We describe a new algorithm for generating pattern collections for pattern database heuristics in optimal classical planning. The algorithm uses the counterexample-guided abstraction refinement (CEGAR) principle to guide the pattern selection process. Our experimental evaluation shows that a single run of the CEGAR algorithm can compute informative pattern collections in a fairly short time. Using multiple CEGAR algorithm runs, we can compute much larger pattern collections, still in shorter time than existing approaches, which leads to a planner that outperforms the state-of-the-art pattern selection methods by a significant margin.

Potential functions are a general class of heuristics for classical planning. For satisficing planning, previous work suggested the use of descending and dead-end avoiding (DDA) potential heuristics, which solve planning tasks by backtrack-free search. In this work we study the complexity of devising DDA potential heuristics for classical planning tasks. We show that verifying or synthesizing DDA potential heuristics is PSPACE-complete, but suitable modifications of the DDA properties reduce the complexity of these problems to the first and second level of the polynomial hierarchy. We also discuss the implications of our results for other forms of heuristic synthesis in classical planning.