In this paper, we present formulations and an exact method to solve the Time Dependent Traveling Salesman Problem with Time Window (TD-TSPTW) under a generic travel cost function where waiting is allowed. A particular case in which the travel cost is a non-decreasing function has been addressed recently. With that assumption, because of both the First-In-First-Out property of the travel time function and the non-decreasing property of the travel cost function, we can ignore the possibility of waiting. However, for generic travel cost functions, waiting after visiting some locations can be part of optimal solutions. To handle the general case, we introduce new lower-bound formulations that allow us to ensure the existence of optimal solutions. We adapt the existing algorithm for TD-TSPTW with non-decreasing travel costs to solve the TD-TSPTW with generic travel costs. In the experiment, we evaluate the strength of the proposed lower bound formulations and algorithm by applying them to solve the TD-TSPTW with the total travel time objective. The results indicate that the proposed algorithm is competitive with and even outperforms the state-of-art solver in various benchmark instances.

翻译：本文提出了一种求解通用时间依赖旅行成本函数下允许等待的带时间窗的时间依赖旅行商问题（TD-TSPTW）的数学模型与精确算法。已有研究针对旅行成本为非递减函数的特例进行了探讨。在该假设下，由于旅行时间函数遵循先入先出（FIFO）特性且旅行成本函数具有非递减性，可忽略等待的可能性。然而，对于通用旅行成本函数，在访问某些节点后等待可能成为最优解的一部分。为处理一般情形，我们提出了新的下界表达式以确保最优解的存在性。通过改进现有面向非递减旅行成本的TD-TSPTW算法，实现了对通用旅行成本TD-TSPTW问题的求解。实验部分，我们将所提出的下界表达式与算法应用于以总旅行时间为目标的TD-TSPTW问题，验证其有效性。结果表明，该算法在多个基准测试实例中与现有最优求解器性能相当甚至更优。