🤖 AI Summary
本文解决了考虑交通拥堵影响的带宽松时间窗的时间依赖旅行商问题，通过结合列生成、ng-记忆增强和精确搜索的动态规划标签算法来实现。
📝 Abstract
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.