URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization

2025-09-27

AI Summary

Existing neural routing solvers rely on predefined constraints or problem-level fine-tuning, limiting zero-shot generalization to unseen Vehicle Routing Problem (VRP) variants. To address this, we propose the first unified framework enabling zero-shot solving across 100+ VRP variants. Our method introduces a Unified Data Representation (UDR) for problem-agnostic modeling; a Hybrid Bias Module (MBM) that jointly encodes geometric and relational priors; and a parameter generator coupled with an LLM-driven executable masking mechanism to ensure solution feasibility automatically. Evaluated on over 100 VRP variants, our framework generates high-quality, feasible solutions for more than 90 previously unseen variants without any fine-tuning. This significantly extends the generalization capability and applicability of neural solvers beyond narrow, task-specific settings—marking a substantial advance in learning-based combinatorial optimization.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Multi-task neural routing solvers have emerged as a promising paradigm for their ability to solve multiple vehicle routing problems (VRPs) using a single model. However, existing neural solvers typically rely on predefined problem constraints or require per-problem fine-tuning, which substantially limits their zero-shot generalization ability to unseen VRP variants. To address this critical bottleneck, we propose URS, a unified neural routing solver capable of zero-shot generalization across a wide range of unseen VRPs using a single model without any fine-tuning. The key component of URS is the unified data representation (UDR), which replaces problem enumeration with data unification, thereby broadening the problem coverage and reducing reliance on domain expertise. In addition, we propose a Mixed Bias Module (MBM) to efficiently learn the geometric and relational biases inherent in various problems. On top of the proposed UDR, we further develop a parameter generator that adaptively adjusts the decoder and bias weights of MBM to enhance zero-shot generalization. Moreover, we propose an LLM-driven constraint satisfaction mechanism, which translates raw problem descriptions into executable stepwise masking functions to ensure solution feasibility. Extensive experiments demonstrate that URS can consistently produce high-quality solutions for more than 100 distinct VRP variants without any fine-tuning, which includes more than 90 unseen variants. To the best of our knowledge, URS is the first neural solver capable of handling over 100 VRP variants with a single model.

Problem

• Enabling zero-shot generalization across unseen vehicle routing problems
• Reducing reliance on predefined constraints and domain expertise
• Ensuring solution feasibility through LLM-driven constraint satisfaction

Innovation

• Unified data representation replaces problem enumeration with data unification
• Mixed Bias Module learns geometric and relational biases efficiently
• LLM-driven constraint satisfaction translates descriptions to masking functions