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Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

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  • G. Tohidi
  • H. Hassasi

Abstract

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.

Suggested Citation

  • G. Tohidi & H. Hassasi, 2018. "Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(3), pages 203-217, April.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:3:p:203-217
    DOI: 10.1002/nav.21805
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    3. Gravel, Marc & Martel, Jean Marc & Nadeau, Raymond & Price, Wilson & Tremblay, Richard, 1992. "A multicriterion view of optimal resource allocation in job-shop production," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 230-244, August.
    4. Harold P. Benson & Serpil Sayin, 1997. "Towards finding global representations of the efficient set in multiple objective mathematical programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 47-67, February.
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    Cited by:

    1. Zachary Feinstein & Niklas Hey & Birgit Rudloff, 2023. "Approximating the set of Nash equilibria for convex games," Papers 2310.04176, arXiv.org, revised Apr 2024.

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