A Cooperative Scheduling Model for Timetable Optimization in Subway Systems
01 Mar 2013-IEEE Transactions on Intelligent Transportation Systems (IEEE)-Vol. 14, Iss: 1, pp 438-447
TL;DR: A cooperative scheduling approach to optimize the timetable so that the recovery energy that is generated by the braking train can directly be used by the accelerating train, and a genetic algorithm with binary encoding to solve the optimal timetable is designed.
Abstract: In subway systems, the energy put into accelerating trains can be reconverted into electric energy by using the motors as generators during the braking phase. In general, except for a small part that is used for onboard purposes, most of the recovery energy is transmitted backward along the conversion chain and fed back into the overhead contact line. To improve the utilization of recovery energy, this paper proposes a cooperative scheduling approach to optimize the timetable so that the recovery energy that is generated by the braking train can directly be used by the accelerating train. The recovery that is generated by the braking train is less than the required energy for the accelerating train; therefore, only the synchronization between successive trains is considered. First, we propose the cooperative scheduling rules and define the overlapping time between the accelerating and braking trains for a peak-hours scenario and an off-peak-hours scenario, respectively. Second, we formulate an integer programming model to maximize the overlapping time with the headway time and dwell time control. Furthermore, we design a genetic algorithm with binary encoding to solve the optimal timetable. Last, we present six numerical examples based on the operation data from the Beijing Yizhuang subway line in China. The results illustrate that the proposed model can significantly improve the overlapping time by 22.06% at peak hours and 15.19% at off-peak hours.
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TL;DR: An analytical formulation is provided to calculate the optimal speed profile with fixed trip time for each section and the algorithm is fast enough to be used in the automatic train operation (ATO) system for real-time control.
Abstract: Given rising energy prices and environmental concerns, train energy-efficient operation techniques are paid more attention as one of the effective methods to reduce operation costs and energy consumption. Generally speaking, the energy-efficient operation technique includes two levels, which optimize the timetable and the speed profiles among successive stations, respectively. To achieve better performance, this paper proposes to optimize the integrated timetable, which includes both the timetable and the speed profiles. First, we provide an analytical formulation to calculate the optimal speed profile with fixed trip time for each section. Second, we design a numerical algorithm to distribute the total trip time among different sections and prove the optimality of the distribution algorithm. Furthermore, we extend the algorithm to generate the integrated timetable. Finally, we present some numerical examples based on the operation data from the Beijing Yizhuang subway line. The simulation results show that energy reduction for the entire route is 14.5%. The computation time for finding the optimal solution is 0.15 s, which implies that the algorithm is fast enough to be used in the automatic train operation (ATO) system for real-time control.
295 citations
TL;DR: A fully comprehensive survey on energy-efficient train operation for urban rail transit is presented and it is concluded that the integrated optimization method jointly optimizing the timetable and speed profile has become a new tendency and ought to be paid more attention in future research.
Abstract: Due to rising energy prices and environmental concerns, the energy efficiency of urban rail transit has attracted much attention from both researchers and practitioners in recent years. Timetable optimization and energy-efficient driving, as two mainly used train operation methods in relation to the tractive energy saving, make major contributions in reducing the energy consumption that has been studied for a long time. Generally speaking, timetable optimization synchronizes the accelerating and braking actions of trains to maximize the utilization of regenerative energy, and energy-efficient driving optimizes the speed profile at each section to minimize the tractive energy consumption. In this paper, we present a fully comprehensive survey on energy-efficient train operation for urban rail transit. First, a general energy consumption distribution of urban rail trains is described. Second, the current literature on timetable optimization and energy-efficient driving is reviewed. Finally, according to the review work, it is concluded that the integrated optimization method jointly optimizing the timetable and speed profile has become a new tendency and ought to be paid more attention in future research.
289 citations
TL;DR: This paper gives an extensive literature review on energy-efficient train control (EETC), from the first simple models from the 1960s of a train running on a level track to the advanced models and algorithms of the last decade dealing with varying gradients and speed limits, and including regenerative braking.
255 citations
Cites background or methods or result from "A Cooperative Scheduling Model for ..."
...X. Yang et al. (2014) further developed the model of X. Yang et al. (2013)....
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...X. Yang et al. (2013) studied the topic of synchronization of accelerating and regenerative braking trains for metro systems....
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...X. Yang et al. (2015) again improved the model of X. Yang et al. (2013)....
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...Their conclusion is that their algorithm leads to 7.0% reduction in energy consumption in comparison with the currently operated timetable, and to 4.3% reduction in comparison with the algorithm of X. Yang et al. (2013)....
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TL;DR: An integrated energy-efficient operation model to jointly optimize the timetable and speed profile is formulates and some numerical experiments based on the actual operation data of Beijing Metro Yizhuang Line of China show that a larger headway leads to smaller energy saving rate.
Abstract: Due to increasing environmental concerns and energy prices, what is very important but has not been given due consideration is the energy efficiency of metro rail systems. Train energy-efficient operation consists of timetable optimization and speed control. The former synchronizes the accelerating and braking actions of trains to maximize the utilization of regenerative energy, and the latter controls the train driving strategy to minimize the tractive energy consumption under the timetable constraints. To achieve a better performance on the net energy consumption, i.e., the difference between the tractive energy consumption and the utilization of regenerative energy, this paper formulates an integrated energy-efficient operation model to jointly optimize the timetable and speed profile. We design a genetic algorithm to solve the model and present some numerical experiments based on the actual operation data of Beijing Metro Yizhuang Line of China. It is shown that a larger headway leads to smaller energy saving rate, and the maximum energy saving rate achieved is around 25% when we use the minimum allowable headway of 90 s. In addition, compared with the two-step approach optimizing the timetable and speed profile separately, the integrated approach can reduce the net energy consumption around 20%.
