In Hierarchical Task Network (HTN) planning, landmarks are facts that must hold true, and tasks or methods that must be included in every solution. Existing landmark generation techniques for HTN planning rely on the Delete and Ordering Free (DOF) relaxation and are known to be sound but incomplete, primarily due to the limitations introduced by Task Insertion. This paper presents a new landmark generation method that builds on a previous AND/OR graph-based approach, extending it to capture additional hierarchical dependencies among tasks and methods. We prove that our approach is sound and dominates existing techniques, though it remains incomplete under the DOF relaxation. Experimental results on IPC benchmarks for totally ordered problems show that our method identifies significantly more task and method landmarks across most domains, improving coverage with minimal computational overhead.

In recent years, large language models (LLMs) have shown remarkable performance in many problems. However, they fail to plan reliably. Specialized attempts to improve their planning capabilities still produce incorrect plans and fail to generalize to larger tasks. Furthermore, LLMs designed for explicit "reasoning" fail to compete with automated planners while increasing computational costs, which reduces one of the advantages of using LLMs. In this paper, we show how to use LLMs to always generate correct plans, even for out-of-distribution tasks of increasing size. For a given planning domain, we ask an LLM to generate several domain-dependent heuristic functions in the form of Python code, evaluate them on a set of training tasks with a greedy best-first search, and choose the best one. The resulting LLM-generated heuristic functions solve substantially more unseen out-of-distribution test tasks than end-to-end LLM planning, particularly for non-reasoning LLMs. Moreover, they also solve many more tasks than state-of-the-art domain-independent heuristics for classical planning, and are competitive with the strongest learning algorithm for domain-dependent planning. These results are impressive given that our implementation is based on a Python planner and the baselines all build upon highly optimized C++ code. In some domains, the LLM-generated heuristics expand fewer states than the baselines, showing that they are not only efficiently computable but also more informative than the state-of-the-art heuristics. Overall, our results show that sampling a set of planning heuristic functions can significantly improve the planning capabilities of LLMs.

We study the problem of learning good heuristic functions for classical planning tasks with neural networks based on samples represented by states with their cost-to-goal estimates. The heuristic function is learned for a state space and goal condition with the number of samples limited to a fraction of the size of the state space, and must generalize well for all states of the state space with the same goal condition. Our main goal is to better understand the influence of sample generation strategies on the performance of a greedy best-first heuristic search (GBFS) guided by a learned heuristic function. In a set of controlled experiments, we find that two main factors determine the quality of the learned heuristic: the algorithm used to generate the sample set and how close the sample estimates to the perfect cost-to-goal are. These two factors are dependent: having perfect cost-to-goal estimates is insufficient if the samples are not well distributed across the state space. We also study other effects, such as adding samples with high-value estimates. Based on our findings, we propose practical strategies to improve the quality of learned heuristics: three strategies that aim to generate more representative states and two strategies that improve the cost-to-goal estimates. Our practical strategies result in a learned heuristic that, when guiding a GBFS algorithm, increases by more than 30% the mean coverage compared to a baseline learned heuristic.

It is well-known that the search algorithms A* and Iterative Deepening A* (IDA*) can fail to solve state-space tasks optimally due to time and memory limits. The former typically fails in memory-restricted scenarios and the latter in time-restricted scenarios. Therefore, several algorithms were proposed to solve state-space tasks optimally using less memory than A* and less time than IDA*, such as A*+IDA*, a hybrid memory-restricted algorithm that combines A* and IDA*. In this paper, we present a hybrid memory-restricted algorithm that combines Partial Expansion A* (PEA*) and IDA*. This new algorithm has two phases, the same structure as the A*+IDA* algorithm. The first phase of PEA*+IDA* runs PEA* until it reaches a memory limit, and the second phase runs IDA* without duplicate detection on each node of PEA*'s Open. First, we present a model that shows how PEA*+IDA* can perform better than A*+IDA* although pure PEA* usually makes more expansions than pure A*. Later, we perform an experimental evaluation using three memory limits and show that, compared to A*+IDA* on classical planning domains, PEA*+IDA* has higher coverage and expands fewer nodes. Finally, we experimentally analyze both algorithms and show that having higher F-limits and better priority-queue composition given by PEA* have a considerable impact on the performance of the algorithms.

