Polynomial-Time in PDDL Input Size: Making the Delete Relaxation Feasible for Lifted Planning

Pascal Lauer, Alvaro Torralba, Daniel Fišer, Daniel Höller, Julia Wichlacz, Joerg Hoffmann

Keywords: Lifted Planning, Heuristic Search, Delete Relaxation

TL;DR: The main focus of the paper is to introduce a relaxation allowing to quickly generate heuristic estimates from a lifted task representation.

Abstract: 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 applicabilty 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.