This research paper focuses on the optimization of train timetables and maintenance windows, both of which significantly impact service quality and cost-effectiveness. Uncertainties in both elements can disrupt established transportation plans, causing train delays and maintenance cancellations. Accordingly, we highlight the necessity of augmenting the robustness of these schedules. In this study, we explored an integrated robust optimization of maintenance windows and train timetables using a distributionally robust optimization (DRO) model. The DRO model was established with two types of binary variables and a cross-resolution consistency constraint was introduced to couple them. We innovatively employed a multi-commodity network flow framework to reconstruct the DRO model and designed an alternating direction method of multipliers (ADMM)-based decomposition mechanism. This mechanism was applied to dualize the cross-resolution consistency and track capacity constraints. To handle the problem, we developed a heuristic algorithm driven by ADMM, along with a nested simulation. The algorithm's effectiveness is demonstrated through numerical experiments.

中文翻译：

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使用 ADMM 驱动和嵌套模拟启发式算法对维护窗口和列车时刻表进行集成鲁棒优化

本研究论文重点关注火车时刻表和维护窗口的优化，这两者都会对服务质量和成本效益产生重大影响。这两个因素的不确定性都会扰乱既定的运输计划，导致火车延误和维护取消。因此，我们强调增强这些时间表的稳健性的必要性。在本研究中，我们使用分布式鲁棒优化 (DRO) 模型探索了维护窗口和列车时刻表的集成鲁棒优化。DRO模型是用两种类型的二元变量建立的，并引入交叉分辨率一致性约束来耦合它们。我们创新性地采用多商品网络流框架来重构DRO模型，并设计了基于交替方向乘子法（ADMM）的分解机制。该机制用于双重化跨分辨率一致性和轨道容量约束。为了解决这个问题，我们开发了一种由 ADMM 驱动的启发式算法以及嵌套模拟。通过数值实验证明了该算法的有效性。