# Automated Large-scale CVRP Solver Design via LLM-assisted Flexible MCTS

arXiv: https://arxiv.org/abs/2605.03339 · HTML: https://mlsanity.com/paper/2605.03339/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 5 May 2026.

## Builds on (most cited first, 24 of 24)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [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)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2407.00312/) (2024)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention](https://mlsanity.com/paper/2412.00346/) (2024)
- [Heuristics for Vehicle Routing Problem: A Survey and Recent Advances](https://mlsanity.com/paper/2303.04147/) (2023)
- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://mlsanity.com/paper/2510.16701/) (2025)
- [Improving word mover's distance by leveraging self-attention matrix](https://mlsanity.com/paper/2211.06229/) (2022)
- [Hybrid Memetic Search for Electric Vehicle Routing with Time Windows, Simultaneous Pickup-Delivery, and Partial Recharges](https://mlsanity.com/paper/2410.19580/) (2024)

## Built on by (most cited first, 1 of 1)

- [Autoresearch in Mixed-Integer Linear and Nonlinear Programming](https://mlsanity.com/paper/2609.39360/) (2026)

## Abstract (arXiv)

Solving large-scale CVRP (LSCVRP) with hundreds to thousands of nodes remains difficult for even state-of-the-art solvers. Divide-and-conquer can scale by decomposing the instance into size-reduced subproblems, but designing decomposition logic and configuring sub-solvers is highly expertise- and labor-intensive. Large Language Models (LLMs) have emerged as promising tools for automated algorithm design. However, existing LLM-driven approaches struggle with LSCVRP primarily due to the difficulty in generating sophisticated search strategies within a limited context window. To bridge this gap, we propose the LLM-assisted Flexible Monte Carlo Tree Search (LaF-MCTS), a novel framework that automates the design of high-performance LSCVRP solvers. We develop a three-tier decision hierarchy to enable incremental design of decomposition policies and sub-solvers for LSCVRP. To enable efficient search within the algorithmic hypothesis space, we introduce semantic pruning to eliminate semantically and structurally redundant codes, and branch regrowth to regenerate codes and preserve diversity. Extensive experiments on CVRPLib demonstrate that LaF-MCTS autonomously composes and optimizes decomposition-enhanced solvers that surpasses various state-of-the-art CVRP solvers.