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Key Takeaways

  • Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routing This paper introduces a new approach to solving large-scale Capacitate...
  • 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.
  • In this work, we propose an adaptive CFRS system that formulates a decomposition procedure as an iterative decision-making process.
  • 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.
Paper AbstractExpand

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.

Adaptive Cluster-First Route-Second Decomposition for Industrial-Scale Vehicle Routing
This paper introduces a new approach to solving large-scale Capacitated Vehicle Routing Problems (CVRPs), where a fleet of vehicles must serve geographically distributed customers with specific demand requirements. While traditional methods often rely on fixed rules to break these massive problems into smaller, manageable pieces, they frequently struggle when faced with the diverse and changing conditions of real-world logistics. The authors propose an adaptive system that uses a Large Language Model (LLM) as a high-level decision maker. By iteratively analyzing the state of the routing plan, the LLM intelligently selects and applies specific tools to refine how customers and vehicles are grouped, allowing the system to adjust its strategy based on the unique characteristics of each problem.

A Flexible Approach to Decomposition

The core of the proposed system is the "Cluster-First Route-Second" (CFRS) paradigm. Instead of attempting to solve a massive routing instance all at once, the system decomposes the problem into smaller subproblems. Unlike existing methods that use static rules—such as simple geometric partitioning—this approach treats decomposition as an ongoing, iterative process. The system maintains a hierarchical "cluster tree" that represents the current state of the routing plan. The LLM acts as an agent that observes this tree and decides when and how to further split, balance, or refine these clusters to improve efficiency.

Agentic Decision-Making

The system functions by treating optimization as a sequence of decisions. The LLM is equipped with a suite of specialized tools—including clustering, balancing, and partition-modification heuristics—that it can invoke as needed. Because the LLM analyzes the evolving state of the partitions, it can identify potential inefficiencies, such as clusters that lack sufficient vehicle capacity to meet customer demand. By jointly partitioning both customers and vehicles, the system ensures that the resulting clusters are not just geographically compact, but also operationally feasible, adapting to the specific fleet and demand constraints of the instance.

Scalability and Performance

The authors evaluated this framework on both synthetic and benchmark-derived CVRP instances, testing its performance on problems containing up to 500,000 customers. The experimental results demonstrate that the LLM-guided approach is highly competitive on standard benchmark sizes while offering significant advantages in scalability for massive, industrial-scale scenarios. By moving away from rigid, predefined partitioning rules, the system maintains robust routing quality even as the complexity and size of the logistics network grow, highlighting the potential for LLMs to serve as effective, adaptive components in complex industrial decision-support systems.

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