LM-cut and Operator Counting Heuristics for Optimal Numeric Planning with Simple Conditions

Abstract

We consider optimal numeric planning with numeric conditions consisting of linear expressions of numeric state variables and actions that increase or decrease numeric state variables by constant quantities. We build on previous research to introduce a new variant of the numeric hmax heuristic based on the delete-relaxed version of such planning tasks. Although our hmax heuristic is inadmissible, it yields a numeric version of the classical LM-cut heuristic which is admissible. Further, we prove that our LM-cut heuristic neither dominates nor is dominated by the existing numeric heuristic hmax(hbd). We show that admissibility also holds when integrating the numeric cuts into the operator-counting (OC) heuristic producing an admissible numeric version of the OC heuristic. Through experiments, we demonstrate that both these heuristics compete favorably with the state-of-the-art heuristics: in particular, while sometimes expanding more nodes than other heuristics, numeric OC solves 19 more problem instances than the next closest heuristic.

LM-Cut Heuristics for Optimal Linear Numeric Planning

“…Then, the weight of the cut W(L) = min e∈L W(e) is admissible for Π 1 OVC,1 . Proof Sketch: The proof is an extension of the proof of Thm.1 in Kuroiwa et al (2021) to account for the 'plus infinity' effects. This case resembles the case of regular LM-cut, from the perspective of the 'plus infinity' action, the fact v = ∞ is binary, and is either achieved or not.…”

“…The progress of methods for satisficing planning gave rise to the question 'can one plan optimally in presence of numeric variables in practice?'. The answer to this question was positive: recently, multiple admissible heuristics were proposed for numeric planning (Scala et al 2020(Scala et al , 2017Piacentini et al 2018b;Kuroiwa et al 2021). These heuristics, however, are limited to tasks with simple effects, i.e., each action increases or decreases the value of a numeric variable by a constant.…”

“…In this paper, we extend the LM-cut heuristic for numeric planning tasks with simple conditions (SCT) (Kuroiwa et al 2021) to linear numeric planning tasks (LT), an extension that includes linear effects which increase or decrease numeric variables by linear combinations of the numeric variables. While several heuristics exist in the satisficing setting of this formalism (Hoffmann 2003;Li et al 2018), our heuristics are the first admissible heuristics exploiting the structure of LT.…”

“…SCT can be reduced to RT by introducing a new numeric variable for each SC and modifying numeric effects so that they change the variable by the net effects on the SC. Given an SCT Π = F , N , A, s I , G , Kuroiwa et al (2021) construct a transformed task Π RT to be the 5tuple F , N RT , A RT , s RT I , G RT defined as follows. For numeric condition ψ : v∈N w ψ v v w 0 , we add an auxiliary numeric variable u ψ ∈ N RT that corresponds to the left-hand side of the condition and replace ψ with u ψ w ψ 0 .…”

“…LM-Cut in Numeric Planning with Simple Effects Helmert and Domshlak (2009) introduced the LM-cut heuristic for classical planning. Kuroiwa et al (2021) adapted this heuristic to the SCT setting by compiling SCT to RT. Here, we briefly present their notations and algorithm.…”