The PASCAL Visual Object Classes Challenge

We propose a theoretically and practically improved density-based, hierarchical clustering method, providing a clustering hierarchy from which a simplified tree of significant clusters can be constructed. For obtaining a “flat” partition consisting of only the most significant clusters (possibly corresponding to different density thresholds), we propose a novel cluster stability measure, formalize the problem of maximizing the overall stability of selected clusters, and formulate an algorithm that computes an optimal solution to this problem. We demonstrate that our approach outperforms the current, state-of-the-art, density-based clustering methods on a wide variety of real world data.

Density-based clustering based on hierarchical density estimates

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.

A Survey on Energy-Efficient Train Operation for Urban Rail Transit

Review of energy-efficient train control and timetabling

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%.

An energy-efficient scheduling and speed control approach for metro rail operations

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.

A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy

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.

An Energy-Efficient Train Operation Approach by Integrating the Metro Timetabling and Eco-Driving

In the practical operation of the Beijing metro systems, cyclic timetables are used, where the dwell times for all train services are the same for a station during the whole day. Since the passenger demand in peak hours is much higher than that of the off-peak hours, the scheduled dwell times for train services in the off-peak hours are in general a few seconds or even more than 10 seconds longer than the required (or valid) dwell times. The difference between the scheduled dwell time and the valid dwell time is called the dwell time supplement. A train regulation approach is proposed to use the dwell time supplements sufficiently, where the dwell times for train services in the off-peak hours are shortened due to the small number of boarding and alighting passengers. The dwell time supplements are then added to the running times of the next interval (i.e., the section between two consecutive stations). The resulting longer running times can reduce the energy consumption of the metro line. Based on the distribution of the dwell time supplements, the running times corresponding to different running grades in Automatic Train Supervision (ATS) systems are determined for different intervals to minimize the total energy consumption during a day. Based on the operational data, a case study for the Beijing Yizhuang line is presented to illustrate the effectiveness of the proposed approach.

Design of Running Grades for Energy-Efficient Train Regulation: A Case Study for Beijing Yizhuang Line

Energy efficiency is paid more and more attention in railway systems for reducing the cost of operation companies and emissions to the environment. In subway systems, the optimizations on timetable and driving strategy are two important and closely dependent parts of energy-efficient operations. The former regulates the fleet size and the trip time at interstations, and the latter determines the control sequences of traction and braking force during the trip. Most conventional research optimized the timetable and the driving strategy separately such that global optimality cannot be achieved. In this paper, we analyze the hierarchy of energy-efficient train operation and then propose an integrated algorithm to generate the globally optimal operation schedule, which can get better energy-saving performance. Within the criteria of meeting the passenger demand, the integrated energy-efficient algorithm can simultaneously obtain the optimal timetable and driving strategy for trains, which realizes the combination of the high-level transportation management and the low-level train operation control. The simulation results based on the Beijing Yizhuang Subway Line illustrate that the integrated algorithm can achieve a 24.0% energy reduction for one day, on average. In addition, the computation time is within 2 s, which is short enough to be applied for real-time control system.

Optimization of Multitrain Operations in a Subway System

Increasing attention is being paid to energy efficiency in subway systems to reduce operational cost and carbon emissions. Optimization of the driving strategy and efficient utilization of regenerative energy are two effective methods to reduce the energy consumption for electric subway systems. Based on a common scenario that an accelerating train can reuse the regenerative energy from a braking train on the opposite track, this paper proposes a cooperative train control model to minimize the practical energy consumption, i.e., the difference between traction energy and the reused regenerative energy. First, we design a numerical algorithm to calculate the optimal driving strategy with the given trip time, in which the variable traction force, braking force, speed limits, and gradients are considered. Then, a cooperative train control model is formulated to adjust the departure time of the accelerating train for reducing the practical energy consumption during the trip by efficiently using the regenerative energy of the braking train. Furthermore, a bisection method is presented to solve the optimal departure time for an accelerating train. Finally, the optimal driving strategy is obtained for the accelerating train with the optimal departure time. Case studies based on the Yizhuang Line, Beijing Subway, China, are presented to illustrate the effectiveness of the proposed approach on energy saving.

Shuai Su

Papers

A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy

An Energy-Efficient Train Operation Approach by Integrating the Metro Timetabling and Eco-Driving

Design of Running Grades for Energy-Efficient Train Regulation: A Case Study for Beijing Yizhuang Line

Optimization of Multitrain Operations in a Subway System

A Cooperative Train Control Model for Energy Saving