Constraints

, Volume 17, Issue 3, pp 205–233

Improved filtering for weighted circuit constraints

  • Pascal Benchimol
  • Willem-Jan van Hoeve
  • Jean-Charles Régin
  • Louis-Martin Rousseau
  • Michel Rueher
Article

DOI: 10.1007/s10601-012-9119-x

Cite this article as:
Benchimol, P., Hoeve, WJ.., Régin, JC. et al. Constraints (2012) 17: 205. doi:10.1007/s10601-012-9119-x

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.

Keywords

Global constraintCircuitOptimization constraintRelaxationConstraint propagation

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Pascal Benchimol
    • 1
  • Willem-Jan van Hoeve
    • 2
  • Jean-Charles Régin
    • 3
  • Louis-Martin Rousseau
    • 4
  • Michel Rueher
    • 3
  1. 1.INRIA Saclay and CMAPÉcole PolytechniquePalaiseauFrance
  2. 2.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA
  3. 3.I3S-CNRSUniversity of Nice-Sophia AntipolisNiceFrance
  4. 4.CIRRELTÉcole Polytechnique de MontréalMontréalCanada