A Numerical Study on MIP Approaches over the Efficient Set

Kuan Lu, Shinji Mizuno, Jianming Shi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose an equivalent mixed integer programming (MIP) problem and compute an optimal solution by solving the MIP problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes an assumption which lets a more general class of problem can be solved and reduces the size of the MIP problem. By conducting the experiments on a well-known application of the OE problem, the minimum maximal flow problem, we find that the proposed approach is more accurate and faster. The MIP problem can be efficiently solved by current state-of-the-art MIP solvers when the objective function is convex or linear.

Original languageEnglish
Title of host publicationOptimization of Complex Systems
Subtitle of host publicationTheory, Models, Algorithms and Applications, 2019
EditorsHoai An Le Thi, Hoai Minh Le, Tao Pham Dinh
PublisherSpringer Verlag
Pages611-616
Number of pages6
ISBN (Print)9783030218027
DOIs
Publication statusPublished - 1 Jan 2020
Event6th World Congress on Global Optimization, WCGO 2019 - Metz, France
Duration: 8 Jul 201910 Jul 2019

Publication series

NameAdvances in Intelligent Systems and Computing
Volume991
ISSN (Print)2194-5357

Conference

Conference6th World Congress on Global Optimization, WCGO 2019
CountryFrance
CityMetz
Period8/07/1910/07/19

Fingerprint

Integer programming
Sun
Linear programming
Experiments

Keywords

  • Efficient set
  • Gloal optimization
  • Linear complementarity conditions
  • Mixed integer programming
  • Multiobjective programming

Cite this

Lu, K., Mizuno, S., & Shi, J. (2020). A Numerical Study on MIP Approaches over the Efficient Set. In H. A. Le Thi, H. M. Le, & T. Pham Dinh (Eds.), Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019 (pp. 611-616). (Advances in Intelligent Systems and Computing; Vol. 991). Springer Verlag. https://doi.org/10.1007/978-3-030-21803-4_61
Lu, Kuan ; Mizuno, Shinji ; Shi, Jianming. / A Numerical Study on MIP Approaches over the Efficient Set. Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. editor / Hoai An Le Thi ; Hoai Minh Le ; Tao Pham Dinh. Springer Verlag, 2020. pp. 611-616 (Advances in Intelligent Systems and Computing).
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Lu, K, Mizuno, S & Shi, J 2020, A Numerical Study on MIP Approaches over the Efficient Set. in HA Le Thi, HM Le & T Pham Dinh (eds), Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. Advances in Intelligent Systems and Computing, vol. 991, Springer Verlag, pp. 611-616, 6th World Congress on Global Optimization, WCGO 2019, Metz, France, 8/07/19. https://doi.org/10.1007/978-3-030-21803-4_61

A Numerical Study on MIP Approaches over the Efficient Set. / Lu, Kuan; Mizuno, Shinji; Shi, Jianming.

Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. ed. / Hoai An Le Thi; Hoai Minh Le; Tao Pham Dinh. Springer Verlag, 2020. p. 611-616 (Advances in Intelligent Systems and Computing; Vol. 991).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Lu K, Mizuno S, Shi J. A Numerical Study on MIP Approaches over the Efficient Set. In Le Thi HA, Le HM, Pham Dinh T, editors, Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019. Springer Verlag. 2020. p. 611-616. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-3-030-21803-4_61