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A branch-and-bound algorithm for hard multiple knapsack problems

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  • Alex Fukunaga

Abstract

The multiple knapsack problem (MKP) is a classical combinatorial optimization problem. A recent algorithm for some classes of the MKP is bin-completion, a bin-oriented, branch-and-bound algorithm. In this paper, we propose path-symmetry and path-dominance criteria for pruning nodes in the MKP branch-and-bound search space. In addition, we integrate the “bound-and-bound” upper bound validation technique used in previous MKP solvers. We show experimentally that our new MKP solver, which successfully integrates dominance based pruning, symmetry breaking, and bound-and-bound, significantly outperforms previous solvers on some classes of hard problem instances. Copyright Springer Science+Business Media, LLC 2011

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  • Alex Fukunaga, 2011. "A branch-and-bound algorithm for hard multiple knapsack problems," Annals of Operations Research, Springer, vol. 184(1), pages 97-119, April.
    • Handle: RePEc:spr:annopr:v:184:y:2011:i:1:p:97-119:10.1007/s10479-009-0660-y
    DOI: 10.1007/s10479-009-0660-y
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    1. Labbe, Martine & Laporte, Gilbert & Martello, Silvano, 2003. "Upper bounds and algorithms for the maximum cardinality bin packing problem," European Journal of Operational Research, Elsevier, vol. 149(3), pages 490-498, September.
    2. Giorgio Ingargiola & James F. Korsh, 1975. "An Algorithm for the Solution of 0-1 Loading Problems," Operations Research, INFORMS, vol. 23(6), pages 1110-1119, December.
    3. Pisinger, David, 1999. "An exact algorithm for large multiple knapsack problems," European Journal of Operational Research, Elsevier, vol. 114(3), pages 528-541, May.
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    1. Dell’Amico, Mauro & Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2019. "Mathematical models and decomposition methods for the multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 274(3), pages 886-899.
    2. Setzer, Thomas & Blanc, Sebastian M., 2020. "Empirical orthogonal constraint generation for Multidimensional 0/1 Knapsack Problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 58-70.
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    6. Olivier Lalonde & Jean-François Côté & Bernard Gendron, 2022. "A Branch-and-Price Algorithm for the Multiple Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3134-3150, November.

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