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Discrepancy-Based Additive Bounding Procedures

D.E.I.S., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
D.E.I.S., University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
Centre for Research on Transportation, Université de Montréal, CP 6128, Succ. Centre-Ville, Montréal, Canada H3C 3J7
alodi{at}deis.unibo.it
mmilano{at}deis.unibo.it
louism{at}crt.umontreal.ca

We model portions of the search tree via so-called search constraints. We focus on a particular kind of search constraint, the k-discrepancy constraint appearing in discrepancy-based search. The property that a node has an associated discrepancy k can be modeled (and enforced) through a linear constraint. Our key result is the exploitation of the k-discrepancy constraint to improve the bound given by any relaxation of a combinatorial optimization problem through the additive bounding technique (Fischetti and Toth 1989). We show how this simple idea can be effectively exploited to tighten relaxations in CP solvers and speed up the proof of optimality by performing a large variety of computational experiments on test problems involving the AllDifferent constraint. In this view, the additive bounding technique represents a non-trivial link between search and bound. Moreover, such a technique is general because it does not depend on either the AllDifferent constraint or the discrepancy search technique.

Key words: limited discrepancy search; additive bounding; relaxations; constraint programming
History: received November 2003; revised June 2005; accepted September 2005.