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

Abstract

Unmanned aerial vehicles (UAVs) enable fast, flexible last-mile and emergency delivery, but their routing 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 generalize 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, with fixed capacity reflecting drone payload constraints, 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 percent.