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Surrogate upper bound sets for bi-objective bi-dimensional binary knapsack problems

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  • Cerqueus, Audrey
  • Przybylski, Anthony
  • Gandibleux, Xavier

Abstract

The paper deals with the definition and the computation of surrogate upper bound sets for the bi-objective bi-dimensional binary knapsack problem. It introduces the Optimal Convex Surrogate Upper Bound set, which is the tightest possible definition based on the convex relaxation of the surrogate relaxation. Two exact algorithms are proposed: an enumerative algorithm and its improved version. This second algorithm results from an accurate analysis of the surrogate multipliers and the dominance relations between bound sets. Based on the improved exact algorithm, an approximated version is derived. The proposed algorithms are benchmarked using a dataset composed of three groups of numerical instances. The performances are assessed thanks to a comparative analysis where exact algorithms are compared between them, the approximated algorithm is confronted to an algorithm introduced in a recent research work.

Suggested Citation

  • Cerqueus, Audrey & Przybylski, Anthony & Gandibleux, Xavier, 2015. "Surrogate upper bound sets for bi-objective bi-dimensional binary knapsack problems," European Journal of Operational Research, Elsevier, vol. 244(2), pages 417-433.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:2:p:417-433
    DOI: 10.1016/j.ejor.2015.01.035
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    References listed on IDEAS

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    Cited by:

    1. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    2. 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.

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