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@incollection{faucris.203352087,
abstract = {Rail freight traffic in Germany has experienced significant growth rates over the last decade, and recent forecasts expect this tendency to continue over the next 20 years due to the increases in national and international trade. Internal predictions of Deutsche Bahn AG, the most important German railway enterprise, assume a mean increase of 2{%} per year for rail freight traffic until 2030. At this pace, the German railway network in its current state would reach its capacity limit way before this date. As investments into the network infrastructure bear a very high price tag, it is crucial to use the available budget in the most efficient manner. Furthermore, the large size of the networks under consideration warrants the development of efficient algorithms to handle the complex network design problems arising for real-world data. This led us to the development of network aggregation procedures which allow for much shorter solution times by compressing the network information. More exactly, our framework works by clustering the nodes of the underlying graph to components and solving the network design problem over this aggregated graph. This kind of aggregation may either be used as a quick heuristic, or it can be extended to an exact method, e.g. by iterative refinement of the clustering, The latter results in a cutting plane algorithm, which also introduces new variables with each refinement. This idea developed in Bärmann et al. (Math Program Comput 7(2):189--217, 2015) is extended in this chapter such that it is able to incorporate the costs for routing flow through the network via lifted Benders optimality cuts. Altogether, our algorithm can be seen as a novel kind of Benders decomposition which allows to shift variables from the subproblem to the master problem in the process. Computations on several benchmark sets demonstrate the effectiveness of the approach.},
address = {Cham},
author = {Bärmann, Andreas and Liers, Frauke},
booktitle = {Handbook of Optimization in the Railway Industry},
doi = {10.1007/978-3-319-72153-8_3},
editor = {Borndörfer R, Klug T, Lamorgese L, Mannino C, Reuther M, Schlechte T},
faupublication = {yes},
isbn = {978-3-319-72153-8},
pages = {47--72},
peerreviewed = {Yes},
publisher = {Springer International Publishing},
title = {{Aggregation} {Methods} for {Railway} {Network} {Design} {Based} on {Lifted} {Benders} {Cuts}},
year = {2018}
}
@inproceedings{faucris.203351150,
abstract = {In this paper, we demonstrate how to learn the objective function of a decision maker while only observing the problem input data and the decision maker’s corresponding decisions over multiple rounds. Our approach is based on online learning techniques and works for linear objectives over arbitrary sets for which we have a linear optimization oracle and as such generalizes previous work based on KKT-system decomposition and dualization approaches. The applicability of our framework for learning linear constraints is also discussed briefly. Our algorithm converges at a rate of O(1/sqrt(T)), and we demonstrate its effectiveness and applications in preliminary computational results.},
address = {International Convention Centre, Sydney, Australia},
author = {Bärmann, Andreas and Pokutta, Sebastian and Schneider, Oskar},
booktitle = {Proceedings of the 34th International Conference on Machine Learning (ICML)},
editor = {Precup D, Teh YW},
faupublication = {yes},
pages = {400--410},
peerreviewed = {Yes},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
title = {{Emulating} the {Expert}: {Inverse} {Optimization} through {Online} {Learning}},
url = {http://proceedings.mlr.press/v70/barmann17a.html},
volume = {70},
year = {2017}
}
@misc{faucris.214630022,
abstract = {Globalized robust optimization has been proposed as a generalization of the standard robust optimization framework in order to allow for a controlled decrease in protection depending on the distance of the realized scenario from the predefined uncertainty set. In this work, we specialize the notion of globalized robustness to Gamma-uncertainty in order to extend its usability for discrete optimization. We show that in this case, the generalized robust counterpart possesses algorithmically tractable reformulations for mixed-integer linear nominal problems. Under mild assumptions, we derive a reformulation which uses only slightly more variables and constraints than the standard robust counterpart under Gamma-uncertainty. For combinatorial problems, our globalized robust counterpart remains fixed-parameter tractable, although with a runtime exponential in Gamma. Furthermore,we showthat globalized robust optimization under scaling of the Gamma-uncertainty-sets is NP-hard already in simple cases. We support our theoretical findings by experimental results on the globalized robust versions of the minimum-spanning-tree, shortest-path and knapsack problems. It turns out that our algorithmically tractable reformulations are not more difficult to solve than the respective standard robust counterparts while globalized robustness is guaranteed. Moreover, they produce solutions which offer suitable protection against uncertainty while performing very well in the nominal objective function.

Clique Problem with Multiple-Choice constraints (CPMC) and characterize a case where it is possible to give an efficient description of the convex hull of its feasible solutions. This special case, which we name *staircase compatibility*, generalizes common properties in several applications and allows for a linear description of the integer feasible solutions to (CPMC) with a totally unimodular constraint matrix of polynomial size. We derive two such totally unimodular reformulations for the problem: one that is obtained by a strengthening of the compatibility constraints and one that is based on a representation as a dual network flow problem. Furthermore, we show a natural way to derive integral solutions from fractional solutions to the problem by determining integral extreme points generating this fractional solution. We also evaluate our reformulations from a computational point of view by applying them to two different real-world problem settings. The first one is a problem in railway timetabling, where we try to adapt a given timetable slightly such that energy costs from operating the trains are reduced. The second one is the piecewise linearization of non-linear network flow problems, illustrated at the example of gas networks. In both cases, we are able to reduce the solution times significantly by passing to the theoretically stronger formulations of the proble},
author = {Bärmann, Andreas and Gellermann, Thorsten and Merkert, Maximilian and Schneider, Oskar},
doi = {10.1016/j.disopt.2018.04.001},
faupublication = {yes},
journal = {Discrete Optimization},
keywords = {Clique problem with multiple-choice constraints; Staircase compatibility; Total unimodularity; Scheduling; Piecewise linearization},
pages = {111-132},
peerreviewed = {Yes},
title = {{Staircase} {Compatibility} and its {Applications} in {Scheduling} and {Piecewise} {Linearization}},
url = {http://www.sciencedirect.com/science/article/pii/S1572528618300306},
volume = {29},
year = {2018}
}
@article{faucris.112089384,
abstract = {We investigate the problem of designing energy-efficient timetables for railway traffic. More precisely, we slightly adapt a given timetable draft before it is published by moderately shifting the departure times of the trains at the stations. To this end, we propose a mixed-integer programming model for feasible adaptations of the timetable draft and investigate its behaviour under different objective functions which fall into two classes: reducing the energy cost and increasing the stability of the power supply system. These tests are performed on real-world problem instances from our industry partner Deutsche Bahn AG. They show a significant potential for improvements in the existing railway timetables.},
author = {Bärmann, Andreas and Martin, Alexander and Schneider, Oskar},
doi = {10.1007/s12469-017-0160-4},
faupublication = {yes},
journal = {Public Transport},
keywords = {Railway timetabling; Power peak reduction; Mixed-integer programming},
pages = {95-113},
peerreviewed = {unknown},
title = {{A} comparison of performance metrics for balancing the power consumption of trains in a railway network by slight timetable adaptation},
volume = {9},
year = {2017}
}