The key principles of optimal train control—Part 2: Existence of an optimal strategy, the local energy minimization principle, uniqueness, computational techniques

Albrecht, Amie; Howlett, Phil; Pudney, Peter; Vu, Xuan; Zhou, Peng

doi:10.1016/j.trb.2015.07.024

Cited by 173 publications

(98 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Recently, the French railway undertaking SNCF (Société Nationale des Chemins de fer Français) applied Energymiser on their TGV high speed trains using tablets to display driving advice to the train drivers (A. Albrecht et al (2015c)). Aradi et al (2013) used a predictive optimization model to calculate the energy-efficient speed profile taking into account varying gradients and speed limits.…”

Section: Exact Methods Without Regenerative Brakingmentioning

confidence: 99%

Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

329

149

View full text Add to dashboard Cite

The energy consumption of trains is highly efficient due to the low friction between steel wheels and rails, although the efficiency is also influenced largely by the driving strategy applied and the scheduled running times in the timetable. Optimal energy-efficient driving strategies can reduce operating costs significantly and contribute to a further increase of the sustainability of railway transportation. The railway sector hence shows an increasing interest in efficient algorithms for energy-efficient train control, which could be used in real-time Driver Advisory Systems (DAS) or Automatic Train Operation (ATO) systems. This paper gives an extensive literature review on energy-efficient train control (EETC) and the related topic of energy-efficient train timetabling (EETT), 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. Pontryagin's Maximum Principle (PMP) has been applied intensively to derive optimal driving regimes that make up the optimal energy-efficient driving strategy of a train under different conditions. Still, the optimal sequence and switching points of the optimal driving regimes are not trivial in general, which led to a wide range of optimization models and algorithms to compute the optimal train trajectories and more recently to use them to optimize timetables with a trade-off between energy efficiency and travel times.

show abstract

Section: Exact Methods Without Regenerative Brakingmentioning

confidence: 99%

Review of energy-efficient train control and timetabling

Scheepmaker

Goverde

Kroon

2017

European Journal of Operational Research

329

149

View full text Add to dashboard Cite

show abstract

“…Optimal control based on the PMP [9] PMP Single [7] PMP Single [10] PMP Single [8] PMP Single [11,12] PMP Single Heuristic algorithm [13] Genetic Algorithm Single [14] Genetic Algorithm, Ant Colony Optimization and Dynamic Programming Single [15] Genetic Algorithm Multiple [16] Brute force, Ant Colony Optimization and Genetic Algorithm Multiple [17] Genetic Algorithm Multiple [18] Genetic Algorithm Single Mathematical programming [19] Sequential Quadratical Programming Single [20] Pseudospectral method and MILP Single [21] Kuhn-Tucker Conditions Multiple [22] Bellman-ford Algorithm Single [6] MILP Single [23] Dynamic Programming Single [4] Pseudospectral method Single [24] Pseudospectral method Multiple [25] Genetic algorithm and Brute Force Multiple [26] Monte Carlo Simulation Multiple This paper MILP & PMP (Distance-based mathematical programming and PMP-based numerical algorithms)…”

Section: Publication Algorithms/theory Multiple/single Train(s)mentioning

confidence: 99%

“…The authors in [40] studied the control operation during the varying gradient and the coasting operation on the slope and provided an analysis of a new local optimization principle. The authors in [11,12] summarized the key principles of optimal train control developed in the past few decades, in which different aspects of optimal train control problem have been summarized and discussed. These two papers are focused on the classic two-station train optimal control problem, where it is proved that an optimal strategy always exists in the proposed optimal train control model, and perturbation analysis is used to show that the strategy is unique.…”

Section: Publication Algorithms/theory Multiple/single Train(s)mentioning

confidence: 99%

Adaptive Partial Train Speed Trajectory Optimization

Tan

Bao

et al. 2018

Energies

View full text Add to dashboard Cite

Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.

show abstract

“…To obtain a high-accuracy speedholding operation by RPM, one may explicitly provide the singular arc conditions as path constraints (Betts, 2010;Patterson and Rao, 2014) in the original optimal control formulation. Regarding this, Howlett et al (2009) and Albrecht et al (2015bAlbrecht et al ( , 2015c have proposed explicit numerical methods that can be used to find the initial and final points of a singular speedholding phase; however, it requires and is worth further investigation in the future whether their method can be combined with RPM and help identify the speedholding phases under the complex settings in this paper with multiple trains and/or multiple nodes.…”

Section: Case Studiesmentioning

confidence: 99%

A multiphase optimal control method for multi-train control and scheduling on railway lines

Liu

2016

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

We consider a combined train control and scheduling problem involving multiple trains in a railway line with a predetermined departure/arrival sequence of the trains at stations and meeting points along the line. The problem is formulated as a multiphase optimal control problem while incorporating complex train running conditions (including undulating track, variable speed restrictions, running resistances, speed-dependent maximum tractive/braking forces) and practical train operation constraints on departure/arrival/running/dwell times.Two case studies are conducted. The first case illustrates the control and scheduling problem of two trains in a small artificial network with three nodes, where one train follows and overtakes the other. The second case optimizes the control and timetable of a single train in a subway line. The case studies demonstrate that the proposed framework can provide an effective approach in solving the combined train scheduling and control problem for reducing energy consumption in railway operations.

show abstract

The key principles of optimal train control—Part 2: Existence of an optimal strategy, the local energy minimization principle, uniqueness, computational techniques

Cited by 173 publications

References 5 publications

Review of energy-efficient train control and timetabling

Review of energy-efficient train control and timetabling

Adaptive Partial Train Speed Trajectory Optimization

A multiphase optimal control method for multi-train control and scheduling on railway lines

Contact Info

Product

Resources

About