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Improved filtering for weighted circuit constraints

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Abstract

We study the weighted circuit constraint in the context of constraint programming. It appears as a substructure in many practical applications, particularly routing problems. We propose a domain filtering algorithm for the weighted circuit constraint that is based on the 1-tree relaxation of Held and Karp. In addition, we study domain filtering based on an additive bounding procedure that combines the 1-tree relaxation with the assignment problem relaxation. Experimental results on Traveling Salesman Problem instances demonstrate that our filtering algorithms can dramatically reduce the problem size. In particular, the search tree size and solving time can be reduced by several orders of magnitude, compared to existing constraint programming approaches. Moreover, for medium-size problem instances, our method is competitive with the state-of-the-art special-purpose TSP solver Concorde.

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Author information

Authors and Affiliations

  1. INRIA Saclay and CMAP, École Polytechnique, Palaiseau, France

    Pascal Benchimol

  2. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA

    Willem-Jan van Hoeve

  3. I3S-CNRS, University of Nice-Sophia Antipolis, Nice, France

    Jean-Charles Régin & Michel Rueher

  4. CIRRELT, École Polytechnique de Montréal, Montréal, Canada

    Louis-Martin Rousseau

Authors
  1. Pascal Benchimol
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  2. Willem-Jan van Hoeve
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  3. Jean-Charles Régin
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  4. Louis-Martin Rousseau
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  5. Michel Rueher
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Correspondence to Willem-Jan van Hoeve.

Additional information

The work of P. Benchimol was performed while being at CIRRELT, École Polytechnique de Montréal.

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Benchimol, P., Hoeve, WJ.v., Régin, JC. et al. Improved filtering for weighted circuit constraints. Constraints 17, 205–233 (2012). https://doi.org/10.1007/s10601-012-9119-x

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