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.
Multi-task neural solvers aim to handle multiple Vehicle Routing Problem (VRP) variants within a unified model, avoiding separate training for each constraint combination. However, VRP variants differ in optimization difficulty, while existing methods lack stage-wise feedback on their training status, making the model biased to some specific variants. Although meta-learning can support adaptive training, it typically requires bi-level optimization and additional gradient updates, increasing computational cost. To address this limitation, we propose LLM-as-Trainer (LaT), a plug-and-play training paradigm that uses a pretrained large language model as an external trainer. LaT periodically analyzes cross-task validation metrics to generate a stage-wise guidance vector. This vector is combined with the current task's constraint vector and injected into each encoder layer, providing the neural solver with additional training information during subsequent policy optimization. Experiments on 16 VRP variants show that LaT improves the solution quality of several state-of-the-art multi-task neural solvers on both trained and unseen variants, supporting the effectiveness and generality of the proposed training paradigm.
Neural autoregressive solvers for the Multi-Attribute Vehicle Routing Problem (MAVRP) reach competitive cost but offer no per-step justification, a problem when dispatchers must validate, accept, or compare them. We open two complementary black boxes in one protocol. On the encoder side, linear probes, spontaneous-organization metrics, rank-based richness measures, and discovered-direction analyses with intervention validation characterize how the latent represents constraint families at the graph, node, and edge level. On the decoder side, three attribution methods (gradient, integrated gradients, DeepLIFT) feed three reading angles: abductive, contrastive against the best feasible alternative, and counterfactual (smallest input change that switches the action or restores feasibility). Explanations are scored on fidelity, concentration, stability, sanity, and actionability. Across six variants combining three encoders (Attention baseline, Unimp, UnimpMoe) with two decoders (Hard-Mask, Recourse), we find that graph inductive bias improves both representational predictability and decoder sanity, that the Mixture-of-Experts encoder represents constraints in a distributed rather than axis-aligned way, and that the Recourse training regime, not merely its softer mask, produces policies that represent infeasibility usefully, exposing make-feasible counterfactuals that Hard-Mask policies fail to produce even when fed infeasible alternatives externally.
Large-scale capacitated vehicle routing problems (CVRPs) are commonly addressed using cluster-first route-second (CFRS) approaches that split a routing instance into smaller, computationally tractable subproblems. Existing splitting methods typically rely on fixed partitioning rules, predefined optimization objectives, or learned policies, which may perform inconsistently across instances exhibiting different spatial, demand, and operational characteristics. In this work, we propose an adaptive CFRS system that formulates a decomposition procedure as an iterative decision-making process. Motivated by the recent success of large language models (LLMs) in reasoning and tool selection, the system employs an LLM as a high-level decision maker that analyzes the evolving decomposition state and selectively applies further clustering, balancing, and refinement operators. The proposed algorithm jointly partitions customers and vehicles, enabling capacity-aware clustering while adapting partitioning decisions to the characteristics of each problem. We evaluate the approach on synthetic and benchmark-derived CVRP instances containing up to 500,000 customers. Experimental results demonstrate competitive performance on benchmark-scale instances while exhibiting improved scalability and robust routing quality on substantially larger problems. These results highlight the potential of adaptive, LLM-guided decision support as a practical approach for industrial-scale vehicle routing and large-scale logistics planning.
This paper introduces RACL, a Reasoning-Agent Control Layer for metaheuristics. RACL places a reasoning agent above an existing optimizer. The agent does not replace the optimizer and does not modify business constraints. Instead, it controls the optimizer's internal search behavior by observing operational memory, reasoning over past behavior, formulating bounded hypotheses, testing interventions, evaluating outcomes, applying guardrails, consolidating useful policies and explaining its decisions. The experiment uses vehicle routing as a testbed, but the contribution is not a new routing solver, a particular ALNS configuration or a specific set of routing rules. The contribution is the RACL method: a way for a reasoning agent to discover, validate, consolidate and explain algorithmic control rules for a metaheuristic. In the current experimental setting, RACL improves or ties the Operational Memory Policy in 21 of 21 feasible cases and improves or ties a non-reasoning Stagnation-Triggered Policy in 18 of 21 feasible cases, with an average RACL vs STP cost delta of -0.641%. In the Sevilla-9/10 runtime sample, RACL improves average cost by -8.337% versus Fixed and -1.605% versus STP without showing material computational overhead. During the proof-of-concept, Codex was used as an in-the-loop reasoning agent observing executions, interpreting logs and proposing live bounded interventions. The policy proxy was later used only to make quantitative evaluation reproducible.
Oleksandr Yakovenko, Mahdi Mostajabdaveh, Cheikh Ahmed +4cs.AI
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.