实时铁路瓶颈路段列车调度模型与算法优化

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本文主要探讨了"铁路瓶颈路段实时列车调度问题的建模与求解"这一关键议题，发表在2015年8月的《IEEE Transactions on Intelligent Transportation Systems》第16卷第4期上。作者包括Lei Chen（IEEE会员）、Clive Roberts（IEEE会员）、Felix Schmid 和 Edward Stewart。铁路线上的瓶颈路段通常面临高密度交通，一旦某个列车出现扰动，可能会导致后续列车长时间延误，严重影响铁路运输效率。针对这种情况，研究者提出了一种混合整数编程模型，用于解决实时列车重新调度问题。在模型设计中，考虑了列车运行的复杂性，包括列车之间的依赖关系、时间约束以及调度决策对整体交通流的影响。该模型旨在找到在遇到突发情况时，如何最有效地调整接近瓶颈路段的列车路径，以最大化通过能力并减少整体的延误。为了验证模型的有效性和算法的性能，研究团队采用了蒙特卡洛方法进行案例分析。实验结果显示，他们开发的改进算法（DE_JRM）能够在满足实时交通控制应用需求的同时，显著降低平均加权延误时间。本文的关键知识点包括：铁路瓶颈路段的特性分析，混合整数编程在列车调度中的应用，以及基于DE_JRM算法的优化策略。此外，蒙特卡洛模拟作为评估工具的重要性，展示了模型在实际场景中的实用性。这项研究对于提高铁路系统的运行效率，提升乘客体验以及应对突发事件具有重要的理论和实践价值。通过深入理解并解决这类问题，铁路部门可以更好地应对未来的挑战，确保高效、安全的交通运输服务。

1896 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 16, NO. 4, AUGUST 2015

Modeling and Solving Real-Time Train Rescheduling

Problems in Railway Bottleneck Sections

Lei Chen, Member, IEEE, Clive Roberts, Member, IEEE, Felix Schmid, and Edward Stewart

Abstract—There usually exists a high density of trafﬁc through

bottleneck sections of mainline railways, where a perturbation of

one single train could result in long consequential delays across

a number of trains. In the event of disturbances, rescheduling

trains approaching the bottleneck will be necessary to increase the

throughput of the section. To model the real-time train reschedul-

ing problems around bottleneck sections, a mixed-integer

programming model is presented in this paper. An innovative

improved algorithm (DE_JRM) is developed to solve the problem.

The model and the algorithms are validated with a case study

using Monte Carlo methodology, which demonstrates that the

proposed algorithm can reduce the weighted average delay and

satisfy the requirements of real-time trafﬁc control applications.

Index Terms—Bottleneck section, differential evolution (DE),

railway trafﬁc management, train rescheduling.

I. INTRODUCTION

S passenger and freight transport volumes increase

throughout Europe, many mainline railways have been

experiencing a high density of railway trafﬁc, resulting in ser-

vices being very susceptible to minor delays and disturbances,

particularly in the sections where different services converge

from a range of origins and diverge to a variety of destinations.

These sections can be called “bottleneck sections.” Generally,

there are two junctions located at either end. A typical example

is the core area of the Thameslink route in London, U.K.,

as shown in Fig. 1. Due to the very high density of trafﬁc

through bottleneck sections, the train headways are relatively

small; thus, the allowance times and the buffer times added in

the original nominal timetables are insufﬁcient to absorb train

delays caused by unexpected disruptions that occur in daily

railway operations. A relatively small perturbation to one train

may cause long knock-on delays for the following trains on the

same route and the merging trains on other routes, because of

resource conﬂicts created by crossing moves and the necessary

signal overlaps.

Manuscript received June 26, 2014; revised October 28, 2014; accepted

December 2, 2014. Date of publication January 8, 2015; date of current version

July 31, 2015. This work was supported in part by the European Commis-

sion Framework Program 7 project ON-TIME and in part by the National

Natural Science Foundation of China under Grant 61304185. The Associate

Editor for this paper was B. Ning.

L. Chen, C. Roberts, and E. Stewart are with the School of Electronic,

Electrical and Computer Engineering, University of Birmingham, Birmingham

B15 2TT, U.K. (e-mail: l.chen.3@bham.ac.uk).

F. Schmid is with the School of Civil Engineering, University of Birming-

ham, Birmingham B15 2TT, U.K. (e-mail: f.schmid@bham.ac.uk).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TITS.2014.2379617

Fig. 1. Sketch map of the core area of the Thameslink route in London, U.K.

(websites of Network Rail).

To maintain a high quality of railway services in bottleneck

sections, train delays need to be well managed to reduce their

propagation. Therefore, the trains approaching bottleneck sec-

tions need to be rescheduled in an optimal manner to minimize

the overall delays following a disturbance, which is regarded

as a key requirement of the next generation of railway trafﬁc

management systems [1]–[3].

In a bottleneck section, there are generally two junctions

located at either end, these are referred to as known “portals.”

Approaching trains from different origins converge at the bot-

tleneck sections through the two portal junctions (arriving at

one portal junction and leaving from another one). In the bot-

tleneck sections, real-time train rescheduling problems of portal

junctions need to simultaneously consider all entry/exit points

to the bottleneck. The rescheduling of approaching trains for

one portal junction needs, therefore, to consider the movements

of the trains approaching this portal junction from another

portal junction.

The authors of this paper will present a systematic method-

ology of real-time trafﬁc management for bottleneck sections,

including retiming and resequencing of trains when approach-

ing the bottleneck sections. The mathematical model for train

rescheduling in bottleneck sections will be introduced ﬁrst. The

improved algorithm, which includes a stochastic modiﬁcation

operator for solving the model, will be described in details. A

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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