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Clique Cuts in Weighted Constraint Satisfaction

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Principles and Practice of Constraint Programming (CP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

Abstract

In integer programming, cut generation is crucial for improving the tightness of the linear relaxation of the problem. This is relevant for weighted constraint satisfaction problems (WCSPs) in which we use approximate dual feasible solutions to produce lower bounds during search. Here, we investigate using one class of cuts in WCSP: clique cuts. We show that clique cuts are likely to trigger suboptimal behavior in the specialized algorithms that are used in WCSP for generating dual bounds and show how these problems can be corrected. At the same time, the additional structure present in WCSP allows us to slightly generalize these cuts. Finally, we show that cliques exist in instances from several benchmark families and that exploiting them can lead to substantial performance improvement.

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Notes

  1. 1.

    This is the micro-structure of the WCSP, restricted only to binary tuples with infinite cost.

  2. 2.

    In this case, triangle-based consistencies [31] achieve the same effect, but not in arbitrary arity cliques.

  3. 3.

    Version 4.4.0, using free search.

  4. 4.

    Using parameter -pe parallel_smp 2 on a SUN Grid Engine to ensure half-load of the cores on the cluster.

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Acknowledgements

This work has been partially funded by the french “Agence nationale de la Recherche”, reference ANR-16-C40-0028. We are grateful to the Bioinfo Genotoul platform Toulouse Midi-Pyrenees for providing computing resources.

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  1. MIAT, UR-875, INRA, 31320, Castanet Tolosan, France

    Simon de Givry & George Katsirelos

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  1. Simon de Givry
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  2. George Katsirelos
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Correspondence to George Katsirelos .

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  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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de Givry, S., Katsirelos, G. (2017). Clique Cuts in Weighted Constraint Satisfaction. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_7

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