Vol.:(0123456789) Operational Research (2021) 21:1691–1721 https://doi.org/10.1007/s12351-019-00523-y 1 3 ORIGINAL PAPER Designing a resilient skip‑stop schedule in rapid rail transit using a simulation‑based optimization methodology Ali Shahabi 1  · Sadigh Raissi 1  · Kaveh Khalili‑Damghani 1  · Meysam Rafei 1 Received: 1 August 2018 / Revised: 21 August 2019 / Accepted: 9 October 2019 / Published online: 19 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract In recent years, rapid rail transit systems have played a unique role in transporta- tion systems due to the demand increase in accommodating passengers. This study proposes a simulation–optimization method to improve the resiliency of the train timetable in rapid transit rail lines under uncertainty associated with the passenger fow and train running times. The aim is to evaluate the resiliency of the train time- table through a discrete-event simulation (DES) model and to provide an optimized schedule with the maximum degree of resiliency against random disruptions caused by passenger fow fuctuations. The problem is frst formulated as a mixed-integer nonlinear programming model. The validity of the DES model is justifed using convergence test analysis of the response variable, i.e., average passenger wait time, during the simulation run. Due to the complexity of the problem, a variable neigh- borhood search (VNS) and a genetic algorithm (GA) are proposed to solve large instances of the problem. A self-adaptive tuning approach is proposed to adjust the GA parameters. The beneft of the simulation–optimization approach is verifed through numerical experiments based on real cases adopted from Line No. 1 of the Tehran underground metro system. The results indicate that the simulation-based optimization method could improve the resiliency of train services by almost 16.7%, on average, as against the all-stop service operation. The average improvement of using VNS as against the GA is about 47%. Also, VNS method provides better-qual- ity solutions by average optimality gap of about 14% in all test instances when com- pared to an exact solution method, i.e., branch-and-reduce algorithm. Keywords Rapid transit · Resiliency · Simulation-based optimization · Train delay · Passenger demand * Sadigh Raissi raissi@azad.ac.ir Extended author information available on the last page of the article