A generalized neural solver based on LLM-guided heuristic evoluation framework for solving diverse variants of vehicle routing problems

Abstract

Vehicle Routing Problems (VRPs) are key combinatorial optimization challenges with broad applications in logistics. While neural solvers based on attention mechanisms offer promising results, they require retraining for each VRP variant, limiting scalability. Existing expert-designed and LLM-based heuristic methods often suffer from limited exploration ability and premature convergence. We propose the Unified VRP Neural Solver (UNS), an LLM-enabled framework that dynamically adjusts attention scores by generating variant-specific heuristics without requiring retraining of neural model parameters. At its core, the LLM-Guided Heuristic Evolution (LHE) algorithm, which is inspired by population-based Differential Evolution (DE) frameworks, iteratively refines heuristics through Mutation, Global Crossover, and Local Crossover to enhance diversity and avoid local optima. Extensive experiments across 16 VRP variants show that LHE outperforms state-of-the-art neural solvers and LLM-based approaches. The similarity analysis of heuristic populations reveals that LHE maintains higher diversity and avoids premature convergence. Additional evaluations on CVRP and TSP, along with ablation studies, validate the effectiveness and generalizability of LHE.