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Towards finding global representations of the efficient set in multiple objective mathematical programming

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  • Harold P. Benson
  • Serpil Sayin

Abstract

We propose and justify the proposition that finding truly global representations of the efficient sets of multiple objective mathematical programs is a worthy goal. We summarize the essential elements of a general global shooting procedure that seeks such representations. This procedure illustrates the potential benefits to be gained from procedures for globally representing efficient sets in multiple objective mathematical programming. © 1997 John Wiley & Sons, Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:1:p:47-67
    DOI: 10.1002/(SICI)1520-6750(199702)44:13.0.CO;2-M
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    Cited by:

    1. 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.
    2. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    3. Jörg Fliege, 2006. "An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 825-845, November.
    4. Jacinto Martín & Concha Bielza & David Ríos Insua, 2005. "Approximating nondominated sets in continuous multiobjective optimization problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 469-480, August.
    5. Katrin Teichert & Tobias Seidel & Philipp Süss, 2024. "Combining discrete and continuous information for multi-criteria optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 153-173, August.
    6. Rafael Lazimy, 2013. "Interactive Polyhedral Outer Approximation (IPOA) strategy for general multiobjective optimization problems," Annals of Operations Research, Springer, vol. 210(1), pages 73-99, November.
    7. E. Filatovas & O. Kurasova & J. L. Redondo & J. Fernández, 2020. "A reference point-based evolutionary algorithm for approximating regions of interest in multiobjective problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 402-423, July.
    8. Serpil Sayin, 2003. "A Procedure to Find Discrete Representations of the Efficient Set with Specified Coverage Errors," Operations Research, INFORMS, vol. 51(3), pages 427-436, June.
    9. Kuan-Min Lin & Matthias Ehrgott & Andrea Raith, 2017. "Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes," 4OR, Springer, vol. 15(4), pages 331-357, December.

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