, Volume 17, Issue 3, pp 205-233

First online:

Improved filtering for weighted circuit constraints

  • Pascal BenchimolAffiliated withINRIA Saclay and CMAP, École Polytechnique
  • , Willem-Jan van HoeveAffiliated withTepper School of Business, Carnegie Mellon University Email author 
  • , Jean-Charles RéginAffiliated withI3S-CNRS, University of Nice-Sophia Antipolis
  • , Louis-Martin RousseauAffiliated withCIRRELT, École Polytechnique de Montréal
  • , Michel RueherAffiliated withI3S-CNRS, University of Nice-Sophia Antipolis

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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 constraint Circuit Optimization constraint Relaxation Constraint propagation