Positional Encoding for Neural Vehicle Routing

A recent study published on arXiv (2605.11910) examines the role of positional encoding (PE) in Transformer models applied to neural combinatorial optimization (NCO) for vehicle routing problems (VRPs). The researchers contend that conventional NLP positional encodings fall short for routing applications due to three key structural characteristics: non-uniform node distances, a cyclic and direction-sensitive topology, and a hierarchical multi-route framework anchored by depots. They introduce a cohesive design principle focused on geometric grounding and present a hierarchical anisometric PE that integrates distance-indexed and circularly consistent in-route encoding. The paper reviews PE techniques from NLP, graph-transformer, and routing-specific categories.