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Solving Bin Packing Problems Using VRPSolver Models

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Abstract

We propose branch-cut-and-price algorithms for the classic bin packing problem and also for the following related problems: vector packing, variable sized bin packing, and variable sized bin packing with optional items. The algorithms are defined as models for VRPSolver, a generic solver for vehicle routing problems. In that way, a simple parameterization enables the use of several branch-cut-and-price advanced elements: automatic stabilization by smoothing, limited-memory rank-1 cuts, enumeration, hierarchical strong branching, and limited discrepancy search diving heuristics. As an original theoretical contribution, we prove that the branching over accumulated resource consumption (Gélinas et al, Ann Oper Res 61(1):91–109, 1995) that does not increase the difficulty of the pricing subproblem is sufficient for those bin packing models. Extensive computational results on instances from the literature show that the VRPSolver models have a performance that is very robust over all those problems, being often superior to the existing exact algorithms on the hardest instances. Several instances could be solved to optimality for the first time.

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Acknowledgments

Experiments presented in this paper were carried out using the PlaFRIM (Federative Platform for Research in Computer Science and Mathematics), created under the Inria PlaFRIM development action with support from Bordeaux INP, LABRI, and IMB and other entities: Conseil Régional d’Aquitaine, Université de Bordeaux, CNRS and ANR in accordance to the “Programme d’Investissements d’Avenir.”

Funding

The research was partially supported by the following grants: CNPq 313601/2018-6 and 306033/2019-4, Faperj E-26/202.887/2017, and CAPES PrInt UFF no 88881.

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Authors and Affiliations

  1. Universidade Federal Fluminense - Engenharia de Produção, Rua Passo da Pátria 156, Niterói, RJ, 24210-240, Brasil

    Artur Pessoa & Ruslan Sadykov

  2. Inria Bordeaux – Sud-Ouest, 200 Avenue de la Vieille Tour, 33405, Talence, France

    Eduardo Uchoa

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  1. Artur Pessoa
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  2. Ruslan Sadykov
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  3. Eduardo Uchoa
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Correspondence to Eduardo Uchoa.

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Pessoa, A., Sadykov, R. & Uchoa, E. Solving Bin Packing Problems Using VRPSolver Models. SN Oper. Res. Forum 2, 20 (2021). https://doi.org/10.1007/s43069-020-00047-8

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