In optimal heuristic search, A* is known to be optimally efficient in terms of node expansions when the only source of information available to guide the search is a heuristic function. However, when a dominance relation is available, dominance pruning can further reduce the number of node expansions while preserving optimality. In this work, we show that pruning nodes does not fully leverage the information dominance relations provide. Instead, one can use dominance to propagate heuristic information between states. This results in a search algorithm that shares information among different regions of the search space. This is always as informative as dominance pruning, and can potentially reduce search effort.

Dominance pruning is a technique to reduce search effort by comparing states against each other and discarding dominated states. However, despite being effective at significantly reducing the number of expansions in many domains, the overhead of comparing states may lead to reduced performance. This is specially critical in hard problems, as the overhead of comparing all pairs of states grows quadratically with the number of explored states. In this paper, we investigate how to use data structures that exploit the inner structure of dominance relations in order to perform this check efficiently. We show that these data structures can avoid the quadratic worst-case in many domains, significantly improving the performance of search with dominance pruning.

Symbolic search has long been recognized as one of the state-of-the-art techniques for exhaustive state-space exploration and cost-optimal planning, leveraging compact state representations and efficient set-based operations. Despite its success in optimal planning, symbolic search has not traditionally been considered suitable for satisficing search, where heuristic guidance is paramount. In this paper, we investigate how to perform symbolic satisficing search aimed at efficiently finding good-quality solutions without guaranteeing optimality. We show that operator-potential heuristics are effective at guiding the search. Empirical results demonstrate that symbolic greedy best-first search with operator-potential heuristics is competitive with explicit state-space search.

LLMs have recently been used to generate Python programs representing generalized plans in PDDL planning, i.e., plans that generalize across the tasks of a given PDDL domain. Previous work proposed a framework consisting of three steps: the LLM first generates a summary and then a strategy for the domain, both in natural language, and then implements that strategy as a Python program, that gets debugged on example planning tasks. In that work, only one strategy is generated and passed directly to the program generation. If the strategy is incorrect, its implementation will therefore result in an incorrect generalized plan. Here, we introduce an approach that generates the strategy in the form of pseudocode and enables automatic debugging of the pseudocode, hence allowing us to identify and fix errors prior to the generation of the generalized plan itself. Additionally, we extend the Python debugging phase with a reflection step prompting the LLM to pinpoint the reason for the observed plan failure. Finally, we take inspiration from LLM code generation to produce several program variants and pick the best one. Running experiments on 17 benchmark domains with two reasoning and two non-reasoning LLMs, we show that these extensions substantially improve the quality of the generalized plans. Our best performing configuration achieves an average coverage of 82% across the domains.

Heuristic search is a prominent method for plan generation in classical planning. Here we address its use for a new problem that we baptize action optimality checking (AOC): checking whether a given action a is optimal in a given state s. AOC has various potential uses, e.g. quality assurance for learned action policies through checking example policy decisions. A vanilla algorithm for AOC is to run two A(star) searches, on each of s and the outcome state s of applying a. We show that one can do much better than this. We introduce early termination criteria across multiple searches. Beyond this, we introduce AOCA(star), which performs a single search on s that gives preference to paths going through s. Our experiments show that AOCA(star) is superior to the vanilla algorithm as well as other multiple search configurations, consistently across three different state-of-theart heuristic functions.

Testing is a natural approach to assess the quality of learned action policies p. Prior work introduced policy testing in AI planning as searching for bugs in p, that is, states where p is sub-optimal with respect to a given testing objective. Beyond quality assurance, an obvious application of these methods is policy selection: given several p to choose from, we can use testing to select the "least buggy" one. Here, we integrate testing-based policy selection into the training process. This includes making more informed decisions when selecting the final policy after training, as well as choosing more promising intermediate policies during the training process. Our experiments with ASNets action policies show that integrating testing allows us to more reliably obtain good-quality policies.

Large language models (LLMs) have revolutionized a large variety of NLP tasks. An active debate is to what extent they can do reasoning and planning. Prior work has assessed the latter in the specific context of PDDL planning, based on manually converting three PDDL domains into natural language (NL) prompts. Here we automate this conversion step, showing how to leverage an LLM to automatically generate NL prompts from PDDL input. Our automatically generated NL prompts result in similar LLM-planning performance as the previous manually generated ones. Beyond this, the automation enables us to run much larger experiments, providing for the first time a broad evaluation of LLM planning performance in PDDL. Our NL prompts yield better performance than PDDL prompts and simple template-based NL prompts. Compared to symbolic planners, LLM planning lags far behind; but in some domains, our best LLM configuration scales up further than A* using LM-cut.

