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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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    1. Jaszkiewicz, Andrzej, 2004. "On the computational efficiency of multiple objective metaheuristics. The knapsack problem case study," European Journal of Operational Research, Elsevier, vol. 158(2), pages 418-433, October.
    2. Clausen, Tommy & Hjorth, Allan Nordlunde & Nielsen, Morten & Pisinger, David, 2010. "The off-line group seat reservation problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1244-1253, December.
    3. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    4. Boyer, V. & Elkihel, M. & El Baz, D., 2009. "Heuristics for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(3), pages 658-664, December.
    5. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.
    6. Freville, Arnaud & Plateau, Gerard, 1993. "An exact search for the solution of the surrogate dual of the 0-1 bidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 68(3), pages 413-421, August.
    7. Fred Glover, 1975. "Surrogate Constraint Duality in Mathematical Programming," Operations Research, INFORMS, vol. 23(3), pages 434-451, June.
    8. George Mavrotas & José Figueira & Alexandros Antoniadis, 2011. "Using the idea of expanded core for the exact solution of bi-objective multi-dimensional knapsack problems," Journal of Global Optimization, Springer, vol. 49(4), pages 589-606, April.
    9. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
    10. Florios, Kostas & Mavrotas, George & Diakoulaki, Danae, 2010. "Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms," European Journal of Operational Research, Elsevier, vol. 203(1), pages 14-21, May.
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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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