Learning graph neural network heuristics for numeric planning problems

Numeric planning extends classical planning by allowing the representation of continuous quantities and resources, making it suitable for modeling complex real-world problems. However, the infinite state space and the complexity of numeric conditions make the derivation of effective domain-independent heuristics particularly challenging. While Graph Neural Networks (GNNs) have shown great promise in learning heuristics for classical planning by exploiting the relational structure of the problems, their application to numeric planning is still in its infancy. Existing approaches often struggle to capture the rich structural dependencies defined by numeric constraints, or they rely on architectures that fail to generalize effectively across different problem sizes. In this thesis, we propose a novel GNN-based architecture designed to learn heuristic functions for numeric planning problems. Unlike previous works that treat numeric fluents as isolated node features, our approach explicitly encodes grounded numeric conditions (both preconditions and goals) as edges in the graph, integrating numeric values directly into the message-passing mechanism. This allows the network to reason about the logical and arithmetic relationships between objects, leading to more informative distance estimates. To support the integration of deep learning with automated planning, we introduce LeapNP (Learning and Planning Framework for Numeric Problems), a modular and extensible Python framework based on Unified Planning. Furthermore, we address the computational bottleneck of evaluating neural networks during search by proposing novel search algorithms tailored for GPU acceleration. Specifically, we introduce Multiple Evaluation Best-First Search (MBFS), which exploits batch processing to evaluate states in parallel, and Adaptive Width Best-First Search (AWBFS), a dynamic algorithm that adjusts the search width based on heuristic feedback to escape plateaus efficiently. Experimental results on domains from the IPC 2023 Numeric Track demonstrate that our architecture significantly outperforms both traditional heuristics and state-of-the-art learning-based approaches in domains with complex numeric structures. Moreover, we show that AWBFS effectively leverages the throughput of modern GPUs, achieving higher coverage and better plan quality compared to standard greedy search strategies.