Learning to Segment for Vehicle Routing Problems

Iterative heuristics are widely recognized as state-of-the-art for Vehicle Routing Problems (VRPs). In this work, we exploit a critical observation: a large portion of the solution remains stable, i.e., unchanged across search iterations, causing redundant computations, especially for large-scale VRPs with long subtours. To address this, we pioneer the formal study of the First-Segment-Then-Aggregate (FSTA) decomposition technique to accelerate iterative solvers. FSTA preserves stable solution segments during the search, aggregates nodes within each segment into fixed hypernodes, and focuses the search only on unstable portions. Yet, a key challenge lies in identifying which segments should be aggregated. To this end, we introduce Learning-to-Segment (L2Seg), a novel neural framework to intelligently differentiate potentially stable and unstable portions for FSTA decomposition. We present three L2Seg variants: non-autoregressive (globally comprehensive but locally indiscriminate), autoregressive (locally refined but globally deficient), and their synergy. Empirical results on CVRP and VRPTW show that L2Seg accelerates state-of-the-art solvers by 2x to 7x. We further provide in-depth analysis showing why synergy achieves the best performance. Notably, L2Seg is compatible with traditional, learning-based, and hybrid solvers, while supporting various VRPs.