VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems

TL;DR

VRPAgent introduces an LLM-driven framework that auto-designs problem-specific operators for a large neighborhood search, refined via a targeted genetic algorithm with elitism and biased crossover. By constraining generation to operators embedded in a correctness-guaranteed metaheuristic, it achieves state-of-the-art performance across CVRP, VRPTW, and PCVRP while running on a single CPU core. The paper demonstrates robust improvement over handcrafted and several learning-based baselines, supported by ablations, LLM-variety analyses, and discovery-process convergence, and makes code and prompts publicly analyzable. This approach signals a practical pathway for automated, adaptable heuristic design in complex VRPs and other combinatorial problems.

Abstract

Designing high-performing heuristics for vehicle routing problems (VRPs) is a complex task that requires both intuition and deep domain knowledge. Large language model (LLM)-based code generation has recently shown promise across many domains, but it still falls short of producing heuristics that rival those crafted by human experts. In this paper, we propose VRPAgent, a framework that integrates LLM-generated components into a metaheuristic and refines them through a novel genetic search. By using the LLM to generate problem-specific operators, embedded within a generic metaheuristic framework, VRPAgent keeps tasks manageable, guarantees correctness, and still enables the discovery of novel and powerful strategies. Across multiple problems, including the capacitated VRP, the VRP with time windows, and the prize-collecting VRP, our method discovers heuristic operators that outperform handcrafted methods and recent learning-based approaches while requiring only a single CPU core. To our knowledge, \VRPAgent is the first LLM-based paradigm to advance the state-of-the-art in VRPs, highlighting a promising future for automated heuristics discovery.

Figures (5)

• Figure 1: VRPAgent overview.
• Figure 2: Ablation results.
• Figure 3: Performance on the CVRP for different LLMs. Detailed cost calculations are provided in \ref{['app:costs']}.
• Figure 4: Performance over the course of the discovery process.
• Figure 5: Results of the sensitivity analyses.