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

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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.

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Authors and Affiliations

  1. Global Edge Institute, Tokyo Institute of Technology, Meguro, Tokyo, Japan

    Alex S. Fukunaga

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  1. Alex S. Fukunaga
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Correspondence to Alex S. Fukunaga.

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Fukunaga, A.S. A branch-and-bound algorithm for hard multiple knapsack problems. Ann Oper Res 184, 97–119 (2011). https://doi.org/10.1007/s10479-009-0660-y

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  • DOI: https://doi.org/10.1007/s10479-009-0660-y

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