USPR: Learning a Unified Solver for Profiled Routing

TL;DR

USPR introduces a versatile, learning-based solver for the Profiled Vehicle Routing Problem that effectively encodes diverse profile preferences, models complex interactions, and generalizes well across different instance types.

Contribution

The paper presents USPR, a novel framework with profile embeddings, multi-head profiled attention, and profile-aware score reshaping, enabling a unified, generalizable solution for PVRP.

Findings

Achieves state-of-the-art results among learning-based methods.

Demonstrates superior flexibility and efficiency across diverse benchmarks.

Outperforms existing RL-based solvers in generalization and adaptability.

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.