Distributed optimization approaches for the integrated problem of real-time railway traffic management and train control

Xiaojie Luan
Section Transport Engineering and Logistics, Delft University of Technology, Delft, The Netherlands

Bart De Schutter
Delft Center for Systems and Control, Delft University of Technology, The Netherlands

Ton van den Boom
Delft Center for Systems and Control, Delft University of Technology, The Netherlands

Lingyun Meng
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, China

Gabriel Lodewijks
School of Aviation, Faculty of Science, University of New South Wales, Australia

Francesco Corman
Institute for Transport Planning and Systems (IVT), ETH Zürich, Switzerland

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Ingår i: RailNorrköping 2019. 8th International Conference on Railway Operations Modelling and Analysis (ICROMA), Norrköping, Sweden, June 17th – 20th, 2019

Linköping Electronic Conference Proceedings 69:55, s. 837-856

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Publicerad: 2019-09-13

ISBN: 978-91-7929-992-7

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


This paper introduces distributed optimization approaches, with the aim of improving the computational efficency of an integrated optimization problem for large-scale railway net-works. We first propose three decomposition methods to decompose the whole problem into a number of subproblems, namely a geography-based (GEO), a train-based (TRA), and a time-interval-based (TIN) decomposition respectively. As a result of the decomposition, couplings exist among the subproblems, and the presence of these couplings leads to a non-separable structure of the whole problem. To handle this issue, we further introduce three distributed optimization approaches. An Alternating Direction Method of Multipliers (ADMM) algorithm is developed to solve each subproblem through coordination with the other subproblems in an iterative manner. A priority-rule-based (PR) algorithm is proposed to sequentially and iteratively solve the subproblems in a priority order with respect to the solutions of the other subproblems solved with a higher priority. A Cooperative Distributed Robust Safe But Knowledgeable (CDRSBK) algorithm is presented, where four types of couplings are de?ned and each subproblem is iteratively solved together with its actively coupled subproblems. Experiments are conducted based on the Dutch railway network to comparatively examine the performance of the three proposed algorithms with the three decomposition methods, in terms of feasibility, computational efficiency, solution quality, and estimated optimality gap. Overall, the combinations GEO-ADMM, TRA-ADMM, and TRA-CDRSBK yield better performance. Based on our findings, a feasible solution can be found quickly by using TRA-ADMM, and then a better solution can be potentially obtained by GEO-ADMM or TRA-CDRSBK at the cost of more CPU time.


Distributed optimization, Decomposition, Integration of real-time traffic management and train control, Mixed-integer linear programming (MILP), Large-scale


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