Multi-train trajectory optimization for energy efficiency and delay recovery on single-track railway lines

Wang, Pengling; Goverde, Rob M.P.

doi:10.1016/j.trb.2017.09.012

Cited by 96 publications

(53 citation statements)

References 25 publications

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“…Thus, many recent studies have explored the optimization of train energy consumption using an optimized train timetable (Canca & Zarzo, 2017;Corman, D'Ariano, Pacciarelli, & Pranzo, 2009;Scheepmaker, Goverde, & Kroon, 2017;Yin, Yang, Tang, Gao, & Ran, 2017a). For example, Wang and Goverde (2017) formulated the energy-efficient train timetable rescheduling problem into a multiple-phase optimal control model that was solved by a pseudospectral method. The technology of using regenerative energy, which can be generated by an electric motor when a train is braking and fed back to the contact lines, has been well applied to some metro systems.…”

Section: Literature Reviewmentioning

confidence: 99%

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

Yin

Yang

Zhou

et al. 2019

Naval Research Logistics

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In urban rail transit systems of large cities, the headway and following distance of successive trains have been compressed as much as possible to enhance the corridor capacity to satisfy extremely high passenger demand during peak hours. To prevent train collisions and ensure the safety of trains, a safe following distance of trains must be maintained. However, this requirement is subject to a series of complex factors, such as the uncertain train braking performance, train communication delay, and driver reaction time. In this paper, we propose a unified mathematical framework to analyze the safety‐oriented reliability of metro train timetables with different corridor capacities, that is, the train traffic density, and determine the most reliable train timetable for metro lines in an uncertain environment. By employing a space‐time network representation in the formulations, the reliability‐based train timetabling problem is formulated as a nonlinear stochastic programming model, in which we use 0‐1 variables to denote the time‐dependent velocity and position of all involved trains. Several reformulation techniques are developed to obtain an equivalent mixed integer programming model with quadratic constraints (MIQCP) that can be solved to optimality by some commercial solvers. To improve the computational efficiency of the MIQCP model, we develop a dual decomposition solution framework that decomposes the primal problem into several sets of subproblems by dualizing the coupling constraints across different samples. An exact dynamic programming combined with search space reduction strategies is also developed to solve the exact optimal solutions of these subproblems. Two sets of numerical experiments, which involve a relatively small‐scale case and a real‐world instance based on the operation data of the Beijing subway Changping Line are implemented to verify the effectiveness of the proposed approaches.

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Section: Literature Reviewmentioning

confidence: 99%

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

Yin

Yang

Zhou

et al. 2019

Naval Research Logistics

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“…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%

“…On the other hand, by modeling the train operations as a standard optimal control problem, researchers from Delft University of Technology and University of Leeds, proposed applying a pseudospectral algorithm and non-linear programming, as a direct method in comparison to an indirect method such as PMP, to solve the train speed trajectory optimization problem under a variety of engineering constraints. The studied cases can be well extended to multi-train problems and is able to take into account more complex signaling and operational constraints ( [4,5,20,24,41]). The authors in [20] applies both a pseudospectral algorithm and MILP to solve the speed trajectory optimization problem with consideration of the passenger riding comfort.…”

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

confidence: 99%

“…The paper put particularly considered the operational (time and speed restrictions) and signal (signal aspects and automatic train protection) constraints for the trajectory optimization under delay and no-delay situations. The authors in [24] applied a pseudospectral method to optimize the multi-train optimization by formulating the problem as a multiple-phase optimal control problem. Multiple objectives including the minimization of energy consumption and train delays exist for the optimization to locate proper driving strategies.…”

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

confidence: 99%

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Adaptive Partial Train Speed Trajectory Optimization

Tan

Bao

et al. 2018

Energies

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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.

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“…Meng and Zhou [13] developed an innovative integer programming model for train dispatching on an N-track network by means of simultaneously rerouting and rescheduling trains. Wang and Goverde [14] have determined a timetable constraints set with accessibility and non-conflict under delay accidents of single-track railway, upon which a train rescheduling model was established aiming to reduce global delay time and energy consumption. Carey and Kwieciński [15] conducted a stochastic simulation of trains on line section to establish an approximation model between scheduled headway and secondary delay for the coefficient modification and schedule optimization of current operation plan.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Congestion Propagation on Urban Rail Transit Oversaturated Conditions: A Framework Based on SIR Epidemic Model

Zeng

2018

Urban Rail Transit

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Simulating the congestion propagation of urban rail transit system is challenging, especially under oversaturated conditions. This paper presents a congestion propagation model based on SIR (susceptible, infected, recovered) epidemic model for capturing the congestion prorogation process through formalizing the propagation by a congestion susceptibility recovery process. In addition, as congestion propagation is the key parameter in the congestion propagation model, a model for calculating congestion propagation rate is constructed. A gray system model is also introduced to quantify the propagation rate under the joint effect of six influential factors: passenger flow, train headway, passenger transfer convenience, time of congestion occurring, initial congested station and station capacity. A numerical example is used to illustrate the congestion propagation process and to demonstrate the improvements after taking corresponding measures.

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Multi-train trajectory optimization for energy efficiency and delay recovery on single-track railway lines

Cited by 96 publications

References 25 publications

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

Adaptive Partial Train Speed Trajectory Optimization

Analyzing Congestion Propagation on Urban Rail Transit Oversaturated Conditions: A Framework Based on SIR Epidemic Model

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