AI 中文总结
本文针对带时间窗的时变旅行商问题，提出结合动态规划标注算法、列生成等技术的精确框架，嵌入分支定价方法后可解决超10000个基准实例中最多含50个客户的实例，扩展了最优求解的实例范围。
AI 中文摘要
带时间窗的时变旅行商问题（TDTSPTW）通过考虑拥堵对出行时间的影响，对著名的带时间窗的旅行商问题进行了推广。本文中，我们为以总完成时间为目标的TDTSPTW开发了一个精确框架，该框架可扩展在宽松时间窗下可最优求解的实例范围，同时在所有时间窗松紧程度下均保持有效性。我们的框架依赖于动态规划标注算法，结合了列生成、ng-memory增强和精确搜索，利用完成界进行状态空间稀疏化、变量固定和精确搜索剪枝。嵌入分支定价方法后，该框架在包含超10000个实例的基准测试中，解决了所有最多含45个客户的实例，包括所有不含时间窗的最多含50个客户的实例。
英文摘要
The time-dependent traveling salesman problem with time windows (TDTSPTW) generalizes the well-known traveling salesman problem with time windows by accounting the effects of congestion on travel times. In this paper, we develop an exact framework for the TDTSPTW with a makespan objective that extends the range of instances solvable to optimality under loose time windows while remaining effective across all levels of time-window tightness. Our framework relies on a dynamic-programming labeling algorithm and combines column generation, ng-memory augmentation, and exact search, using completion bounds for state-space sparsification, variable fixing, and exact search pruning. Embedded within a branch-and-price method, the framework solves all instances with up to 45 customers in a benchmark comprising more than 10,000 instances, including all instances without time windows with up to 50 customers.
Comments24 pages, 2 figures
