Robust dynamic train regulation integrated with stop-skipping strategy in urban rail networks: An outer approximation based solution method

In dense urban rail networks with high passenger demands, uncertain disturbances occur frequently, and the resulting train delays will likely spread over the whole network rapidly, hence degrading the service quality offered to passengers. To cope with the uncertainties of frequent disturbances in urban rail networks, this paper proposes a robust train regulation strategy based on the information gap decision theory, which allows the operators to adjust the conservativeness of adjustment schemes flexibly by varying system performances but without the need for prior knowledge of uncertain disturbances. Specifically, considering the coupling relationship between train dynamic flows and passenger dynamic flows, a mixed integer quadratically constrained programming (MIQCP) model is constructed for the robust train regulation problem to generate solutions with immunity against disturbance uncertainties, in which the envelope-bound model is used to characterizing the uncertain sets of disturbances. To meet the real-time requirements of train operation adjustment, a tailored outer approximation algorithm incorporating a two-phase heuristics method is devised to effectively solve the developed robust train regulation model, thereby quickly generating high-quality solutions. Moreover, the warm start technique and domain reduction technique are carefully developed to accelerate the solving procedure. Numerical experiments based on the Beijing metro network illustrate the robustness of the proposed train regulation strategies and the effectiveness of the designed solution approach.