Improved Constraint Propagation via Lagrangian Decomposition

Constraint propagation is inherently restricted to the local information that is available to each propagator. We propose to improve the communication between constraints by introducing Lagrangian penalty costs between pairs of constraints, based on the Lagrangian decomposition scheme. The role of these penalties is to force variable assignments in each of the constraints to correspond to one another. We apply this approach to constraints that can be represented by decision diagrams, and show that propagating Lagrangian cost information can help improve the overall bound computation as well as the solution time.