Integrated robust optimization of maintenance windows and train timetables using ADMM-driven and nested simulation heuristic algorithm.

• We developed a distributionally robust optimization (DRO) model that takes into account the train operation and maintenance costs, and the robustness of the train timetables and maintenance windows. • We introduced an innovative approach to reconstructed the DRO model using a multi-commodity network flow framework. We designed a decomposition mechanism based on the alternating direction method of multipliers (ADMM) to dualize the cross-resolution consistency constraint and track capacity constraints. Further, we linearized the quadratic penalty items, thereby decomposing the original problem into a series of sub-problems. • We developed an ADMM-driven and nested simulation heuristic algorithm aligned with the problem's characteristics. The algorithm involves variable penalty parameters, with the delay costs of the arcs being iteratively updated based on simulation. • We verify the quality and efficiency of the proposed algorithm using a series of cases based on actual data. 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. [ABSTRACT FROM AUTHOR]