Towards Numerical TOHTN Planning with SMT-based HTN-SAT Encoding

In this paper, we present a procedure for numeric planning based on Symbolic Pattern Planning (SPP). Given a numeric planning problem $Π$, a pattern $\prec$ is a sequence of actions used to define a formula encoding the subsequences of $\prec$ executable from a starting state $S$. Cardellini, Giunchiglia, and Maratea (2024a) follow the Planning as Satisfiability approach by defining, at each step $n \ge 0$, a formula $Π^\prec_n$ in which $(i)$ the pattern $\prec$ is computed only for $n=0$ in the initial state $I$ of $Π$, and then exploited at each step $n$, $(ii)$ the starting state $S$ is set to $I$, and $(iii)$ the set $G$ of goals is required to hold in the last state that can be reached by one of the subsequences of $\prec$ concatenated $n$ times. The procedure begins with $n=0$, terminates as soon as $Π^\prec_n$ is satisfiable, and otherwise proceeds by incrementing $n$. In this paper, possibly at each step, $(i)$ we symbolically search for an intermediate state $P$ reachable from $I$, closer to a goal state, $(ii)$ dynamically recompute the pattern $\prec_h$ -- to be used in the next step -- in $P$, $(iii)$ refine the pattern $\prec_g$ used to reach $P$, and $(iv)$ start the new search from the state $S$ which can be either the initial state $I$ or the last computed intermediate state $P$, exploiting the computed patterns $\prec_g$ and $\prec_h$ to define the pattern $\prec$ to be used in the search. In particular, at each step, we define a formula $Π^{\prec}_{S,P}$ encoding the existence of a state $P'$ closer than $P$ to a goal state, with $P'$ reachable from the starting state $S$ when using the pattern $\prec$. We present different techniques for producing such formulas, each corresponding to a different strategy for exploring the search space. We prove their correctness and completeness, the latter under certain conditions.

Factored tasks are a classical planning representation that extends SAS+ with limited forms of disjunctive preconditions, conditional effects, and angelic nondeterminism. This allows for a more compact representation of tasks than traditional formalisms such as STRIPS or SAS+, and supports a wide range of task transformations. However, existing planning approaches for factored tasks have been limited to heuristic search methods. In this work, we investigate how to encode factored tasks in SAT. We propose several ways to encode the tasks, focusing on different strategies for translating the factored transition relation into propositional logic. We also analyze how to exploit parallelism at various levels in this setting and study the impact of common task transformations on the performance of SAT-based planners.

HTN planning is a variation of classical planning where, instead of searching for a linear sequence of actions, an algorithm decomposes higher-level tasks using a method library until only executable actions remain. On one hand, this allows one to introduce domain knowledge that can speed up the search for a solution through the method library. On the other hand, it creates challenges that go beyond those of classical state-space search. While recent research produced a number of heuristics and novel algorithms that speed up HTN planning, these heuristics are not yet as informative as those available in classical planning algorithms. We investigate whether large language models (LLMs) can generate effective search heuristics for HTN planning, extending the methodology of Corrêa, Pereira, and Seipp (2025) from classical to hierarchical planning. Using the Pytrich planner on six standard total-order HTN benchmark domains, we evaluate heuristics generated by nine LLMs under domain-specific prompting and compare them against the TDG and LMCount domain-independent baselines and the PANDA planner. Our results show that LLM-generated heuristics nearly match the coverage of the best available HTN planner, while substantially reducing search effort on 83% of shared problems.