, Volume 17, Issue 3, pp 205–233

Improved filtering for weighted circuit constraints


  • Pascal Benchimol
    • INRIA Saclay and CMAPÉcole Polytechnique
    • Tepper School of BusinessCarnegie Mellon University
  • Jean-Charles Régin
    • I3S-CNRSUniversity of Nice-Sophia Antipolis
  • Louis-Martin Rousseau
    • CIRRELTÉcole Polytechnique de Montréal
  • Michel Rueher
    • I3S-CNRSUniversity of Nice-Sophia Antipolis

DOI: 10.1007/s10601-012-9119-x

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


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.


Global constraintCircuitOptimization constraintRelaxationConstraint propagation
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© Springer Science+Business Media, LLC 2012