Compiling CP subproblems to MDDs and d-DNNFs

Abstract

Modeling discrete optimization problems is not straightforward. It is often the case that precompiling a subproblem that involves only a few tightly constrained variables as a table constraint can improve solving time. Nevertheless, enumerating all the solutions of a subproblem into a table can be costly in time and space. In this work we propose using Multivalued Decision Diagrams (MDDs) and formulas in Deterministic Decomposable Negation Normal Form (d-DNNFs) rather than tables to compute and store all solutions of a subproblem. This, in turn, can be used to enhance the solver thanks to stronger propagation via specific propagators for these structures. We show how to precompile part of a problem into both these structures, which can then be injected back in the model by substituting the constraints it encodes, or simply adding it as a redundant constraint. Furthermore, in the case of MDDs, they can also be used to create edge-valued MDDs for optimization problems with an appropriate form. From our experiments we conclude that all three techniques are valuable in their own right, and show when each one should be chosen over the others.