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A new method for optimizing a linear function over the efficient set of a multiobjective integer program

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  • Boland, Natashia
  • Charkhgard, Hadi
  • Savelsbergh, Martin

Abstract

We present a new algorithm for optimizing a linear function over the set of efficient solutions of a multiobjective integer program (MOIP). The algorithm’s success relies on the efficiency of a new algorithm for enumerating the nondominated points of a MOIP, which is the result of employing a novel criterion space decomposition scheme which (1) limits the number of subspaces that are created, and (2) limits the number of sets of disjunctive constraints required to define the single-objective IP that searches a subspace for a nondominated point. An extensive computational study shows that the efficacy of the algorithm. Finally, we show that the algorithm can be easily modified to efficiently compute the nadir point of a multiobjective integer program.

Suggested Citation

  • Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2017. "A new method for optimizing a linear function over the efficient set of a multiobjective integer program," European Journal of Operational Research, Elsevier, vol. 260(3), pages 904-919.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:904-919
    DOI: 10.1016/j.ejor.2016.02.037
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    References listed on IDEAS

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    1. Abbas, Moncef & Chaabane, Djamal, 2006. "Optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1140-1161, October.
    2. Ehrgott, Matthias & Tenfelde-Podehl, Dagmar, 2003. "Computation of ideal and Nadir values and implications for their use in MCDM methods," European Journal of Operational Research, Elsevier, vol. 151(1), pages 119-139, November.
    3. Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.
    4. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
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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.
    2. Satya Tamby & Daniel Vanderpooten, 2021. "Enumeration of the Nondominated Set of Multiobjective Discrete Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 72-85, January.
    3. De Santis, Marianna & Grani, Giorgio & Palagi, Laura, 2020. "Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming," European Journal of Operational Research, Elsevier, vol. 283(1), pages 57-69.
    4. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    5. Mansini, Renata & Zanella, Marina & Zanotti, Roberto, 2023. "Optimizing a complex multi-objective personnel scheduling problem jointly complying with requests from customers and staff," Omega, Elsevier, vol. 114(C).
    6. 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.
    7. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2019. "Preprocessing and cut generation techniques for multi-objective binary programming," European Journal of Operational Research, Elsevier, vol. 274(3), pages 858-875.
    8. 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.

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