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A Criterion Space Method for Biobjective Mixed Integer Programming: The Boxed Line Method

Author

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  • Tyler Perini

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;)

  • Natashia Boland

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;)

  • Diego Pecin

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;)

  • Martin Savelsbergh

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

Despite recent interest in multiobjective integer programming, few algorithms exist for solving biobjective mixed integer programs. We present such an algorithm: the boxed line method. For one of its variants, we prove that the number of single-objective integer programs solved is bounded by a linear function of the number of nondominated line segments in the nondominated frontier. This is the first such complexity result. An extensive computational study demonstrates that the box line method is also efficient in practice and that it outperforms existing algorithms on a diverse set of instances.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:32:y:2020:i:1:p:16-39
    DOI: 10.1287/ijoc.2019.0887
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    References listed on IDEAS

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    3. 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.
    4. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    5. Soylu, Banu, 2018. "The search-and-remove algorithm for biobjective mixed-integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 268(1), pages 281-299.
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    Cited by:

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    3. 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.
    4. Vahid Mahmoodian & Iman Dayarian & Payman Ghasemi Saghand & Yu Zhang & Hadi Charkhgard, 2022. "A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1453-1470, May.
    5. Moritz Link & Stefan Volkwein, 2023. "Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs," Journal of Global Optimization, Springer, vol. 87(1), pages 97-132, September.
    6. Fritz Bökler & Sophie N. Parragh & Markus Sinnl & Fabien Tricoire, 2024. "An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 263-290, August.

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