PyVRP$^+$: LLM-Driven Metacognitive Heuristic Evolution for Hybrid Genetic Search in Vehicle Routing Problems

TL;DR

This paper introduces a metacognitive evolutionary framework using LLMs to develop superior heuristics for vehicle routing problems, outperforming existing methods in solution quality and efficiency.

Contribution

It presents a novel LLM-driven metacognitive approach that explicitly diagnoses failures and formulates hypotheses, leading to improved heuristics for VRP.

Findings

Heuristics evolved with MEP outperform baseline by up to 2.70% in solution quality.

Runtime reduced by over 45% using the new heuristics.

The approach generalizes across various VRP variants.

Abstract

Designing high-performing metaheuristics for NP-hard combinatorial optimization problems, such as the Vehicle Routing Problem (VRP), remains a significant challenge, often requiring extensive domain expertise and manual tuning. Recent advances have demonstrated the potential of large language models (LLMs) to automate this process through evolutionary search. However, existing methods are largely reactive, relying on immediate performance feedback to guide what are essentially black-box code mutations. Our work departs from this paradigm by introducing Metacognitive Evolutionary Programming (MEP), a framework that elevates the LLM to a strategic discovery agent. Instead of merely reacting to performance scores, MEP compels the LLM to engage in a structured Reason-Act-Reflect cycle, forcing it to explicitly diagnose failures, formulate design hypotheses, and implement solutions grounded in pre-supplied domain knowledge. By applying MEP to evolve core components of the state-of-the-art Hybrid Genetic Search (HGS) algorithm, we discover novel heuristics that significantly outperform the original baseline. By steering the LLM to reason strategically about the exploration-exploitation trade-off, our approach discovers more effective and efficient heuristics applicable across a wide spectrum of VRP variants. Our results show that MEP discovers heuristics that yield significant performance gains over the original HGS baseline, improving solution quality by up to 2.70\% and reducing runtime by over 45\% on challenging VRP variants.