Performance improvement of energy consumption, passenger time and robustness in metro systems: A multi-objective timetable optimization approach

Highlights

• We firstly use the concept of robustness to tackle the uncertain dwell time.

• A three-objective integer programming model is formulated.

• The real-world passenger arrival rate is considered in the formulation.

• A detailed NSGA-II procedure is designed to solve the developed model.

• A real-world case study based on the Beijing Metro Yizhuang Line is conducted.

Abstract

As an effective transport mode to reduce the impact of urban mobility with great capacity and low pollution, metro systems have received rapid development all over the world in recent years. Since a well-designed timetable can improve the service level of passengers, increase the revenue of operating companies, and reduce the environmental pollution, the issue of timetable design/optimization is usually represented as a multi-objective decision problem. This paper develops a multi-objective integer programming model which integrates the energy consumption, the passenger waiting time, and the robustness by optimizing departure and arrival time of trains at each station. A non-dominated sorting genetic algorithm II (NSGA-II) is designed to find the optimal solution. Finally, a case study of Yizhuang line in Beijing metro system is conducted to illustrate the efficiency and effectiveness of the suggested timetable optimization approach.

Introduction

Metro system has received fast development all over the world due to its great capacity, high reliability and low pollution. In some metropolises such as London, New York and Beijing, the metro system has become a large-scale complex network (Yang, Yin, Wu, Qu, & Gao, 2019). The network mileages and number of lines and stations for some big cities around the world until the end of 2017 are listed in Table 1 (ChinaDaily, 2017, Wikipedia, 2018, Yang et al., 2019). From the operation perspective, the networking operation has taken the place of the traditional single-line operation mode.

Under the background of networking operation, as a crucial element of a metro system, timetable bears much more significance in terms of transport efficiency, operation cost and service quality. Although per capita energy consumption in metro systems is low, the total energy consumption is considerable (Cao, Wang, Liu, Li, & Xie, 2019). For example in Beijng, the Beijing Metro is the first large industry in electricity consumption. Minimization of the energy consumption is important to reduce the operation cost of metro operating companies. In the other hand, the essential mission of metro systems is transporting passengers efficiently and conveniently. Reduction of passenger travel time should be also taken into consideration. Therefore, it is significant to study a well-designed timetable considering the benefits of both metro passengers and operating companies. A number of existing literature on the timetable design/optimization problem considered both passenger time and energy consumption as research objectives (Ghoseiri et al., 2004, Li et al., 2013, Xu et al., 2016, Yang et al., 2015b, Yang et al., 2014, Yin et al., 2017).

In real-world metro systems, trains are stipulated to complete the travel task strictly according to the published timetable. However, there are a number of uncertain perturbations during the normal operation period (Cao et al., 2017, Corman et al., 2017, Zhang et al., 2018). For example, crowding passengers at stations can lead to the delay of departure time; and trains often have an early departure perturbation at off-peak hours due to the over abundant dwell time. In these cases, the actual train record in time level (i.e., recorded timetable) has a disordered deviation in comparison with the published timetable. Fig. 1 provides an illustration of deviations between recorded and published timetables according to the real-world data from the Beijing Metro Yizhuang line (Zhang, 2018).

Both energy consumption and passenger time are sensitive to the spatially and temporally relative position of trains scheduled by timetable. Therefore, it is difficult to achieve the optimal expected objectives under the condition of these perturbations, although the published timetable is the optimal one. For this issue, we introduce the robustness in the published timetable optimization problem to deal with the uncertain perturbations. Note that the traditional research on robustness in timetable problems aims to absorb perturbations for improving the punctuality rate. It is easily see that the robustness in this paper is a different concept, which is used to eliminate or reduce the influence of perturbations to energy consumption and passenger time.

Overall, this paper develops a multi-objective integer programming model and a non-dominated sorting genetic algorithm II (NSGA-II) to improve the performance of energy consumption, passenger waiting time and robustness for metro systems. The main contributions of this paper are summarized as follows:

• We firstly use the concept of robustness to tackle the uncertain dwell time in real-world train operations for improving the performance of timetable optimization approaches applied to real-world metro systems.

• We develop a multi-objective integer programming model to solve the timetable optimization problem with dwell time uncertainty, where the energy consumption, passenger waiting time, as well as robustness are optimized of compromise. Traditional studies assumed the passenger arrival rate as a uniform distribution, such that the average passenger waiting time equals to a half of headway. As we use the real-world passenger arrival rate (i.e., a random distribution) in the formulation, we can capture the wispy sensibility of dwell time and section running time to the passenger waiting time.

• We design a detailed NSGA-II procedure to solve the complicated multi-objective integer programming model, and come up with some indicators to evaluate the performance of the Pareto-optimal solutions.

The remainder of this research is organized as follows. In Section 2, we review the literature on the timetable optimization problem for metro/rail systems. In Section 3, we formulate the problem as a multi-objective integer programming model. In Section 4, we design a NSGA-II to find the optimal solution. In Section 5, we present a case study based on the real-world data from the Beijing Metro Yizhuang Line. Conclusions are provided in Section 6.