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The WeightedCircuitsLmax Constraint

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10848))

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Abstract

The travelling salesman problem is a well-known problem that can be generalized to the m-travelling salesmen problem with min-max objective. In this problem, each city must be visited by exactly one salesman, among m travelling salesmen. We want to minimize the longest circuit travelled by a salesman. This paper generalizes the Circuit and WeightedCircuit constraints and presents a new constraint that encodes m cycles all starting from the same city and whose lengths are bounded by a variable \(L_{max}\). We propose two filtering algorithms, each based on a relaxation of the problem that uses the structure of the graph and the distances between each city. We show that this new constraint improves the solving time for the m travelling salesmen problem.

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Authors and Affiliations

  1. Université Laval, Québec City, Canada

    Kim Rioux-Paradis & Claude-Guy Quimper

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  1. Kim Rioux-Paradis
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  2. Claude-Guy Quimper
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Correspondence to Claude-Guy Quimper .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Willem-Jan van Hoeve

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Rioux-Paradis, K., Quimper, CG. (2018). The WeightedCircuitsLmax Constraint. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_35

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  • DOI: https://doi.org/10.1007/978-3-319-93031-2_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93030-5

  • Online ISBN: 978-3-319-93031-2

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