243 citations
TL;DR: In this article, the authors developed a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains.
Abstract: In a heavily congested metro line, unexpected disturbances often occur to cause the delay of the traveling passengers, infeasibility of the current timetable and reduction of the operational efficiency. Due to the uncertain and dynamic characteristics of passenger demands, the commonly used method to recover from disturbances in practice is to change the timetable and rolling stock manually based on the experiences and professional judgements. In this paper, we develop a stochastic programming model for metro train rescheduling problem in order to jointly reduce the time delay of affected passengers, their total traveling time and operational costs of trains. To capture the complexity of passenger traveling characteristics, the arriving ratio of passengers at each station is modeled as a non-homogeneous poisson distribution, in which the intensity function is treated as time-varying origin-to-destination passenger demand matrices. By considering the number of on-board passengers, the total energy usage is modeled as the difference between the tractive energy consumption and the regenerative energy. Then, we design an approximate dynamic programming based algorithm to solve the proposed model, which can obtain a high-quality solution in a short time. Finally, numerical examples with real-world data sets are implemented to verify the effectiveness and robustness of the proposed approaches.
221 citations
References
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TL;DR: The impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented and the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods.
1,782 citations
"A Cooperative Scheduling Model for ..." refers background in this paper
...Due to its extensive generality, strong robustness, high efficiency, and practical applicability, GA has widely been applied to solve integer programming problems [37]–[41] and the research on transportation system [41]–[45]....
[...]
TL;DR: An overview of the main works on train timetabling is presented, underlining the differences between models and methods that have been developed to tackle the nominal and the robust versions of the problem.
356 citations
TL;DR: In this paper, the authors describe the development and use of a model designed to optimise train schedules on single line rail corridors, which is used as a decision support tool for train dispatchers to schedule trains in real time in an optimal way.
Abstract: This paper describes the development and use of a model designed to optimise train schedules on single line rail corridors. The model has been developed with two major applications in mind, namely: as a decision support tool for train dispatchers to schedule trains in real time in an optimal way; and as a planning tool to evaluate the impact of timetable changes, as well as railroad infrastructure changes. The mathematical programming model described here schedules trains over a single line track. The priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay, as well as the current delay. This priority is used in a branch and bound procedure to allow and optimal solution to reasonable size train scheduling problems to be determined efficiently. The use of the model in an application to a “real life” problem is discussed. The impacts of changing demand by increasing the number of trains, and reducing the number of sidings for a 150 km section of single line track are discussed. It is concluded that the model is able to produce useful results in terms of optimal schedules in a reasonable time for the test applications shown here.
336 citations
01 Apr 1996
TL;DR: In this paper, the authors describe the development and use of a model designed to optimise train schedules on single line rail corridors, which is used as a decision support tool for train dispatchers to schedule trains in real time in an optimal way.
Abstract: This paper describes the development and use of a model designed to optimise train schedules on single line rail corridors. The model has been developed with two major applications in mind, namely: as a decision support tool for train dispatchers to schedule trains in real time in an optimal way; and as a planning tool to evaluate the impact of timetable changes, as well as railroad infrastructure changes. The mathematical programming model described here schedules trains over a single line track. The priority of each train in a conflict depends on an estimate of the remaining crossing and overtaking delay, as well as the current delay. This priority is used in a branch and bound procedure to allow and optimal solution to reasonable size train scheduling problems to be determined efficiently. The use of the model in an application to a 'real life' problem is discussed. The impacts of changing demand by increasing the number of trains, and reducing the number of sidings for a 150 kilometre section of single line track are discussed. It is concluded that the model is able to produce useful results in terms of optimal schedules in a reasonable time for the test applications shown here.
321 citations
"A Cooperative Scheduling Model for ..." refers background in this paper
...[8] proposed a two-objective optimization model that minimizes the delay time and the cost...
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06 Jun 2003
TL;DR: A mathematical model for optimizing cyclic railway timetables is presented, and the theoretical aspects behind the model are studied, including cyclic sequencing, periodic tensions, cycles in graphs, cycle bases of graphs, algorithms for constructing cycle bases, and cutting planes for the model.
Abstract: textCyclic Railway Timetable Optimization describes mathematical models
and solution methods for constructing high quality cyclic railway timetables.
In a cyclic timetable, a train for a certain destination leaves
a certain station at the same time every cycle time, say every half an
hour, every hour, or every two hours. Cyclic timetables are widely used
in European railways. They offer a clear and transparant product to the
railway customers, who only need to memorize the minutes of the hour
at which their regular trains depart. Because of the important role of
timetable planning for railway operators and railway infrastructure
managers, models and methods for optimizing cyclic railway timetables
provide a valuable tool for these organizations. The thesis presents
a mathematical model for optimizing cyclic railway timetables, and
studies the theoretical aspects behind the model. The investigated
aspects include cyclic sequencing, periodic tensions, cycles in graphs,
cycle bases of graphs, algorithms for constructing cycle bases, and
cutting planes for the model. The developed theoretical ideas are
tested on some real-life cyclic railway timetabling instances. The thesis
further develops several extensions of the basic model.
300 citations
"A Cooperative Scheduling Model for ..." refers background in this paper
...to take variable travel time [18], different periods [19], safety and frequency constraints [20], and variable demand [21] into account....
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