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Using dual relaxations in multiobjective mixed-integer convex quadratic programming

Author

Listed:
  • Marianna Santis

    (Università degli Studi di Firenze)

  • Gabriele Eichfelder

    (Technische Universität Ilmenau)

  • Daniele Patria

    (Sapienza Università di Roma)

  • Leo Warnow

    (Technische Universität Ilmenau)

Abstract

We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values of certain integer variables are fixed. The devised pruning conditions and a tailored preprocessing phase allow a fast enumeration of the nodes. Despite we do not require any boundedness of the feasible set, we are able to prove that the method stops after having explored a finite number of nodes. Numerical experiments on a broad set of instances with two, three, and four objectives are presented.

Suggested Citation

  • Marianna Santis & Gabriele Eichfelder & Daniele Patria & Leo Warnow, 2025. "Using dual relaxations in multiobjective mixed-integer convex quadratic programming," Journal of Global Optimization, Springer, vol. 92(1), pages 159-186, May.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:1:d:10.1007_s10898-024-01440-x
    DOI: 10.1007/s10898-024-01440-x
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    References listed on IDEAS

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    1. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "Correction to: A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 229-229, May.
    2. Han Zhong & Wei Guan & Wenyi Zhang & Shixiong Jiang & Lingling Fan, 2018. "A bi-objective integer programming model for partly-restricted flight departure scheduling," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-18, May.
    3. 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.
    4. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    5. Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2015. "On the representation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 245(3), pages 767-778.
    6. 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.
    7. Gabriele Eichfelder & Leo Warnow, 2022. "An approximation algorithm for multi-objective optimization problems using a box-coverage," Journal of Global Optimization, Springer, vol. 83(2), pages 329-357, June.
    8. Eichfelder, Gabriele & Warnow, Leo, 2023. "Advancements in the computation of enclosures for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 310(1), pages 315-327.
    9. Sophie N. Parragh & Fabien Tricoire, 2019. "Branch-and-Bound for Bi-objective Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 805-822, October.
    10. Gabriele Eichfelder & Peter Kirst & Laura Meng & Oliver Stein, 2021. "A general branch-and-bound framework for continuous global multiobjective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 195-227, May.
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