Title: ARS: Automatic Routing Solver with Large Language Models
Primary area: optimization
Keywords: Vehicle Routing Problem, Large Language Model, Automatic Heuristic Design, Benchmark.

Abstract: Real-world Vehicle Routing Problems (VRPs) are characterized by a variety of practical constraints, making manual solver design both knowledge-intensive and time-consuming. Although there is increasing effort in automating the design of routing solvers, existing research has explored only a limited array of VRP variants and fails to adequately address the complex and prevalent constraints encountered in real-world situations. To fill this gap, we propose the Automatic Routing Solver (ARS), which leverages Large Language Model (LLM) agents to enhance a backbone metaheuristic framework. ARS automatically generates constraint-aware heuristic code from natural language problem descriptions, enabling the framework to handle a wider range of VRP variants without relying on cumbersome modeling rules. Alongside ARS, we introduce RoutBench, a benchmark comprising 1,000 VRP variants derived from 24 attributes, designed to rigorously evaluate the effectiveness of automatic routing solvers in handling VRPs with diverse practical constraints. In our experiments, ARS achieves a success rate of over 90\% on common VRPs and over 60\% on RoutBench, outperforming the other seven LLM-based methods by at least 30\% in success rate. Compared to three general-purpose solvers, the ARS framework not only makes it easier for an LLM to generate correct code, with approximately 25\% higher correctness, but also achieves superior solving efficiency across many VRP variants.