Integrated optimization of train timetabling and rolling stock circulation problem with flexible short-turning and energy-saving strategies

In daily operations, passenger demand for metro lines traversing city centers often exhibits pronounced tidal characteristics, particularly during morning and evening peak hours. Given the unbalanced spatial and temporal distribution of passenger demand in a bi-directional metro line, this paper investigates an integrated optimization method for train timetabling and rolling stock circulation plans with flexible short-turning and energy-saving strategies. In particular, this approach simultaneously considers constraints such as limited train capacity, turnaround operations, the finite number of available trains, and regenerative energy utilization. Firstly, by introducing decisions involving service frequency, service headway, train route selection, rolling stock circulation plan, and the overlap time indicator, a nonlinear integer programming (NLIP) model is formulated to minimize the weighted sum of passenger waiting time and energy costs, accounting for both passenger and operator perspectives. Subsequently, the model is reformulated into a quadratically constrained quadratic programming (QCQP) model which can be solved directly by commercial solvers. To address large-scale real-world experiments, an adaptive large neighborhood search (ALNS) algorithm is developed. Finally, numerical experiments are conducted on a simplified metro line and Fuzhou Metro Line 1. The results demonstrate that, compared to the full-length strategy, the proposed method reduces total passenger waiting time and energy costs by approximately 8.7% and 5.7%, respectively. Moreover, the methods could support decision-makers with different passenger and operator preferences.