# ARS: Automatic Routing Solver with Large Language Models

arXiv: https://arxiv.org/abs/2502.15359 · HTML: https://mlsanity.com/paper/2502.15359/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 83 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [RepoCoder: Repository-Level Code Completion Through Iterative Retrieval and Generation](https://mlsanity.com/paper/2303.12570/) (2023)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [DocPrompting: Generating Code by Retrieving the Docs](https://mlsanity.com/paper/2207.05987/) (2022)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention](https://mlsanity.com/paper/2412.00346/) (2024)
- [Solving General Natural-Language-Description Optimization Problems with Large Language Models](https://mlsanity.com/paper/2407.07924/) (2024)
- [Heuristics for Vehicle Routing Problem: A Survey and Recent Advances](https://mlsanity.com/paper/2303.04147/) (2023)
- [A hybrid adaptive Iterated Local Search with diversification control to the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2012.11021/) (2020)

## Built on by (most cited first, 13 of 13)

- [MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver](https://mlsanity.com/paper/2506.02935/) (2025)
- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
- [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://mlsanity.com/paper/2510.16701/) (2025)
- [Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM](https://mlsanity.com/paper/2510.11121/) (2025)
- [Empowering Real-World: A Survey on the Technology, Practice, and Evaluation of LLM-driven Industry Agents](https://mlsanity.com/paper/2510.17491/) (2025)
- [Rudder: Steering Prefetching in Distributed GNN Training using LLM Agents](https://mlsanity.com/paper/2602.23556/) (2026)
- [Agentic MIP Research: Accelerated Constraint Handler Generation](https://mlsanity.com/paper/2605.09186/) (2026)
- [MiniOpt: Reasoning to Model and Solve General Optimization Problems with Limited Resources](https://mlsanity.com/paper/2606.25832/) (2026)
- [Reinforcement Learning Enhanced LLM Agents for Complex Vehicle Routing Problems](https://mlsanity.com/paper/2609.00859/) (2026)
- [Constraint-aware Path Planning from Natural Language Instructions Using Large Language Models](https://mlsanity.com/paper/2603.19257/) (2026)
- [CDEoH: Category-Driven Automatic Algorithm Design With Large Language Models](https://mlsanity.com/paper/2603.19284/) (2026)
- [Learning to Staff: Offline Reinforcement Learning and Fine-Tuned LLMs for Warehouse Staffing Optimization](https://mlsanity.com/paper/2603.24883/) (2026)
- [Large Language Models in Transportation Systems Management and Operations: From Text Reasoning to Multi-modal Decision Support](https://mlsanity.com/paper/2606.00991/) (2026)

## Abstract (arXiv)

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.