Explaining Flow-Based Propagation

Lazy clause generation is a powerful approach to reducing search in constraint programming. For use in a lazy clause generation solver, global constraints must be extended to explain themselves. In this paper we present two new generic flow-based propagators (for hard and soft flow-based constraints) with several novel features, and most importantly, the addition of explanation capability. We discuss how explanations change the tradeoffs for propagation compared with the previous generic flow-based propagator, and show that the generic propagators can efficiently replace specialized versions, in particular for gcc and sequence constraints. Using real-world scheduling and rostering problems as examples, we compare against a number of standard Constraint Programming implementations of these contraints (and in the case of soft constraints, Mixed-Integer Programming models) to show that the new global propagators are extremely beneficial on these benchmarks.