Energy-efficient train operation is regarded as an effective way to reduce the operational cost and carbon emissions in metro systems. Reduction of the traction energy and increasing of the regenerative energy are two important ways for saving energy, which is closely related to the train timetable and driving strategy. To minimize the systematic net energy consumption, i.e., the difference between the traction energy consumption and the reused regenerative energy, this paper proposes an integrated train operation approach by jointly optimizing the train timetable and driving strategy. A precise train driving strategy is presented and the timetable model considers the headway between successive trains, the distribution of the trip time, and passenger demand in this paper. In addition, a distributed regenerative braking energy model is proposed, based on which the integrated optimization model is formulated. Then, a two-level approach is proposed to solve the problem. At the driving strategy level, the train control problem is transferred into a multi-step decision problem and the Dynamic Programming method is introduced to calculate the energy-efficient driving strategy with the given trip time. As for the timetable level, the trip times and headway of trains are optimized by using the Simulated Annealing algorithm based on the results of dynamic programming method. The timetable optimization level balances the mechanical traction energy of multi-interstations and the amount of the reused regenerative energy such that the net mechanical energy consumption of the metro system is minimized. Furthermore, two numerical examples are conducted for train operations in the peak and off-peak hours separately based on the real-world data of a metro line. The simulation results illustrate that the proposed approach can produce a good performance on energy-saving.

In metro systems, a tactical train schedule with the rolling stock circulation plan aims to determine the movements of all physical trains. To utilize the regenerative energy as much as possible, this paper proposes an integrated model to simultaneously generate the optimal train schedule and rolling stock circulation plan, in which the brake-traction overlapping time at stations is maximized. In particular, our model rigorously considers the train turn-around constraints, train circulation constraints, and dynamic passenger demands to tackle the train loading capacity constraints. To eliminate the effect of non-linear constraints, we reformulate the original model into its equivalent linear model that can be efficiently solved by linear programming solvers. Finally, the numerical experiments based on Beijing Yizhuang Metro Line are implemented to demonstrate the effectiveness of our proposed model.

Owing to environmental concerns, the energy-efficient subway train scheduling problem is necessary in subway operation management. This paper designs an approximate dynamic programming (DP) approach for energy-efficient subway train scheduling problem with time-dependent demand. The train traffic model is proposed with the dynamic equations for the evolution of train headway, train passenger loads, and the energy consumption along the subway line. For the dynamic changing of the onboard passengers with time, the total train energy usage is modeled as the sum of energy consumptions from the traction system and auxiliary facilities. A nonlinear DP problem is formulated to generate a near optimal timetable to realize the tradeoff among the utilization of trains, passenger waiting time, service levels, and energy consumption. To overcome the curse of dimensionality in this optimization problem, we construct an approximate DP framework, where the conceptions of states, policies, state transitions, and reward function are introduced. And this algorithm is able to converge to a good solution with a short time compared to the genetic algorithm and differential evolution algorithm. Finally, the numerical experiments are given to demonstrate the effectiveness of the proposed model and algorithm.

Due to the inventible disruptions caused by e.g., flood, hurricane and blizzard, metro managers in recent years have gradually shifted their attention from prevention of disruptions to ability to withstand and quick recovery from these disruptions, hence the need for enhancing the resilience of an urban rail system. In this paper, we propose a resilience-oriented train rescheduling framework, which helps the rail transit system recover to the normal state as soon as possible in case of disruptions, with the help of pre-allocated rolling stocks at the depots, side tracks and timetable rescheduling of grains. Specifically, we first construct an event-activity network for an urban rail line with multiple depots and side tracks, in which the arrival and departure of trains are modeled as a set of events. Several groups of decision variables and linear constraints are denoted to model the rescheduling of trains. Considering the use of short-turning train rescheduling strategy and pre-allocated rolling stocks, we then formulate the problem into a mixed-integer linear programming (MILP) model, where the objective is to maximize the resilience of the urban rail line against disruptions. Through the analysis of model properties, we develop a branch-and-cut algorithm by deriving a series of linear inequalities, which we prove are valid inequalities, to strength the tightness of the MILP model. Finally, numerical experiments based on real-world data of Beijing metro are conducted to verify the effectiveness of our approach.