Implementing Global Constraints with Index-Sets and Constraint Templates

Abstract

In order to improve the deductive power of ffinite domain constraint solvers usually redundant and global constraints are added to the constraint system. The objective of this work [2] is to develop a new constraint solving scheme designed as an extension of a classical arc-consistency algorithm. Associated to a declarative language, it allows the user to implement his own global relations without the need of manipulating internal structures of the solver or modifying in depth the original model of the studied problem. This system relies on two new structures: index-sets and constraint templates. The former consist in sets of integers used as indices over tables. They collect variables sharing some properties (for instance tasks in a scheduling problem assigned to the same machine). The latter are descriptions of constraints that must be applied (possibly) over selected sets of variables (for instance the fact that a set of tasks must be scheduled before another set). Both, set-index and constraint template deffnitions are evaluated dynamically and depend on the variables’ domains. Indeed, the new constraints are automatically generated by the constraint solver based on the set contents and variable domain values. The index-set and constraint deffinition language uses a mathematic style notation. The deffnitions are compiled to the solver representation which can be directly handled by the propagation mechanism. This organisation guarantees a high level of efficiency.