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

Han-Seul Jeong, Youngjoon Park, Hyungseok Song, Woohyung Lim

Keywords: Cross-problem Learning, NCO, Compositional Learning, Vehicle Routing, VRP variants, Analogy-Making, Representation Learning

TL;DR: ARC improves VRP solving by learning compositional representations of constraints as reusable attributes, enabling effective cross-problem knowledge sharing and strong generalization to unseen constraint combinations.

Abstract: Cross-problem learning offers an efficient and generalizable approach to solving Vehicle Routing Problems (VRPs), whose diverse constraint combinations give rise to exponentially many variants. Training separate models for individual problem variants is not only computationally inefficient but also makes it difficult to exploit patterns and characteristics that are commonly shared across multiple tasks. It is crucial to develop a unified model that can share knowledge across problems, learn each task effectively, and generalize to new problems by utilizing elements from previously learned tasks. We propose ARC ($\textbf{A}$ttribute $\textbf{R}$epresentation via $\textbf{C}$ompositional Learning), a novel cross-problem learning solver for VRPs. ARC leverages the fact that a VRP instance can be represented as a composition of base attributes, allowing it to decompose complex VRP instances and effectively capture attribute semantics. To address potential attribute interference, we enhance the representation with Attribute Mixer that models the complex interactions between constraints. Empirical evaluation demonstrates that ARC not only outperforms existing methods on seen problem configurations but also exhibits robust zero-shot generalization to novel constraint combinations and adapts efficiently to previously unseen attributes, with further validation in real-world settings.

Submission Number: 16