Local search plays a central role in many effective heuristic algorithms for the vehicle routing problem (VRP) and its variants. However, neighborhood exploration is known to be computationally expensive and time consuming, especially for large instances or problems with complex constraints. In this study, we explore a promising direction to address this challenge by introducing an original tensor-based GPU acceleration method designed to speed up the commonly used local search operators in vehicle routing. By using an attribute-based representation, the method offers broad extensibility, making it applicable to different VRP variants. Its low-coupling architecture, with intensive computations completely offloaded to the GPU, ensures seamless integration in various local search-based algorithms and frameworks, leading to significant improvements in computational efficiency and potentially improved solution quality. Through comparative experiments on benchmark instances of three routing problems, we demonstrate the substantial computational advantages of the proposed approach over traditional CPU-based implementations. We also provide a detailed analysis of the strengths and limitations of the method, providing valuable insights into its performance characteristics and identifying potential bottlenecks in practical applications. These findings contribute to a better understanding and suggest directions for future improvements.

翻译：局部搜索在车辆路径问题及其变体的许多有效启发式算法中扮演着核心角色。然而，邻域探索在计算上通常代价高昂且耗时，特别是对于大规模算例或具有复杂约束的问题。在本研究中，我们通过引入一种新颖的、基于张量的GPU加速方法来应对这一挑战，该方法旨在加速车辆路径规划中常用的局部搜索算子。通过使用基于属性的表示，该方法提供了广泛的扩展性，使其适用于不同的VRP变体。其低耦合架构将密集计算完全卸载至GPU，确保了在各种基于局部搜索的算法和框架中的无缝集成，从而显著提高了计算效率，并可能改善解的质量。通过对三个路径规划问题的基准算例进行对比实验，我们证明了所提方法相较于传统基于CPU的实现方式具有显著的计算优势。我们还对该方法的优势与局限性进行了详细分析，为其性能特征提供了有价值的见解，并指出了实际应用中的潜在瓶颈。这些发现有助于更好地理解该方法，并为未来的改进指明了方向。