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Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making

Author

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  • Esra Karasakal

    (Department of Industrial Engineering, Middle East Technical University, Ankara 06531, Turkey)

  • Murat Köksalan

    (Department of Industrial Engineering, Middle East Technical University, Ankara 06531, Turkey)

Abstract

In this paper, we address the problem of generating a discrete representation of the nondominated frontier in multiple objective linear problems. We find a surface that approximates the shape of the nondominated frontier. Utilizing the surface, we generate a set of discrete points that is representative of the frontier. Our experience on randomly generated problems demonstrates that the approach performs well in terms of both the quality of the representation and the computation time.

Suggested Citation

  • Esra Karasakal & Murat Köksalan, 2009. "Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making," Operations Research, INFORMS, vol. 57(1), pages 187-199, February.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:187-199
    DOI: 10.1287/opre.1080.0581
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    References listed on IDEAS

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    1. M. Murat Köksalan & Paul N. S. Sagala, 1995. "Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions," Management Science, INFORMS, vol. 41(7), pages 1158-1171, July.
    2. 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.
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    5. Yan Fu & Urmila Diwekar, 2004. "An Efficient Sampling Approach to Multiobjective Optimization," Annals of Operations Research, Springer, vol. 132(1), pages 109-134, November.
    6. M. Murat Köksalan, 1999. "A heuristic approach to bicriteria scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 777-789, October.
    7. Dauer, Jerald P. & Gallagher, Richard J., 1996. "A combined constraint-space, objective-space approach for determining high-dimensional maximal efficient faces of multiple objective linear programs," European Journal of Operational Research, Elsevier, vol. 88(2), pages 368-381, January.
    8. H. P. Benson, 1998. "Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 17-35, July.
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    Cited by:

    1. Ceyhan, Gökhan & Köksalan, Murat & Lokman, Banu, 2019. "Finding a representative nondominated set for multi-objective mixed integer programs," European Journal of Operational Research, Elsevier, vol. 272(1), pages 61-77.
    2. Doğan, Ilgın & Lokman, Banu & Köksalan, Murat, 2022. "Representing the nondominated set in multi-objective mixed-integer programs," European Journal of Operational Research, Elsevier, vol. 296(3), pages 804-818.
    3. Özarık, Sami Serkan & Lokman, Banu & Köksalan, Murat, 2020. "Distribution based representative sets for multi-objective integer programs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 632-643.

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