ARS: Automatic Routing Solver with Large Language Models

TL;DR

This work tackles the challenge of solving real-world Vehicle Routing Problems (VRPs) with diverse constraints by introducing ARS, an LLM-assisted framework that automatically designs constraint-aware heuristics to augment a backbone VRP solver. It also presents RoutBench, a benchmark of 1,000 VRP variants derived from 24 constraints to assess generalization and constraint handling. Empirical results show ARS achieving up to 91.67% success on common problems and substantial improvements across RoutBench relative to other LLM-based methods and standard solvers, demonstrating strong capability to adapt to complex, unseen VRPs. The combination of a constraint-aware generation pipeline and a versatile backbone solver offers a scalable and interpretable path toward automated algorithm design for practical routing tasks with broad industrial impact.

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 interest in automating the design of routing algorithms, 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, this paper introduces RoutBench, a benchmark of 1,000 VRP variants derived from 24 attributes, for evaluating the effectiveness of automatic routing solvers in addressing complex constraints. Along with RoutBench, we present the Automatic Routing Solver (ARS), which employs Large Language Model (LLM) agents to enhance a backbone algorithm framework by automatically generating constraint-aware heuristic code, based on problem descriptions and several representative constraints selected from a database. Our experiments show that ARS outperforms state-of-the-art LLM-based methods and commonly used solvers, automatically solving 91.67% of common VRPs and achieving at least a 30% improvement across all benchmarks.

Figures (8)

• Figure 1: Overview of the proposed ARS framework. The left side of the figure shows the test instance, including the problem description, corresponding data, and validation code for result verification. The right side comprises the database, generation module, and VRP solver. The generation module selects relevant constraints from the database and generates constraint-aware heuristics for the VRP solver to address different VRP variants.
• Figure 2: Analysis of problem distribution across common problems, RoutBench, and all problems.
• Figure 3: The frequency of constraint usage is analyzed for RoutBench-S and RoutBench-H.
• Figure 4: Comparison of the success rate for different solvers with standard prompting.
• Figure 5: Compares the lines of code generated by LLMs for different solvers on four VRP variants.