Discrepancy-based additive bounding procedures

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 All Different 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.