多臂老虎机与骨干增强 Lin-Kernighan-Helsgaun 算法求解旅行商问题
Multi-armed Bandit and Backbone boost Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problems
AI总结：
针对 LKH 中 α 值未利用历史信息且引导单一的问题，本文提出动态骨干信息，并通过多臂老虎机自适应组合骨干、α 值与距离，显著提升 LKH/LKH-3 在 TSP、CTSP 和 CVRPTW 上的性能与泛化性。
摘要：
Lin-Kernighan-Helsgaun（LKH）启发式算法是求解旅行商问题（TSP）的经典局部搜索算法。LKH 引入 α 值来替代传统距离度量，以评估边的质量，从而带来显著性能提升。然而，我们观察到 α 值在搜索过程中没有充分利用历史信息，而且单一的引导信息往往使 LKH 难以逃离某些局部最优。为解决上述问题，我们提出了一种在 TSP 局部搜索过程中提取骨干信息的新方法，该信息是动态的，并可在每次找到局部最优解后更新。我们进一步提出将骨干信息、α 值和距离相结合来评估边的质量，从而引导搜索。此外，我们将它们的不同组合抽象为多臂老虎机（MAB）中的臂，并使用 MAB 模型帮助算法动态选择合适的评估度量。骨干信息和 MAB 都能够提供多样化的引导信息，并从搜索历史中学习，以推荐最佳度量。我们将所提方法应用于 LKH 和 LKH-3；LKH-3 是 LKH 的扩展版本，可用于求解约 40 种 TSP 和车辆路径问题（VRP）的变体问题。大量实验表明，我们提出的方法具有优异的性能和泛化能力，显著改进了用于 TSP 的 LKH，以及用于两种代表性 TSP 和 VRP 变体（即 Colored TSP（CTSP）和带时间窗的容量约束 VRP（CVRPTW））的 LKH-3。
英文摘要：
The Lin-Kernighan-Helsguan (LKH) heuristic is a classic local search algorithm for the Traveling Salesman Problem (TSP). LKH introduces an $α$-value to replace the traditional distance metric for evaluating the edge quality, which leads to a significant improvement. However, we observe that the $α$-value does not make full use of the historical information during the search, and single guiding information often makes LKH hard to escape from some local optima. To address the above issues, we propose a novel way to extract backbone information during the TSP local search process, which is dynamic and can be updated once a local optimal solution is found. We further propose to combine backbone information, $α$-value, and distance to evaluate the edge quality so as to guide the search. Moreover, we abstract their different combinations to arms in a multi-armed bandit (MAB) and use an MAB model to help the algorithm select an appropriate evaluation metric dynamically. Both the backbone information and MAB can provide diverse guiding information and learn from the search history to suggest the best metric. We apply our methods to LKH and LKH-3, which is an extension version of LKH that can be used to solve about 40 variant problems of TSP and Vehicle Routing Problem (VRP). Extensive experiments show the excellent performance and generalization capability of our proposed method, significantly improving LKH for TSP and LKH-3 for two representative TSP and VRP variants, the Colored TSP (CTSP) and Capacitated VRP with Time Windows (CVRPTW).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
