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Branch-and-Bound for Bi-objective Integer Programming

Author

Listed:
  • Sophie N. Parragh

    (Institute of Production and Logistics Management, Johannes Kepler University Linz, 4040 Linz, Austria)

  • Fabien Tricoire

    (Institute of Production and Logistics Management, Johannes Kepler University Linz, 4040 Linz, Austria)

Abstract

In bi-objective integer optimization the optimal result corresponds to a set of nondominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions and takes advantage of integer objective coefficients. The developed algorithm is applied to bi-objective facility location problems and the bi-objective set covering problem, as well as to the bi-objective team orienteering problem with time windows. In the latter case, lower bound sets are computed by means of column generation. Comparison with state-of-the-art exact algorithms shows the effectiveness of the proposed branch-and-bound algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:31:y:2019:i:4:p:805-822
    DOI: 10.1287/ijoc.2018.0856
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Sophie N. Parragh & Fabien Tricoire & Walter J. Gutjahr, 2022. "A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 419-459, June.
    2. 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.
    3. Miriam Enzi & Sophie N. Parragh & Jakob Puchinger, 2022. "The bi-objective multimodal car-sharing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 307-348, June.
    4. Torbjörn Larsson & Nils-Hassan Quttineh & Ida Åkerholm, 2024. "A Lagrangian bounding and heuristic principle for bi-objective discrete optimization," Operational Research, Springer, vol. 24(2), pages 1-34, June.
    5. Forget, Nicolas & Gadegaard, Sune Lauth & Nielsen, Lars Relund, 2022. "Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 302(3), pages 909-924.
    6. 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.
    7. Hongming Li & Xintao Li, 2022. "A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy," Mathematics, MDPI, vol. 10(24), pages 1-20, December.

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