Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to define tight upper bounds for this problem by reusing the information gained when solving instances with similar features. This is customary in distribution management, where vehicle routes have to be generated over and over again with similar input data. To this aim, we devise an upper bounding technique based on the solution of a classical (and simpler) time-independent Asymmetric Travelling Salesman Problem, where the constant arc costs are suitably defined by the combined use of a Linear Program and a mix of unsupervised and supervised Machine Learning techniques. The effectiveness of this approach has been assessed through a computational campaign on the real travel time functions of two European cities: Paris and London. The overall average gap between our heuristic and the best-known solutions is about 0.001\%. For 31 instances, new best solutions have been obtained.

中文翻译：

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时间相关旅行商问题的学习上限

给定一个图，其弧遍历时间随时间变化，时间依赖旅行商问题包括找到覆盖图顶点的总持续时间最短的哈密顿游。这项工作的主要目标是通过重用在解决具有相似特征的实例时获得的信息来为这个问题定义严格的上限。这在配送管理中很常见，其中必须使用类似的输入数据一遍又一遍地生成车辆路线。为此，我们设计了一种基于经典（和更简单）时间无关的非对称旅行商问题的解决方案的上限技术，其中恒定弧成本通过线性规划和无监督混合的组合使用适当地定义和监督机器学习技术。这种方法的有效性已通过对两个欧洲城市（巴黎和伦敦）的实际旅行时间函数的计算活动进行评估。我们的启发式和最著名的解决方案之间的总体平均差距约为 0.001\%。对于 31 个实例，获得了新的最佳解决方案。