Reinforcement Learning Enhanced LLM Agents for Complex Vehicle Routing Problems

Vehicle Routing Problems (VRPs) are fundamental combinatorial optimization problems with widespread applications in various scenarios. The advanced optimization solvers can effectively solve such problems. However, modeling complex VRP variants for solvers often requires substantial domain expertise, which limits the accessibility of advanced optimization technologies. In this paper, we propose Reinforcement Learning Enhanced LLMAgents(RLEA), a multi-agent framework designed to automate the modeling of complex VRPs. RLEA introduces a lightweight neural Planner trained with Soft Q-learning to efficiently orchestrate the actions of LLM-based agents. In addition, we equip the system with an evolutionary memory module and retrieval-augmented generation, enabling the agent to leverage both accumulated experience and external solver knowledge during program generation and refinement for solving VRPs. We evaluated 48 distinct VRP variants across various solvers. The experimental results demonstrate that RLEA outperforms the previous state-of-the-ar method, achieving a 16.67% higher success rate while significantly reducing runtime errors. These results validate that integrating reinforcement learning with LLM-based reasoning is highly effective for automated optimization modeling. The appendix is available at: https://doi.org/10.5281/zenodo.19134435.