Rethinking Light Decoder-based Solvers for Vehicle Routing Problems
Ziwei Huang, Jianan Zhou, Zhiguang Cao, Yixin Xu
TL;DR
Rethinking Light Decoder-based Solvers analyzes why light decoder VRP solvers struggle to generalize to larger or unseen problem variants. It identifies that static embeddings produced by a heavy encoder impose a high information density task on the encoder, while an overly simple decoder cannot effectively leverage this dense information. The authors propose ReLD, combining direct context integration via an identity-mapped residual, a non-linear query through a feed-forward block, and generalizable training with a distance heuristic and attribute variation. Empirically, ReLD improves OOD generalization across cross-size and cross-problem benchmarks and narrows the gap with heavy decoder methods, offering a practical efficiency-accuracy trade-off for VRP solvers.
Abstract
Light decoder-based solvers have gained popularity for solving vehicle routing problems (VRPs) due to their efficiency and ease of integration with reinforcement learning algorithms. However, they often struggle with generalization to larger problem instances or different VRP variants. This paper revisits light decoder-based approaches, analyzing the implications of their reliance on static embeddings and the inherent challenges that arise. Specifically, we demonstrate that in the light decoder paradigm, the encoder is implicitly tasked with capturing information for all potential decision scenarios during solution construction within a single set of embeddings, resulting in high information density. Furthermore, our empirical analysis reveals that the overly simplistic decoder struggles to effectively utilize this dense information, particularly as task complexity increases, which limits generalization to out-of-distribution (OOD) settings. Building on these insights, we show that enhancing the decoder capacity, with a simple addition of identity mapping and a feed-forward layer, can considerably alleviate the generalization issue. Experimentally, our method significantly enhances the OOD generalization of light decoder-based approaches on large-scale instances and complex VRP variants, narrowing the gap with the heavy decoder paradigm. Our code is available at: https://github.com/ziweileonhuang/reld-nco.