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

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.