USPR: Learning a Unified Solver for Profiled Routing

2025-05-08

AI Summary

In Profiled Vehicle Routing Problems (PVRP), vehicle–customer preferences and constraints vary across profile distributions, yet existing reinforcement learning (RL) solvers require costly retraining and exhibit poor generalization to unseen profiles. Method: We propose the first unified RL-based framework for PVRP that generalizes zero-shot to arbitrary new profile distributions without retraining. Built upon a graph neural network architecture, it integrates self-attention, differentiable decoding, and profile-driven logit calibration. Contributions/Results: Key innovations include (1) Profile Embedding (PE) to explicitly encode profile semantics; (2) Multi-Head Profile Attention (MHPA) for profile-aware graph-structured interaction; and (3) Profile-Sensitive Logit Rescaling (PSR) for dynamic decoding-logit calibration. Evaluated on diverse PVRP benchmarks, our method achieves state-of-the-art performance, accelerates inference by 40%, and significantly enhances out-of-distribution generalization.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Machine Learning: Reinforcement Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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 (RL) solvers have shown promise, 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 USPR (Unified Solver for Profiled Routing), a novel framework that natively handles arbitrary profile types. USPR introduces 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 at https://github.com/ai4co/uspr.

Problem

• Solves Profiled Vehicle Routing with diverse constraints
• Overcomes retraining and generalization issues in RL solvers
• Handles arbitrary profile types via unified framework

Innovation

• Profile Embeddings encode diverse profile types
• Multi-Head Profiled Attention models vehicle-client interactions
• Profile-aware Score Reshaping dynamically adjusts decoder logits