Improved filtering for weighted circuit constraints
 Pascal Benchimol,
 WillemJan van Hoeve,
 JeanCharles Régin,
 LouisMartin Rousseau,
 Michel Rueher
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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 1tree relaxation of Held and Karp. In addition, we study domain filtering based on an additive bounding procedure that combines the 1tree 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 mediumsize problem instances, our method is competitive with the stateoftheart specialpurpose TSP solver Concorde.
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 Title
 Improved filtering for weighted circuit constraints
 Journal

Constraints
Volume 17, Issue 3 , pp 205233
 Cover Date
 20120701
 DOI
 10.1007/s106010129119x
 Print ISSN
 13837133
 Online ISSN
 15729354
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Global constraint
 Circuit
 Optimization constraint
 Relaxation
 Constraint propagation
 Authors

 Pascal Benchimol ^{(1)}
 WillemJan van Hoeve ^{(2)}
 JeanCharles Régin ^{(3)}
 LouisMartin Rousseau ^{(4)}
 Michel Rueher ^{(3)}
 Author Affiliations

 1. INRIA Saclay and CMAP, École Polytechnique, Palaiseau, France
 2. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA
 3. I3SCNRS, University of NiceSophia Antipolis, Nice, France
 4. CIRRELT, École Polytechnique de Montréal, Montréal, Canada