Robust integrated optimization for train rescheduling and rolling stock circulation of metro lines under disruptions

Urban public transportation systems are critical for mass mobility, but unexpected disruptions can cause delays and passenger congestion, challenging operational reliability and safety. This paper investigates the integrated optimization of train rescheduling, rolling stock circulation, and passenger flow control under metro disruptions. We develop a mixed-integer nonlinear programming model to minimize timetable deviation, passenger waiting time, and operating costs associated with skip-stop operations and short-turning strategies. To handle uncertain passenger demand, we adopt a scenario-based robust optimization model that remains feasible across all scenarios. To reduce the computational complexity introduced by bilinear terms in passenger waiting time, we apply a piecewise McCormick envelope method combined with a bound contraction algorithm, enabling rapid generation of high-quality solutions. The proposed approach is validated using data on the Beijing Yizhuang Line, demonstrating its robustness and practical applicability for punctuality and safety in disrupted metro operations.