Angelo Aliano FilhoEmail author
  • Antonio Carlos Moretti
  • Margarida Vaz Pato
  • Washington Alves de Oliveira
S.I.: MOPGP 2017
  • 65 Downloads

Abstract

This paper presents an exact scalarization method to solve bi-objective integer linear optimization problems. This method uses diverse reference points in the iterations, and it is free from any kind of a priori chosen weighting factors. In addition, two new adapted scalarization methods from literature and the modified Tchebycheff method are studied. Each one of them results in different ways to obtain the Pareto frontier. Computational experiments were performed with random real size instances of two special problems related to the manufacturing industry, which involve lot sizing and cutting stock problems. Extensive tests confirmed the very good performance of the new scalarization method with respect to the computational effort, the number of achieved solutions, the ability to achieve different solutions, and the spreading and spacing of solutions at the Pareto frontier.

Keywords

Bi-objective optimization problems Integer linear optimization Exact scalarization methods 

Notes

Acknowledgements

The authors are indebted to the anonymous reviewers for their helpful comments. In addition, we thank the Federal Technological University of Parana for the support of this research. The research of Margarida Vaz Pato was supported by National Funding from FCT - Fundação para Ciência e a Tecnologia, Portugal, under Project UID/MAT/04561/2019 and UID/Multi/00491/2013.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Academic Department of MathematicsFederal Technological University of ParanáApucaranaBrazil
  2. 2.Institute of Mathematics, Statistics and Scientific ComputationUniversity of CampinasCampinasBrazil
  3. 3.ISEG and CMAFcIOUniversidade de LisboaLisbonPortugal
  4. 4.School of Applied SciencesUniversity of CampinasLimeiraBrazil

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