Continuing the Quest for Polynomial Time Heuristics in PDDL Input Size: Tractable Cases for Lifted hᵃᵈᵈ

Recent interest in solving planning tasks, where full grounding is infeasible, has highlighted the need to compute heuristics at a lifted level. We turn our attention to the evaluation of the hᵃᵈᵈ heuristic, which is an important cornerstone in many classical planning approaches, including the best performing lifted planning approach. We show that hᵃᵈᵈ’s grounded efficiency does not extend to lifted tasks, where the computation is EXPTIME-complete. This prompts to identify tractability islands matching practical use cases. We identify two, where a lifted computation is feasible while grounding may fail: The first constraints to acyclic action schemata and bounds predicate arity. For the second case we introduce a novel computation, operating without grounding. Assuming the extraction encounters only acyclic conditions, and hᵃᵈᵈ values per subgoal are bounded, it remains tractable. (Even with unbounded predicate and action arity.) In an empirical evaluation of the new technique, we observe complementary behavior to the existing lifted forward hᵃᵈᵈ evaluation. Combining both sets a new state-of-the-art in pure-heuristic performance on the hard-to-ground benchmarks.