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

ARC: Leveraging Compositional Representations for Cross-Problem Learning on VRPs Han-Seul Jeong, Youngjoon Park, Hyungseok Song, Woohyung Lim LG AI Research Republic of Korea {hanseul.jeong, yj.park, hyungseok.song, w.lim}@lgresearch.ai Abstract Vehicle Routing Problems (VRPs) with diverse real-world attributes have driven re- cent 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 In- trinsic Attribute Embedding (IAE) for invariant attribute semantics and a Contextual Interaction Embedding (CIE) for attribute-combination effects. This disentangle- ment 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. 1 Introduction Capacitated Vehicle Routing Problem (CVRP) represents a fundamental NP-hard combinatorial optimization challenge [26, 12, 7]. While deep learning-based approximation algorithms within the Neural Combinatorial Optimization (NCO) paradigm have demonstrated near-optimal performance [1, 24, 6, 17, 13, 14, 22], real-world routing applications must address diverse attributes such as time windows [23] or open routing [25]. To efficiently leverage information of shared attributes across multiple VRP variants, recent research has focused on cross-problem learning, where a single unified model is trained to solve multiple VRP variants defined by different attribute combinations [30, 2, 15], improving efficiency and generalization compared to variant-specific models [16]. However, prior works [16, 30, 2, 15] often conflate invariant attribute semantics with contextual effects among attributes, leading to entangled representations that hinder efficient knowledge sharing across different VRP variants. To address this limitation, we propose ARC, which disentangles individual attribute embeddings by decomposing representation into intrinsic components that remain consistent across combinations and contextual components that capture combination-specific interactions. ARC learns distinct attribute representations through analogical compositional learning, ensuring identical attributes maintain their intrinsic semantics regardless of their combinations by enforcing analogous transformations across different problem contexts. Contextual components then model attribute interactions by leveraging the learned intrinsic representations within specific problem contexts, enabling efficient cross-problem learning and zero-shot generalization to unseen combinations. Extensive experiments demonstrate that ARC outperforms existing baselines on trained configurations while achieving robust zero-shot generalization to unseen attribute combinations and efficient few- 39th Conference on Neural Information Processing Systems (NeurIPS 2025) Workshop: Differentiable Learning of Combinatorial Algorithms. arXiv:2512.18633v1 [cs.LG] 21 Dec 2025 shot adaptation to new attributes, with validation on real-world benchmarks. Our main contributions are as followed: • We propose ARC, a novel cross-problem learning framework that disentangles attribute repre- sentations by decomposing them into intrinsic and contextual components, facilitating effective knowledge sharing across different VRP variants. • We introduce a compositional learning mechanism that enforces analogical embedding relation- ships, establishing the first analogical embedding framework for NCO to our knowledge. • We demonstrate superior performance across four scenarios: (1) in-distribution, (2) zero-shot generalization to unseen attribute combinations, (3) few-shot adaptation to new attributes, and (4) real-world benchmark, CVRPLib. 2 Related Works Cross-Problem CO Solvers Recent work has shifted toward cross-problem learning, developing universal architectures capable of solving diverse problems. This research spans two branches: heterogeneous CO tasks [5, 21] and VRP variants with different attribute combinations, to which our work belongs. Existing VRP approaches include joint training and Mixture-of-Experts [16, 30], foundation models [2], and attribute-aware attention mechanisms [15]. However, these methods learn mixed representations where shared attribute semantics are entangled with combination-specific interactions, inducing inefficient knowledge sharing across attribute combinations. Our approach explicitly decomposes attribute representations into intrinsic characteristics an

This content is AI-processed based on open access ArXiv data.