Learning The Parameters Of Global Constraints Using Branch-And-Bound

Precise constraint satisfaction modeling requires specific knowledge acquired from multiple past cases. We address this issue with a general branch-and-bound algorithm that learns the parameters of a given global constraint from a small set of positive solutions. The idea is to cleverly explore the possible combinations taken by the constraint's parameters without explicitly enumerating all combinations. We apply our method to learn parameters of global constraints used in timetabling problems such as Sequence and SubsetFocus. The later constraint is our adaptation of the constraint Focus to timetabling problems.