A hybrid constraint model for the routing and wavelength assignment problem
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
The extended global cardinality constraint: An empirical survey
Artificial Intelligence
View-based propagator derivation
Constraints
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We study in this thesis three well known global constraints. The A LL-DIFFERENT constraint restricts a set of variables to be assigned to distinct values. The global cardinality constraint (GCC) ensures that a value v is assigned to at least lv variables and to at most u v variables among a set of given variables where l v and uv are non-negative integers such that lv ≤ uv. The INTER-DISTANCE constraint ensures that all variables, among a set of variables x1,..., xn, are pairwise distant from p, i.e. |xi - xj| for all i ≠ j. The ALL-DIFFERENT constraint, the GCC, and the INTER-DISTANCE constraint are largely used in scheduling problems. For instance, in scheduling problems where tasks with unit processing time compete for a single resource, we have an ALL-DIFFERENT constraint on the starting time variables. When there are k resources, we have a GCC with lv = 0 and uv = k over all starting time variables. Finally, if tasks have processing time t and compete for a single resource, we have an INTER-DISTANCE constraint with p = t over all starting time variables. We present new propagators for the ALL-DIFFERENT constraint, the GCC, and the INTER-DISTANCE constraint i.e., new filtering algorithms that reduce the search space according to these constraints. For a given consistency, our propagators outperform previous propagators both in practice and in theory. The gains in performance are achieved through judicious use of advanced data structures combined with novel results on the structural properties of the constraints.