an:06506229
Zbl 1327.90130
Cambazard, Hadrien; Fages, Jean-Guillaume
New filtering for \textsc{AtMostNValue} and its weighted variant: a Lagrangian approach
EN
Constraints 20, No. 3, 362-380 (2015).
00344716
2015
j
90C11
global constraint; filtering algorithm; Lagrangian relaxation; at most n values
Summary: The \textsc{AtMostNValue} global constraint, which restricts the maximum number of distinct values taken by a set of variables, is a well known NP-Hard global constraint. The weighted version of the constraint, \textsc{AtMostWValue}, where each value is associated with a weight or cost, is a useful and natural extension. Both constraints occur in many industrial applications where the number and the cost of some resources have to be minimized. This paper introduces a new filtering algorithm based on a Lagrangian relaxation for both constraints. This contribution is illustrated on problems related to facility location, which is a fundamental class of problems in operations research and management sciences. Preliminary evaluations show that the filtering power of the Lagrangian relaxation can provide significant improvements over the state-of-the-art algorithm for these constraints. We believe it can help to bridge the gap between constraint programming and linear programming approaches for a large class of problems related to facility location.