LM-Cut Heuristics for Optimal Linear Numeric Planning

Abstract

While numeric variables play an important, sometimes central, role in many planning problems arising from real world scenarios, most of the currently available heuristic search planners either do not support such variables or impose heavy restrictions on them. In particular, most admissible heuristics are restricted to domains where actions can only change numeric variables by predetermined constants. In this work, we consider the setting of optimal numeric planning with linear effects, where actions can have numeric effects that assign the result of the evaluation of a linear formula. We extend a recent formulation of Numeric LM-cut for simple effects by adding conditional effects and second-order simple effects, allowing the heuristic to produce admissible estimates for tasks with linear numeric effects. Empirical comparison shows that the proposed LM-cut heuristics favorably compete with the currently available state-of-the-art heuristics and achieve significant improvement in coverage in the domains with second-order simple effects.

OMTPlan: A Tool for Optimal Planning Modulo Theories

“…This is particularly evident in domains that feature a high-degree of parallelism, which OMTPlan can exploit to build more succinct encodings. Similar results have also been reported by [10], where OMTPlan outperformed SoA planners on linear domains. We highlight that C SC does not support planning with state-dependent costs; ENHSP does not provide admissible heuristics for linear numeric planning.…”

Symbolic Numeric Planning with Patterns

“…For the experimental analysis we considered all the domains and problems of the 2023 Numeric International Planning Competition (IPC) (Arxer and Scala 2023). We compared our planner PATTY with the three symbolic planners SPRINGROLL (based on the rolled-up Π R encoding (Scala et al 2016b)), a version of PATTY computing the R 2 ∃ <encoding Π < with < compatible with ≺, and called it R 2 ∃; and OMTPLAN (based on the Π S standard encoding), and the three search-based planners ENHSP (Scala et al 2016a), METRICFF (Hoffmann 2003) and NUMERICFASTDOWN-WARD (NFD) (Kuroiwa, Shleyfman, and Beck 2022). NFD and OMTPLAN are the two planners that competed in the last IPC, ranking first and second, respectively.…”

Extracting and Exploiting Bounds of Numeric Variables for Optimal Linear Numeric Planning

“…Linear numeric planning is a subset of PDDL 2.1 [4] (see the PICKUP domain explained in Sec. 5.1 and supplementary materials [11]). A task is represented by a 5-tuple F , N , A, s 0 , G , where F is the set of propositions, N is the set of numeric variables, s 0 is the initial state, and G is the set of goal conditions.…”

“…A case in point is numeric planning, an extension of classical planning with numeric state variables, that has recently had a resurgence in popularity. While early research focused only on the satisficing setting, where the objective is to find an executable plan regardless of its length or cost [8,3], recent work has developed techniques to solve numeric planning problems optimally using model-based approaches [16,13] and heuristic search [21,19,17,12,10]. In particular, heuristic search approaches use A * search [5] with admissible heuristic functions, which compute a lower bound of the optimal cost, and achieve state-of-the-art performance.…”

“…We obtain bounds on numeric variables using inductive equations and prove that their fixed point yields valid bounds. While such bounds can be useful for both model-based and heuristic search approaches, we incorporate them in LM-cut [10], a state-ofthe-art admissible heuristic for linear numeric planning, without loss of the admissibility. We empirically show that the use of the bounds improves the performance of LM-cut in almost all of the existing numeric planning domains.…”