With the rapid increase in residents in megacities, the passenger demand of metro systems is rising sharply and steadily, bringing immense pressure to train operations. To improve the service quality, this paper discusses systematically investigating a joint optimization of the robust passenger flow control strategy and train timetable on a congested metro line. A deterministic model for train timetabling and passenger flow control at each station is first developed to make a trade-off between operation efficiency and service fairness. Then, the uncertain passenger demand is further considered at each station, and three integer linear programming models are formulated to derive the robust passenger flow control strategies. The first two models are related to the technique of Light Robustness, in which the uncertainty is handled by inserting expected protection levels at stations or on trains. In addition, with a stochastic scenario set that characterizes the uncertain passenger information, the last model aims to find a solution that is feasible for all involved scenarios, and thus, reduces the impact of the uncertainty in metro systems. To improve the computational efficiency of large-scale instances, a customized decomposition-based algorithm is developed. Finally, some real-world case studies based on the operation data of the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.@en

Regular coronavirus disease 2019 (COVID-19) epidemic prevention and control have raised new requirements that necessitate operation-strategy innovation in urban rail transit. To alleviate increasingly serious congestion and further reduce the risk of cross-infection, a novel two-stage distributionally robust optimization (DRO) model is explicitly constructed, in which the probability distribution of stochastic scenarios is only partially known in advance. In the proposed model, the mean-conditional value-at-risk (CVaR) criterion is employed to obtain a tradeoff between the expected number of waiting passengers and the risk of congestion on an urban rail transit line. The relationship between the proposed DRO model and the traditional two-stage stochastic programming (SP) model is also depicted. Furthermore, to overcome the obstacle of model solvability resulting from imprecise probability distributions, a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form. A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming (MILP) solver is developed to improve the computational efficiency of large-scale instances. Finally, a series of numerical examples with real-world operation data are executed to validate the proposed approaches. @en

Aiming to increase successful transfers at stations for late-night passengers, we first propose an efficient dwell time adjustment strategy for the last-train coordination planning problem under transfer-passenger flows uncertainty. Unlike the traditional robust optimization model, we present a novel distributionally robust chance-constrained program to model this problem, where the probability distributions of the uncertain parameters are only partially available. By introducing a pessimistic ambiguous chance constraint, the proposed distributionally robust model guarantees that the probability of satisfying the service-oriented objective, i.e., maximum successful transfer-passenger flows in the whole subway system is larger than a predetermined confidence level in the worst case. We then draw the connection of the distributionally robust model with the traditional robust optimization model, and show that the proposed model can be interpreted as a generalized version of the robust optimization model. We further propose a safe tractable approximation method to reformulate the original model as a mixed-integer second-order conic programming under the bounded-perturbation ambiguous set, which can be solved to optimality on only small instances by the CPLEX. Hence, we develop a tabu search heuristic algorithm to obtain high-quality solutions for large-sized instances. We also use local search as a baseline algorithm to observe the improvements of the tabu search algorithm. Finally, we illustrate the superiority of the developed model on the Nanjing and Beijing subway networks and compare the performance of the proposed algorithms.@en