Hybrid Set Domains to Strengthen Constraint Propagation and Reduce Symmetries

In CP literature combinatorial design problems such as sport scheduling, Steiner systems, error-correcting codes and more, are typically solved using Finite Domain (FD) models despite often being more naturally expressed as Finite Set (FS) models. Existing FS solvers have difficulty with such problems as they do not make strong use of the ubiquitous set cardinality information. We investigate a new approach to strengthen the propagation of FS constraints in a tractable way: extending the domain representation to more closely approximate the true domain of a set variable. We show how this approach allows us to reach a stronger level of consistency, compared to standard FS solvers, for arbitrary constraints as well as providing a mechanism for implementing certain symmetry breaking constraints. By experiments on Steiner Systems and error correcting codes, we demonstrate that our approach is not only an improvement over standard FS solvers but also an improvement on recently published results using FD 0/1 matrix models as well.