Homomorphisms of Lifted Planning Tasks: The Case for Delete-Free Relaxation Heuristics

Abstract

Classical planning tasks are modelled in PDDL which is a schematic language based on first-order logic. Most of the current planners turn this lifted representation into a propositional one via a grounding process. However, grounding may cause an exponential blowup. Therefore it is important to investigate methods for searching for plans on the lifted level. To build a lifted state-based planner, it is necessary to invent lifted heuristics. We introduce maps between PDDL tasks preserving plans allowing to transform a PDDL task into a smaller one. We propose a novel method for computing lifted (admissible) delete-free relaxed heuristics via grounding of the smaller task and computing the (admissible) delete-free relaxed heuristics there. This allows us to transfer the knowledge about relaxed heuristics from the grounded level to the lifted level.

Gaifman Graphs in Lifted Planning

“…In this section, we apply the results from the previous section in order to improve the delete-free relaxation heuristics based on PDDLhomomorphisms described in [14]. We first recall the relevant details.…”

“…Let D be a domain language, and P = B, A, ψ I , ψ G , P = B , A , ψ I , ψ G PDDL tasks over D. A map σ : B → B is called a PDDL homomorphism, denoted by σ : P → P , if the following conditions are satisfied: Consequently, if we are able to compute an admissible heuristic on P , we can use it to lower bound h * P (s). To find a suitable P , the paper [14] proposed the following construction. Let P = B, A, ψ I , ψ G ∈ PDDL + be a delete-free PDDL task.…”

“…We define a new delete-free PDDL task σ(P) = σ(B), A, σ(ψ I ), σ(ψ G ) where the action costs in σ(P) are defined as ca(σ b) = min{c a ( c) | c ∈ B ar(a) , σ c = σ b}. The map σ is a PDDL homomorphism from P to σ(P); see [14,Theorem 8].…”

“…for any reachable state s in P. The paper [14] generated the self maps σ randomly and considered the map giving the most informative heuristic for the initial state. Instead of generating σ randomly, we provide a strategy for finding good self maps σ.…”

“…The second part of the paper applies our theoretical results to improve delete-free relaxation heuristics introduced in [14], where it was proved that any self-map σ : B → B on the set of objects B of a PDDL task P is a PDDL homomorphism from P to a smaller PDDL task P , whose set of objects is σ(B). Consequently, any admissible heuristic computed on P induces an admissible heuristic on P via σ.…”