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 if predicate and action arity is unbounded. 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.

In classical planning, admissible potential heuristics are computed by solving linear programs (LPs) with constraints expressing consistency and goal-awareness of the heuristic. Potential heuristics can return negative estimates. So, given a potential heuristic h(P), the actual heuristic used in search is another heuristic defined as h(0+)(P)(s)= max(h(P) (s), 0) for every reachable state s. In this paper, we reformulate the LP constraints for consistency of h(P) so that they ensure consistency of h(0+)(P) instead. This leads to more informative heuristics with positive impact on the overall performance in exchange for a more time and memory demanding computation using mixed integer linear programs instead of LPs.

Polynomial-time heuristic functions for planning are commonplace since 20 years. But polynomial-time in which input? Almost all existing approaches are based on a grounded task representation, not on the actual PDDL input which is exponentially smaller. This limits practical applicability to cases where the grounded representation is "small enough". Previous attempts to tackle this problem for the delete relaxation leveraged symmetries to reduce the blow-up. Here we take a more radical approach, applying an additional relaxation to obtain a heuristic function that runs in time polynomial in the size of the PDDL input. Our relaxation splits the predicates into smaller predicates of fixed arity K. We show that computing a relaxed plan is still NP-hard (in PDDL input size) for K>=2, but is polynomial-time for K=1. We implement a heuristic function for K=1 and show that it can improve the state of the art on benchmarks whose grounded representation is large.

LM-cut is one of the most popular heuristics in optimal planning that computes strong admissible estimates of the perfect delete relaxation heuristic h. The heuristic iteratively computes disjunctive action landmarks for the current state, reducing their action costs until no more landmarks with remaining action costs can be found. These landmarks are generated by finding cuts in the justification graph, which depends on a precondition choice function mapping each action to its most expensive precondition according to h. This precondition is not necessarily unique, yet the performance of the heuristic heavily depends on this choice. We introduce and analyze several new tie breaking strategies for the precondition choice function, and evaluate their effectiveness on the IPC benchmarks. Furthermore, we suggest a modification to the computation of the cut, which trades a negligible loss in heuristic accuracy for a significant speedup of the LM-cut

Learning programming can be hard, especially for inexperienced freshman. An aMAZEing team of 30 students decided to lighten that challenge for their fellow students. This paper will present the attempt of volunteers to prepare their fellow students for their programming course, resulting in a week full of lectures, projects, coachings and didactical effort.