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Column Elimination for Capacitated Vehicle Routing Problems

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13884))

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Abstract

We introduce a column elimination procedure for the capacitated vehicle routing problem. Our procedure maintains a decision diagram to represent a relaxation of the set of feasible routes, over which we define a constrained network flow. The optimal solution corresponds to a collection of paths in the decision diagram and yields a dual bound. The column elimination process iteratively removes infeasible paths from the diagram to strengthen the relaxation. The network flow model can be solved as a linear program with a conventional solver or via a Lagrangian relaxation. To solve the Lagrangian subproblem more efficiently, we implement a special successive shortest paths algorithm. We introduce several cutting planes to strengthen the dual bound, including a new type of clique cut that exploits the structure of the decision diagram. We experimentally compare the bounds from column elimination with those from column generation for capacitated vehicle routing problems.

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Acknowledgements

This work is partially supported by Office of Naval Research Grant No. N00014-21-1-2240 and National Science Foundation Award #1918102. This material is also based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1745016, DGE2140739. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Anthony Karahalios & Willem-Jan van Hoeve

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  1. Anthony Karahalios
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  2. Willem-Jan van Hoeve
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Correspondence to Anthony Karahalios .

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Editors and Affiliations

  1. Department of Management, University of Toronto Scarborough and Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Andre A. Cire

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Karahalios, A., van Hoeve, WJ. (2023). Column Elimination for Capacitated Vehicle Routing Problems. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_3

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  • DOI: https://doi.org/10.1007/978-3-031-33271-5_3

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