ARC: Leveraging Compositional Representations for Cross-Problem Learning on VRPs

Abstract: Vehicle Routing Problems (VRPs) with diverse real-world attributes have driven recent interest in cross-problem learning approaches that efficiently generalize across problem variants. We propose ARC (Attribute Representation via Compositional Learning), a cross-problem learning framework that learns disentangled attribute representations by decomposing them into two complementary components: an Intrinsic Attribute Embedding (IAE) for invariant attribute semantics and a Contextual Interaction Embedding (CIE) for attribute-combination effects. This disentanglement is achieved by enforcing analogical consistency in the embedding space to ensure the semantic transformation of adding an attribute (e.g., a length constraint) remains invariant across different problem contexts. This enables our model to reuse invariant semantics across trained variants and construct representations for unseen combinations. ARC achieves state-of-the-art performance across in-distribution, zero-shot generalization, few-shot adaptation, and real-world benchmarks.