Combining Arc-Consistency and Dual Lagrangean Relaxation for Filtering CSPs

This paper presents a CSPs filtering method combining arc-consistency and dual Lagrangean relaxation techniques. First, we model the constraint satisfaction problem as a 0/1 linear integer program (IP); then, the consistency of a value is defined as an optimization problem on which a dual Lagrangean relaxation is defined. While solving the dual Lagrangean relaxation, values inconsistencies may be detected (dual Lagrangean inconsistent values); the constraint propagation of this inconsistency can be performed by arc-consistency. After having made the CSP arc-consistent, the process iteratively selects values of variables which may be dual Lagrangean inconsistent. Computational experiments performed over randomly generated problems show the advantages of the hybrid filtering technique combining arc-consistency and dual Lagrangean relaxation.

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