In the urban rail transit system, train timetabling according to the dynamic passenger demand is important to offer high-quality service. Timetable optimization with the predetermined train route plan cannot synchronously consider the spatial and temporal characteristics of demand. Based on the Automated Fare Collection (AFC) data, this study proposes the integrated optimization (IO) to make route plan and timetable. A mixed-integer nonlinear programming (MINLP) model is formulated with the aim of reducing passenger penalty travel time and operation penalty cost. An improved non-dominated sorted genetic algorithm-II (Improved NSGA-II) is applied to deal with the bi-objective problem. A numerical experiment is used to prove the effectiveness and efficiency of the model and the algorithm. Then, the IO approach is applied in a bi-directional urban rail transit line. The results show that the IO performs the best compared with two other feasible strategies, namely the current optimization (CO) and phased optimization (PO).

The key features of an intercity high-speed railway (IHSR) include its high frequency, the short intervals, and the short distances covered. The mode of rolling stock scheduling generally uses fixed segments. In view of the fact that intercity passenger demand has the characteristics of large fluctuations in terms of time and direction, the use of the traditional rolling stock scheduling plan with a fixed train formation will result in a mismatch between the train formation and passenger demand. In order to improve the matching of train formation and passenger demand and increase the utilization rate of rolling stocks, this paper puts forward the concept of flexible train formation by time period and constructs an integrated optimization model of the rolling stock scheduling and flexible train formation based on passenger demand. The model aims at minimizing the number of rolling stocks, the amount of coupling/decoupling necessary, and the deadhead time. The model takes into account constraints such as the connection method used, the source and destination of the rolling stock, the total amount of rolling stock, and the use of a flexible train formation. In addition, the Gurobi solver is used to accurately solve the problem through the linearization of the model. This paper also provides an example of the Beijing–Tianjin IHSR as a verification of the feasibility and effectiveness of the proposed model. The example compares the indicators in the fixed and flexible train formation modes. The results of the research show that, on the premise of meeting passenger demand, the flexible train formation mode can reduce the cost of rolling stock; increase the efficiency of rolling stock; improve the balance of rolling stock scheduling; and, consequently, provide a reference for the optimization of rolling stock scheduling plan with the background of “cost reduction and efficiency increase” in the railway industry.

When passengers are oversaturated in the urban rail transit system and a further increase of train frequency is impossible, passenger flow control strategy is an indispensable approach to avoid congestion and ensure safety. To make the best use of train capacity and reduce the passenger waiting time, coordinative flow control is necessary at each station on a line. In most published studies, the equilibrium of passenger distributions among different stations and periods is not considered. As a result, two issues occur making it hard to implement in practical. First, a large number of passengers are held up outside a small number of stations for very long time. Second, there is a large variation of controlled flows for successive time intervals. To alleviate this problem, a single-line equilibrium passenger flow control model is constructed, which minimizes the total passenger delay. By applying different forms of the delay penalty function (constant and linear), flow control strategies such as independent flow control and equilibrium flow control can be reproduced. An improved simulated annealing algorithm is proposed to solve the model. A numerical case is studied to analyze the sensitivity of the functions, and the best parameter relationship in different functions could be confirmed. A real-world case from Batong Line corridor in Beijing subway is used to test the applicability of the model and algorithm, and the result shows that the solution with linear delay penalty functions can not only reduce the total passenger delay but also equilibrate the number of flow control passengers on spatial and temporal.

In recent years, with increasing passenger travel demand, high-speed railways have developed rapidly. The stop planning and timetabling problems are the core contents of high-speed railway transport planning and have important practical significance for improving efficiency of passenger travel and railway operation Dong et al. (2020). This study proposes a collaborative optimization approach that can be divided into two phases. In the first phase, a mixed-integer nonlinear programming model is constructed to obtain a stop plan by minimizing the total passenger travel time. The constraints of passenger origin-destination (OD) demand, train capacity, and stop frequency are considered in the first phase. In the second phase, the train timetable is optimized after the stop plan is obtained. A multiobjective mixed-integer linear optimization model is formulated by minimizing the total train travel time and the deviation between the expected and actual departure times from the origin station for all trains. Multiple types of trains and more refined headways are considered in the timetabling model. Finally, the approach is applied to China’s high-speed railway, and the GUROBI optimizer is used to solve the models in the above two stages. By analyzing the results, the total passenger travel time and train travel time decreased by 2.81% and 3.34% respectively. The proposed method generates a more efficient solution for the railway system.