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Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming

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  • Piercy, Craig A.
  • Steuer, Ralph E.

Abstract

This paper describes an approach for markedly reducing the time required to obtain all efficient extreme points of a multiple objective linear program (MOLP) with three objectives. The approach is particularly useful when working with such MOLPs possessing large numbers of efficient extreme points. By subdividing the criterion cone into sub-cones, the paper shows how the task of computing all efficient extreme points can be broken down into parts so that the parts can be solved concurrently, thus allowing all efficient extreme points to be computed in much reduced elapsed time. The paper investigates several schemes for conducting this task and reports on a volume of computational experience.

Suggested Citation

  • Piercy, Craig A. & Steuer, Ralph E., 2019. "Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 277(2), pages 653-666.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:2:p:653-666
    DOI: 10.1016/j.ejor.2019.02.042
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    References listed on IDEAS

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    1. Lizhen Shao & Matthias Ehrgott, 2008. "Approximating the nondominated set of an MOLP by approximately solving its dual problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 469-492, December.
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    4. Steuer, Ralph E. & Piercy, Craig A., 2005. "A regression study of the number of efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 162(2), pages 484-496, April.
    5. Miettinen, Kaisa & Eskelinen, Petri & Ruiz, Francisco & Luque, Mariano, 2010. "NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point," European Journal of Operational Research, Elsevier, vol. 206(2), pages 426-434, October.
    6. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
    7. Benson, Harold P. & Sun, Erjiang, 2002. "A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program," European Journal of Operational Research, Elsevier, vol. 139(1), pages 26-41, May.
    8. Matthias Ehrgott & Andreas Löhne & Lizhen Shao, 2012. "A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming," Journal of Global Optimization, Springer, vol. 52(4), pages 757-778, April.
    9. Kirlik, Gokhan & Sayın, Serpil, 2014. "A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 479-488.
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    Cited by:

    1. Hadjer Belkhiri & Mohamed El-Amine Chergui & Fatma Zohra Ouaïl, 2022. "Optimizing a linear function over an efficient set," Operational Research, Springer, vol. 22(4), pages 3183-3201, September.

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