The offline pickup and delivery problem with time windows (PDPTW) is a classical combinatorial optimization problem in the transportation community, which has proven to be very challenging computationally. Due to the complexity of the problem, practical problem instances can be solved only via heuristics, which trade-off solution quality for computational tractability. Among the various heuristics, a common strategy is problem decomposition, that is, the reduction of a large-scale problem into a collection of smaller sub-problems, with spatial and temporal decompositions being two natural approaches. While spatial decomposition has been successful in certain settings, effective temporal decomposition has been challenging due to the difficulty of stitching together the sub-problem solutions across the decomposition boundaries. In this work, we introduce a novel temporal decomposition scheme for solving a class of PDPTWs that have narrow time windows, for which it is able to provide both fast and high-quality solutions. We utilize techniques that have been popularized recently in the context of online dial-a-ride problems along with the general idea of rolling horizon optimization. To the best of our knowledge, this is the first attempt to solve offline PDPTWs using such an approach. To show the performance and scalability of our framework, we use the optimization of paratransit services as a motivating example. We compare our results with an offline heuristic algorithm using Google OR-Tools. In smaller problem instances, the baseline approach is as competitive as our framework. However, in larger problem instances, our framework is more scalable and can provide good solutions to problem instances of varying degrees of difficulty, while the baseline algorithm often fails to find a feasible solution within comparable compute times.

翻译：离线带时间窗的取送货问题（PDPTW）是交通运输领域的经典组合优化问题，其计算复杂度已被证明极高。由于该问题的复杂性，实际算例只能通过启发式方法求解，这些方法在解的质量与计算可行性之间进行权衡。在众多启发式方法中，一种常见策略是问题分解，即将大规模问题分解为一系列规模较小的子问题，其中空间分解和时间分解是两种自然方法。尽管空间分解在某些场景下取得了成功，但由于难以跨分解边界拼接子问题的解，有效的时间分解一直面临挑战。本文提出了一种新颖的时间分解方案，用于求解一类具有窄时间窗的PDPTW问题，该方案能够同时提供快速且高质量的解。我们借鉴了近期在在线按需出行问题中广泛使用的技术，并结合滚动时域优化的总体思想。据我们所知，这是首次尝试采用此类方法求解离线PDPTW问题。为展示我们框架的性能与可扩展性，我们以辅助公交服务的优化为例进行验证。我们将结果与基于Google OR-Tools的离线启发式算法进行对比。在较小规模算例中，基线方法与我们框架的表现相当；然而在较大规模算例中，我们的框架更具可扩展性，能够为不同难度的算例提供优质解，而基线算法在可比计算时间内通常无法找到可行解。