Neural Cluster First, Route Second: One-Shot Capacitated Vehicle Routing via Differentiable Optimal Transport

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.

Neural Combinatorial Optimization (NCO) has emerged as a powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance solution quality and generalization. Specifically, we modify the Random Re-Construct (RRC) approach of the Light Encoder Heavy Decoder (LEHD) model by incorporating Simulated Annealing (SA). Unlike the conventional RRC, which greedily replaces suboptimal segments, our SA-based modification introduces a probabilistic acceptance mechanism that allows the model to escape local optima and explore a more diverse solution space. Additionally, we enhance the Policy Optimization with Multiple Optima (POMO) approach by integrating Beam Search, enabling systematic exploration of multiple promising solutions while maintaining diversity in the search space. We further investigate different inference strategies, including Softmax Sampling, Greedy, Gumbel-Softmax, and Epsilon-Greedy, analyzing their impact on solution quality. Furthermore, we explore instance augmentation techniques, such as horizontal and vertical flipping and rotation-based augmentations, to improve model generalization across different CVRP instances. Our extensive experiments demonstrate that these modifications significantly reduce the optimality gap across various Capacitated Vehicle Routing Problem (CVRP) benchmarks, with Beam Search and SA-based RRC consistently yielding superior performance. By refining inference techniques and leveraging enhanced search strategies, our work contributes to the broader applicability of NCO models in real-world combinatorial optimization tasks.

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.