Recent work has shown that successful per-domain generalizing action policies can be learned. Scaling behavior, from small training instances to large test instances, is the key objective; and the use of validation instances larger than training instances is one key to achieve it. Prior work has used fixed validation sets. Here, we introduce a method generating the validation set dynamically, on the fly, increasing instance size so long as informative and feasible.We also introduce refined methodology for evaluating scaling behavior, generating test instances systematically to guarantee a given confidence in coverage performance for each instance size. In experiments, dynamic validation improves scaling behavior of GNN policies in all 9 domains used.

In classical planning, admissible potential heuristics are computed by solving linear programs (LPs) with constraints expressing consistency and goal-awareness of the heuristic. Potential heuristics can return negative estimates. So, given a potential heuristic h(P), the actual heuristic used in search is another heuristic defined as h(0+)(P)(s)= max(h(P) (s), 0) for every reachable state s. In this paper, we reformulate the LP constraints for consistency of h(P) so that they ensure consistency of h(0+)(P) instead. This leads to more informative heuristics with positive impact on the overall performance in exchange for a more time and memory demanding computation using mixed integer linear programs instead of LPs.

Heuristic search guides the exploration of states via heuristic functions h estimating remaining cost. Symbolic search instead replaces the exploration of individual states with that of state sets, compactly represented using binary decision diagrams (BDDs). In cost-optimal planning, heuristic explicit search performs best overall, but symbolic search performs best in many individual domains, so both approaches together constitute the state of the art. Yet combinations of the two have so far not been an unqualified success, because (i) h must be applicable to sets of states rather than individual ones, and (ii) the different state partitioning induced by h may be detrimental for BDD size. Many competitive heuristic functions in planning do not qualify for (i), and it has been shown that even extremely informed heuristics can deteriorate search performance due to (ii).Here we show how to achieve (i) for a state-of-the-art family of heuristic functions, namely potential heuristics. These assign a fixed potential value to each state-variable/value pair, ensuring by LP constraints that the sum over these values, for any state, yields an admissible and consistent heuristic function. Our key observation is that we can express potential heuristics through fixed potential values for operators instead, capturing the change of heuristic value induced by each operator. These reformulated heuristics satisfy (i) because we can express the heuristic value change as part of the BDD transition relation in symbolic search steps. We run exhaustive experiments on IPC benchmarks, evaluating several different instantiations of potential heuristics in forward, backward, and bi-directional symbolic search. Our operator-potential heuristics turn out to be highly beneficial, in particular they hardly ever suffer from (ii). Our best configurations soundly beat previous optimal symbolic planning algorithms, bringing them on par with the state of the art in optimal heuristic explicit search planning in overall performance.

Testing was recently proposed as a method to gain trust in learned action policies in classical planning. Test cases in this setting are states generated by a fuzzing process that performs random walks from the initial state. A fuzzing bias attempts to bias these random walks towards policy bugs, that is, states where the policy performs sub-optimally. Prior work explored a simple fuzzing bias based on policy-trace cost. Here, we investigate this topic more deeply. We introduce three new fuzzing biases based on analyses of policy-trace shape, estimating whether a trace is close to looping back on itself, whether it contains detours, and whether its goal-distance surface does not smoothly decline. Our experiments with two kinds of neural action policies show that these new biases improve bug-finding capabilities in many cases.

In this article, we present an overview of the 2023 International Planning Competition. It featured five distinct tracks designed to assess cutting-edge methods and explore the frontiers of planning within these settings: the classical (deterministic) track, the numeric track, the Hierarchical Task Networks (HTN) track, the learning track, and the probabilistic and reinforcement learning track. Each of these tracks evaluated planning methodologies through one or more subtracks, with the goal of pushing the boundaries of current planner performance. To achieve this objective, the competition introduced a combination of well-established challenges and entirely novel ones. Within this article, each track offers an exploration of its historical context, justifies its relevance within the planning landscape, discusses emerging domains and trends, elucidates the evaluation methodology, and ultimately presents the results.

Potential heuristics assign numerical values (potentials) to state features, where each feature is a conjunction of facts. It was previously shown that the informativeness of potential heuristics can be significantly improved by considering complex features, but computing potentials over all pairs of facts is already too costly in practice. In this paper, we investigate whether using just a few high-dimensional features instead of all conjunctions up to a dimension n can result in improved heuristics while keeping the computational cost at bay. We focus on (a) establishing a framework for studying this kind of potential heuristics, and (b) whether it is reasonable to expect improvement with just a few conjunctions. For (a), we propose two compilations that encode each conjunction explicitly as a new fact so that we can compute potentials over conjunctions in the original task as one-dimensional potentials in the compilation. Regarding (b), we provide evidence that informativeness of potential heuristics can be significantly increased with a small set of conjunctions, and these improvements have positive impact on the number of solved tasks.