Goal recognition aims to recognize the set of candidate goals that are compatible with the observed behavior of an agent. In this paper, we develop a method based on the operator-counting framework that efficiently computes solutions that satisfy the observations and uses the information generated to solve goal recognition tasks. Our method reasons explicitly about both partial and noisy observations: estimating uncertainty for the former, and satisfying observations given the unreliability of the sensor for the latter. We evaluate our approach empirically over a large data set, analyzing its components on how each can impact the quality of the solutions. In general, our approach is superior to previous methods in terms of agreement ratio, accuracy, and spread. Finally, our approach paves the way for new research on combinatorial optimization to solve goal recognition tasks.

Procedural generation of initial states of state-space search problems have applications in human and machine learning as well as in the evaluation of planning systems. In this paper we deal with the task of generating hard and solvable initial states of Sokoban puzzles. We propose hardness metrics based on pattern database heuristics and the use of novelty to improve the exploration of search methods in the task of generating initial states. We then present a system called Beta that uses our hardness metrics and novelty to generate initial states. Experiments show that Beta is able to generate initial states that are harder to solve by a specialized solver than those designed by human experts.

For a given state space and admissible heuristic function h there is always a tie-breaking strategy for which A* expands the minimum number of states [Dechter and Pearl, 1985]. We say that these strategies have optimal expansion. Although such a strategy always exists it may depend on the instance, and we currently do not know a tie-breaker that always guarantees optimal expansion. In this paper, we study tie-breaking strategies for A*. We analyze common strategies from the literature and prove that they do not have optimal expansion. We propose a novel tie-breaking strategy using cost adaptation that has always optimal expansion. We experimentally analyze the performance of A* using several tie-breaking strategies on domains from the IPC and zero-cost domains. Our best strategy solves significantly more instances than the standard method in the literature and more than the previous state-of-the-art strategy. Our analysis improves the understanding of how to develop effective tie-breaking strategies and our results also improve the state-of-the-art of tie-breaking strategies for A*.

Pattern databases have been successfully applied to several problems. Their use assumes that the goal state is known, and once the pattern database is built, commonly it can be used by all instances. However, in Sokoban, before solving the puzzle, the goal position of each stone is unknown. Moreover, each Sokoban instance has its own state space search. In this paper we apply pattern databases to Sokoban. The proposed approach uses an instance decomposition, that allows multiple possible goal states to be abstracted into a single state. Thus, an instance dependent pattern database is employed. Experiments with the standard set of instances show that the proposed approach overcomes the current best lower bounds in initial states for several instances. Furthermore, three of these new best lower bounds match exactly with the optimal solution length. Finally, we run experiments of 5 million explored states for each instance. Nine instances were solved with optimality guarantees, while only four instances were solved under the same conditions by previous methods.

The use of numerical prediction models are essential to modern society. Data assimilation is a technique that aims to increase the prediction accuracy by combining a model output with observational data, resulting in a state that is closer to the true state of the problem. Depending on the size of the model output and the number of observations to assimilate, the combination of these two sources of information may require intensive computing and become a challenge, even for supercomputers used in this type of application. Thus neural networks have been proposed as an alternative to perform high quality data assimilation at lower computational cost. This paper investigates the use of NeuroEvolution of Augmenting Topologies (NEAT) in data assimilation. NEAT is capable of adapting the connections weights and the neural network topology using principles of evolutionary computation in a search for a minimum topology and best performance. In this work, two different models were used for testing: the Lorenz Attractor and Shallow Water model. The experiments compared the results obtained with NEAT and backpropagation neural networks, using as benchmark the Best Linear Unbiased Estimator (BLUE). In the experiment with the Lorenz Attractor, NEAT was able to emulate the data assimilation task with smaller error at lower computational cost. For the Shallow Water model, tested using different grid sizes, it was observed that the errors obtained with both neural networks were small, but NEAT showed high error values. On the other hand, NEAT always gets a topology with significantly fewer operations, and the computational cost difference increases with the grid size.