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

Sofiene Lassoued, Devara Tertia, Stefan Lier, Andreas Schwung

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…