In oversubscription planning (OSP), not all goals can be achieved. If a global optimization objective is difficult to fix, then an iterative planning process in which users refine their objective based on sample plans is suitable. Recent work has shown that, in such a process, explanations of plan trade-offs based on goal conflicts - minimal unsolvable goal subsets (MUGS) - are useful. A fundamental limitation of this approach is scalability. Computing MUGS is feasible only in relatively small planning instances; sometimes plan generation in iterative planning also is a limiting factor as users tend to be impatient. Here we address both these limitations by restricting the space of plans considered. We assume that an action policy p for the OSP task has been learned. We restrict both plan generation and MUGS analysis to the action sequences within a given radius r around p, so that r controls the tradeoff between scalability and the degree of approximation. We instantiate this idea with two different kinds of radii around a policy. We experimentally analyze performance as a function of r, for Action Schema Network policies. The results confirm that our approach can scale up further than prior work, and results on instances small enough to compute MUGS exactly indicate that we obtain informative MUGS even with limited runtime and memory.

A lifted mutex group is a schematic first-order description of sets of facts such that each set contains facts out of which at most one can hold in any reachable state. It was previously shown that lifted mutex groups can be used for pruning of operators during grounding of PDDL tasks, i.e., it is possible to prune unreachable and dead-end operators even before the grounded representation is known. Here, we show that applying such a pruning technique does not require a modification of the grounding procedure. Instead, it is possible to compile the conditions under which we can use lifted mutex groups to prune operators directly into the preconditions of lifted actions on the PDDL level. In fact, we show that such compilation captures the pruning power of lifted mutex groups perfectly.

Lifted planning – finding plans directly on the PDDL input model – has attracted renewed attention during the last years. This avoids the process of grounding, which can become computationally prohibitive very easily. However, the main focus of recent research in this area has been on satisficing, i.e., (potentially) suboptimal planning. We present a novel heuristic for optimal lifted planning. Our basic idea is inspired by the LM-cut heuristic, which has been very successful in grounded optimal planning. Like LM-cut, we generate cut-based landmarks via back-chaining from the goal, generating cuts of partially grounded actions. However, exactly mimicking the ground formulation is not feasible, this includes computing the hmax heuristic several times for one computation of the LM-cut heuristic (which is already NP-hard to compute). We show that our heuristic is admissible and evaluate it in a cost optimal setting.

Large language models (LLMs) have revolutionized a large variety of NLP tasks. An active debate is to what extent they can do reasoning and planning. Prior work has assessed the latter in the specific context of PDDL planning, based on manually converting three PDDL domains into natural language (NL) prompts. Here we automate this conversion step, showing how to leverage an LLM to automatically generate NL prompts from PDDL input. Our automatically generated NL prompts result in similar LLM-planning performance as the previous manually generated ones. Beyond this, the automation enables us to run much larger experiments, providing for the first time a broad evaluation of LLM planning performance in PDDL.

We introduce the metric induced by Gaifman graphs into lifted planning. We analyze what kind of information this metric carries and how it can be utilized for constructing lifted delete-free relaxation heuristics. In particular, we prove how the action dynamics influence the distances between objects. As a corollary, we derive a lower bound on the length of any plan. Finally, we apply our theoretical findings on the Gaifman graphs to improve the delete-free relaxation heuristics induced by PDDL homomorphisms.

Oversubscription planning (OSP) is a planning formalism that can deal with planning scenarios where not all goals can be achieved. If the global optimization goal is not fixed, an iterative process in which users refine their preferences based on the sample plans is suitable. To help the users, the planning systems should be able to provide answers to questions such as “Why is goal g not satisfied by the sample plan?” In this paper, we focus on explaining the behavior of a given black-box policy under the aforementioned planning scenario. That is, we assume that sample plans are provided by a state-dependent deterministic policy φ (in our case a neural network policy), and we try to automatically answer the question “Why is the goal g not satisfied by φ?” by providing information how much the policy φ would need to diverge from its decision in order to satisfy the goal g. Moreover, we also provide information in which state and how the policy should diverge. To this end, we extended action policies based on action schema networks to support OSP tasks, and design an algorithm that is able to provide the desired explanations. We evaluate the performance of the proposed algorithm and provide a case study with sample explanations.

Symbolic search, using Binary Decision Diagrams (BDDs) to represent sets of states, is a competitive approach to optimal planning. Yet heuristic search in this context remains challenging. The many advances on admissible planning heuristics are not directly applicable, as they evaluate one state at a time. Indeed, progress using heuristic functions in symbolic search has been limited and even very informed heuristics have been shown to be detrimental. Here we show how this connection can be made stronger for LP-based potential heuristics. Our key observation is that, for this family of heuristic functions, the change of heuristic value induced by each operator can be precomputed. This facilitates their smooth integration into symbolic search. Our experiments show that this can pay off significantly: we establish a new state of the art in optimal symbolic planning.