Summary
Routing drones to deliver parcels efficiently becomes harder when the number of delivery points changes. The authors study a type of AI model called Pointer Networks trained with reinforcement learning and find why their performance drops when used on different sized problems. They improve the model by adding ways to better understand the whole delivery map, helping it work better whether there are few or many delivery points. Their system also picks the best version of the model depending on the delivery size, which notably improves routing performance even on sizes it was not trained for.
What this means in practice
- •For drone fleet operators: Optimize drone delivery routes efficiently when the number of delivery locations changes without retraining models.
- •For logistics software developers: Create routing software that maintains good performance for vehicle routing problems at various scales using adaptive neural network models.$Commercial implications: Enables more scalable and versatile commercial delivery planning systems that adapt to different delivery sizes.
Authors
Sofiene Lassoued, Devara Tertia, Stefan Lier, Andreas Schwung
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.