**Reference:**

X. Luan,
Y. Wang,
B. De Schutter,
L. Meng,
G. Lodewijks, and
F. Corman,
"Integration of real-time traffic management and train control for
rail networks - Part 2: Extensions towards energy-efficient train
operations," *Transportation Research Part B*, vol. 115, pp.
72-94, Sept. 2018.

**Abstract:**

We study the integration of real-time traffic management and train
control by using mixed-integer nonlinear programming (MINLP) and
mixed-integer linear programming (MILP) approaches. In Part 1 of the
paper, three integrated optimization problems, namely the
P_{NLP} problem (NLP: nonlinear programming), the
P_{PWA} problem (PWA: piecewise affine), and the
P_{TSPO} problem (TSPO: train speed profile option),
have been developed for real-time traffic management that inherently
include train control. A two-level approach and a custom-designed
two-step approach have been proposed to solve these optimization
problems. In Part 2 of the paper, aiming at energy-efficient train
operation, we extend the three proposed optimization problems by
introducing energy-related formulations. We first evaluate the energy
consumption of a train motion. A set of nonlinear constraints is first
proposed to calculate the energy consumption, which is further
reformulated as a set of linear constraints for the
P_{TSPO} problem and approximated by using a
piecewise constant function for the P_{NLP} and
P_{PWA} problems. Moreover, we consider the option
of regenerative braking and present linear formulations to calculate
the utilization of the regenerative energy obtained through braking
trains. We focus on two objectives, i.e., delay recovery and energy
efficiency, through using a weighted-sum formulation and an
ϵ-constraint formulation. With these energy-related
extensions, the nature of the three optimization problems remains same
to Part 1. In numerical experiments conducted based on the Dutch test
case, we consider the P_{NLP} approach and the
P_{TSPO} approach only and compare their performance
with the inclusion of the energy-related aspects; the
P_{PWA} approach is neglected due to its bad
performance, as evaluated in Part 1. According to the experimental
results, the P_{TSPO} approach still yields a better
performance within the required computation time. The trade-off
between train delay and energy consumption is investigated. The
results show the possibility of reducing train delay and saving energy
at the same time through managing train speed, by up to 4.0% and 5.6%
respectively. In our case study, applying regenerative braking leads
to a 22.9% reduction of the total energy consumption.

Online version of the paper

@article{LuaWan:18-015,

author={X. Luan and Y. Wang and B. {D}e Schutter and L. Meng and G. Lodewijks and F. Corman},

title={Integration of real-time traffic management and train control for rail networks -- {Part} 2: {Extensions} towards energy-efficient train operations},

journal={Transportation Research Part B},

volume={115},

pages={72--94},

month=sep,

year={2018},

doi={10.1016/j.trb.2018.06.011}

}

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