USPR: Learning a Unified Solver for Profiled Routing

Abstract

The Profiled Vehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle–client-specific preferences and constraints, reflecting real‑world requirements such as zone restrictions and service‑level preferences. While recent reinforcement‑learning solvers have shown promising performance, they require retraining for each new profile distribution, suffer from poor representation ability, and struggle to generalize to out‑of‑distribution instances. In this paper, we address these limitations by introducing Unified Solver for Profiled Routing (USPR), a novel framework that natively handles arbitrary profile types. USPR introduces on three key innovations: (i) Profile Embeddings (PE) to encode any combination of profile types; (ii) Multi‑Head Profiled Attention (MHPA), an attention mechanism that models rich interactions between vehicles and clients; (iii) Profile‑aware Score Reshaping (PSR), which dynamically adjusts decoder logits using profile scores to improve generalization. Empirical results on diverse PVRP benchmarks demonstrate that USPR achieves state‑of‑the‑art results among learning‑based methods while offering significant gains in flexibility and computational efficiency. We make our source code publicly available to foster future research.