From Comparison to Selection: Enhancing Cross-Scale Generalization of Pointer Networks Trained with Reinforcement Learning for Capacitated Vehicle Routing Problem

Abstract

Vehicle routing in delivery and logistics remains challenging as the number of clients varies. Classical approaches based on mixed-integer programming and heuristics can scale poorly or require problem-specific design, motivating learning-based alternatives. Reinforcement learning is particularly promising, provided a single policy can generalise across problem sizes without retraining. Although attention-based Pointer Networks are inherently size-agnostic, their solution quality degrades under both upscaling and downscaling. Using the Capacitated Vehicle Routing Problem (CVRP) as a controlled proxy, we investigate this degradation and identify three contributing factors: shifts in node density, attention dispersion, and dilution of the mean-pooled graph context. We systematically compare architecture-wide, encoder-side, and decoder-side modifications to address these limitations and propose a learned, permutation-invariant graph-context aggregation mechanism, implemented as a weighted average and as Set2Set. Results reveal distinct requirements for transfer in each direction: entropy-based attention scaling reduces the CVRP20-to-CVRP100 performance gap by 1.41 percentage points, while the proposed aggregation methods achieve the largest improvement on the more challenging CVRP100-to-CVRP20 transfer, approximately 0.9 percentage points. Exploiting this complementarity, we introduce an approach selector that chooses the best model for each training-target size pair. The selector reduces cost relative to the reference model across all nine seen train-test pairs and eight of nine pairs involving unseen sizes (CVRP35, CVRP75, and CVRP200), achieving improvements of up to 3.2%.