COAgents: Multi-Agent Framework to Learn and Navigate Routing Problems Search Space
Authors: Oleksandr Yakovenko, Mahdi Mostajabdaveh, Cheikh Ahmed, Abdullah Ali Sivas, Xiaorui Li, Zirui Zhou, Mao Kun
Organizations: Huawei Technologies Canada, 4321 Still Creek Dr, Burnaby, BC, Canada V5C 6S7 · Huawei Technologies, China
Abstract
Although Vehicle Routing Problems (VRP) are essential to many real-world systems, they remain computationally intractable at scale due to their combinatorial complexity. Traditional heuristics rely on handcrafted rules for local improvements and occasional \textit{jumps} to escape local minima, but often struggle to generalize across diverse instances. We introduce \textbf{COAgents}, a cooperative multi-agent framework that models the search process as a graph: nodes represent solutions, and edges correspond to either local refinements or large perturbations for diversification (i.e., jumps). A \textit{Partial Search Graph} (PSG) is dynamically constructed during search, enabling COAgents to train a Node Selection Agent and a Move Selection Agent to guide intensification, and a Jump Agent to trigger well-timed explorations of new regions. Unlike end-to-end learning approaches, COAgents cleanly separates problem-agnostic search control from compact domain-specific encoding, facilitating adaptability across tasks. Extensive experiments on the CVRP and VRPTW benchmarks show that COAgents remains competitive with several learn-to-search baselines on CVRP and sets a new state of the art among learning-based methods on the more challenging VRPTW instances, reducing the gap to the best-known solutions by 14% at N=100 and 44% at N=50 relative to the strongest neural solver (POMO), and by 21% and 40% respectively relative to ALNS. Code is available at https://github.com/mahdims/COAgents.
Large-scale Capacitated Vehicle Routing Problems (CVRPs) are commonly solved by partitioning customers into smaller routing problems that can be optimized independently. While this substantially reduces computational complexity, independently constructed routing solutions may leave some customer demand unserved even when sufficient resources exist elsewhere in the fleet. We present Collaborative Routing Constructors (CoRC), a routing framework that enables independently solved subproblems to exchange customers and vehicles during optimization rather than relying solely on a fixed partition or a subsequent global re-optimization stage. Computational experiments on AGS benchmark instances and synthetic instances containing up to 200,000 customers compare CoRC against independent routing, post-routing global re-optimization, and state-of-the-art, end-to-end routing frameworks. Across all evaluated partitioning strategies, CoRC consistently constructs feasible routing solutions where competing partition-based methods do not. Furthermore, it remains effective on problem instances for which the evaluated end-to-end routing frameworks did not produce solutions under the same computational budget. These results demonstrate that collaboration between routing subproblems provides a robust and scalable approach for feasible large-scale route construction.
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.
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.