Optimization Bounds from Decision Diagrams in Haddock.

We study the automatic generation of primal and dual bounds from decision diagrams in constraint programming. In particular, we expand the functionality of the Haddock system to optimization problems by extending its specification language to include an objective function. We describe how restricted decision diagrams can be compiled in Haddock similar to the existing relaxed decision diagrams. Together, they provide primal and dual bounds on the objective function, which can be seamlessly integrated into the constraint programming search. The entire process is automatic and only requires a high-level user model specification. We evaluate our method on the sequential ordering problem and compare the performance of Haddock to a dedicated decision diagram approach. The results show that Haddock achieves comparable results in similar time, demonstrating the viability of our automated decision diagram procedures for constraint optimization problems.