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A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems

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  • Fattahi, Ali
  • Turkay, Metin

Abstract

The nondominated frontier (NDF) of a biobjective optimization problem is defined as the set of feasible points in the objective function space that cannot be improved in one objective function value without worsening the other. For a biobjective mixed-binary linear programming problem (BOMBLP), the NDF consists of some combination of isolated points and open, closed, or half-open/half-closed line segments. Some algorithms have been proposed in the literature to find an approximate or exact representation of the NDF. We present a one direction search (ODS) method to find the exact NDF of BOMBLPs. We provide a theoretical analysis of the ODS method and show that it generates the exact NDF. We also conduct a comprehensive experimental study on a set of benchmark problems and show the solution quality and computational efficacy of our algorithm.

Suggested Citation

  • Fattahi, Ali & Turkay, Metin, 2018. "A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 415-425.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:415-425
    DOI: 10.1016/j.ejor.2017.09.026
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    References listed on IDEAS

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    1. Zhang, Weihua & Reimann, Marc, 2014. "A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 15-24.
    2. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    3. Thomas Stidsen & Kim Allan Andersen & Bernd Dammann, 2014. "A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs," Management Science, INFORMS, vol. 60(4), pages 1009-1032, April.
    4. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 735-754, November.
    5. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: The Triangle Splitting Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 597-618, November.
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    Cited by:

    1. Nathan Adelgren & Akshay Gupte, 2022. "Branch-and-Bound for Biobjective Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 909-933, March.
    2. Diego Pecin & Ian Herszterg & Tyler Perini & Natashia Boland & Martin Savelsbergh, 2024. "A fast and robust algorithm for solving biobjective mixed integer programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 221-262, August.
    3. Alvaro Sierra Altamiranda & Hadi Charkhgard, 2019. "A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 823-840, October.
    4. Tyler Perini & Natashia Boland & Diego Pecin & Martin Savelsbergh, 2020. "A Criterion Space Method for Biobjective Mixed Integer Programming: The Boxed Line Method," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 16-39, January.
    5. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    6. Acuna, Jorge A. & Zayas-Castro, José L. & Charkhgard, Hadi, 2020. "Ambulance allocation optimization model for the overcrowding problem in US emergency departments: A case study in Florida," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    7. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.

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