A generic exact solver for vehicle routing and related problems

Abstract

Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best existing VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, path enumeration, and rounded capacity cuts; all generalized through the new concepts of “packing set” and “elementarity set”. The concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the Ryan and Foster branching rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

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Acknowledgements

We would like to thank Teobaldo Bulhoes and Guillaume Marques for a large part of the implementation of the Julia–JuMP interface to the solver; Teobaldo Bulhoes, Guillaume Marques and Eduardo Queiroga for implementing, over that interface, the models corresponding to the examples of this paper; and Laurent Facq for a general support of the computing environment. 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”. This study was financed in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Grant 313601/2018-6 (Produtividade 1B), and by the Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant E-26/202.887/2017 (Cientista do Estado).

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Pessoa, A., Sadykov, R., Uchoa, E. et al. A generic exact solver for vehicle routing and related problems. Math. Program. (2020). https://doi.org/10.1007/s10107-020-01523-z

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Keywords

  • Integer programming
  • Column generation
  • Routing

Mathematics Subject Classification

  • 90C11 Mixed integer programming
  • 90C06 Large-scale problems in mathematical programming
  • 90B06 Transportation
  • logistics and supply chain management
  • 90-04 Software
  • source code
  • etc. for problems pertaining to operations research and mathematical programming