arXiv:2602.00580cs.AI2026-02

用无监督神经网络改造传统算法,让老方法也能智能探索更优路径。

Small Shifts, Large Gains: Unlocking Traditional TSP Heuristic Guided-Sampling via Unsupervised Neural Instance Modification

  • 通过神经网络微调节点位置生成新实例,让传统算法实现多路径探索。
  • 在大规模测试中性能接近神经网络方法,训练时间仅需数秒。
  • 无需真实答案监督,适合想快速提升传统算法的工程师使用。

旅行商问题(TSP)是组合优化中的经典难题,传统启发式算法如最远插入或最近插入虽高效实用,但因行为确定性易陷入局部最优。而基于神经网络的算法虽能通过引导采样获得更优解,却需大量训练和真实标签,难以实用。为此,本文提出TSP-MDF框架,利用神经网络对原始实例进行坐标微调,生成多个修改后的实例,再由传统启发式算法在这些实例上构造路径并映射回原问题,从而突破局部最优。该框架中神经修饰器可无监督训练,效率极高。在大规模及真实场景基准测试中,TSP-MDF显著提升了传统算法性能,达到与神经网络方法相当的解质量,且训练时间极短。

原文摘要 · Abstract (English)

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest Insertion, are computationally efficient and highly practical, but their deterministic behavior limits exploration and often leads to local optima. In contrast, neural-based heuristic tour constructors alleviate this issue through guided-sampling and typically achieve superior solution quality, but at the cost of extensive training and reliance on ground-truth supervision, hindering their practical use. To bridge this gap, we propose TSP-MDF, a novel instance modification framework that equips traditional deterministic heuristic tour constructors with guided-sampling capability. Specifically, TSP-MDF introduces a neural-based instance modifier that strategically shifts node coordinates to sample multiple modified instances, on which the base traditional heuristic tour constructor constructs tours that are mapped back to the original instance, allowing traditional tour constructors to explore higher-quality tours and escape local optima. At the same time, benefiting from our instance modification formulation, the neural-based instance modifier can be trained efficiently without any ground-truth supervision, ensuring the framework maintains practicality. Extensive experiments on large-scale TSP benchmarks and real-world benchmarks demonstrate that TSP-MDF significantly improves the performance of traditional heuristics tour constructors, achieving solution quality comparable to neural-based heuristic tour constructors, but with an extremely short training time.

TSP启发式算法无监督学习路径优化

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