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

Author

Listed:
  • Angelo Aliano Filho

    (Federal Technological University of Paraná)

  • Antonio Carlos Moretti

    (University of Campinas)

  • Margarida Vaz Pato

    (Universidade de Lisboa)

  • Washington Alves Oliveira

    (University of Campinas)

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.

Suggested Citation

  • Angelo Aliano Filho & Antonio Carlos Moretti & Margarida Vaz Pato & Washington Alves Oliveira, 2021. "An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems," Annals of Operations Research, Springer, vol. 296(1), pages 35-69, January.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-019-03317-9
    DOI: 10.1007/s10479-019-03317-9
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    1. Amanda O. C. Ayres & Betania S. C. Campello & Washington A. Oliveira & Carla T. L. S. Ghidini, 2021. "A Bi-Integrated Model for coupling lot-sizing and cutting-stock problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1047-1076, December.

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