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Documents authored by Goerigk, Marc

Document
DOI: 10.4230/OASIcs.ATMOS.2021.6
A Phase I Simplex Method for Finding Feasible Periodic Timetables

Authors: Marc Goerigk, Anita Schöbel, and Felix Spühler

Published in: OASIcs, Volume 96, 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)

Abstract
The periodic event scheduling problem (PESP) with various applications in timetabling or traffic light scheduling is known to be challenging to solve. In general, it is already NP-hard to find a feasible solution. However, depending on the structure of the underlying network and the values of lower and upper bounds on activities, this might also be an easy task. In this paper we make use of this property and suggest phase I approaches (similar to the well-known phase I of the simplex algorithm) to find a feasible solution to PESP. Given an instance of PESP, we define an auxiliary instance for which a feasible solution can easily be constructed, and whose solution determines a feasible solution of the original instance or proves that the original instance is not feasible. We investigate different possibilities on how such an auxiliary instance can be defined theoretically and experimentally. Furthermore, in our experiments we compare different solution approaches for PESP and their behavior in the phase I approach. The results show that this approach can be especially helpful if the instance admits a feasible solution, while it is generally outperformed by classic mixed-integer programming formulations when the instance is infeasible.
Cite as

Marc Goerigk, Anita Schöbel, and Felix Spühler. A Phase I Simplex Method for Finding Feasible Periodic Timetables. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{goerigk_et_al:OASIcs.ATMOS.2021.6,
  author =	{Goerigk, Marc and Sch\"{o}bel, Anita and Sp\"{u}hler, Felix},
  title =	{{A Phase I Simplex Method for Finding Feasible Periodic Timetables}},
  booktitle =	{21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)},
  pages =	{6:1--6:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-213-6},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{96},
  editor =	{M\"{u}ller-Hannemann, Matthias and Perea, Federico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2021.6},
  URN =		{urn:nbn:de:0030-drops-148753},
  doi =		{10.4230/OASIcs.ATMOS.2021.6},
  annote =	{Keywords: train timetable optimization, periodic event scheduling problem, modulo simplex}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2019.5
Robust Network Capacity Expansion with Non-Linear Costs

Authors: Francis Garuba, Marc Goerigk, and Peter Jacko

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
The network capacity expansion problem is a key network optimization problem practitioners regularly face. There is an uncertainty associated with the future traffic demand, which we address using a scenario-based robust optimization approach. In most literature on network design, the costs are assumed to be linear functions of the added capacity, which is not true in practice. To address this, two non-linear cost functions are investigated: (i) a linear cost with a fixed charge that is triggered if any arc capacity is modified, and (ii) its generalization to piecewise-linear costs. The resulting mixed-integer programming model is developed with the objective of minimizing the costs. Numerical experiments were carried out for networks taken from the SNDlib database. We show that networks of realistic sizes can be designed using non-linear cost functions on a standard computer in a practical amount of time within negligible suboptimality. Although solution times increase in comparison to a linear-cost or to a non-robust model, we find solutions to be beneficial in practice. We further illustrate that including additional scenarios follows the law of diminishing returns, indicating that little is gained by considering more than a handful of scenarios. Finally, we show that the results of a robust optimization model compare favourably to the traditional deterministic model optimized for the best-case, expected, or worst-case traffic demand, suggesting that it should be used whenever computationally feasible.
Cite as

Francis Garuba, Marc Goerigk, and Peter Jacko. Robust Network Capacity Expansion with Non-Linear Costs. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{garuba_et_al:OASIcs.ATMOS.2019.5,
  author =	{Garuba, Francis and Goerigk, Marc and Jacko, Peter},
  title =	{{Robust Network Capacity Expansion with Non-Linear Costs}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{5:1--5:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.5},
  URN =		{urn:nbn:de:0030-drops-114175},
  doi =		{10.4230/OASIcs.ATMOS.2019.5},
  annote =	{Keywords: Robust Optimization, Mobile Network, Network Capacity Design \& Expansion, Non-linear Cost, Traffic and Transport Routing}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2017.12
An Improved Algorithm for the Periodic Timetabling Problem

Authors: Marc Goerigk and Christian Liebchen

Published in: OASIcs, Volume 59, 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

Abstract
We consider the computation of periodic timetables, which is a key task in the service design process of public transportation companies. We propose a new approach for solving the periodic timetable optimisation problem. It consists of a (partially) heuristic network aggregation to reduce the problem size and make it accessible to standard mixed-integer programming (MIP) solvers. We alternate the invocation of a MIP solver with the well-known problem specific modulo network simplex heuristic (ModSim). This iterative approach helps the ModSim-method to overcome local minima efficiently, and provides the MIP solver with better initial solutions. Our computational experiments are based on the 16 railway instances of the PESPlib, which is the only currently available collection of periodic event scheduling problem instances. For each of these instances, we are able to reduce the objective values of previously best known solutions by at least 10.0%, and up to 22.8% with our iterative combined method.
Cite as

Marc Goerigk and Christian Liebchen. An Improved Algorithm for the Periodic Timetabling Problem. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{goerigk_et_al:OASIcs.ATMOS.2017.12,
  author =	{Goerigk, Marc and Liebchen, Christian},
  title =	{{An Improved Algorithm for the Periodic Timetabling Problem}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{12:1--12:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-042-2},
  ISSN =	{2190-6807},
  year =	{2017},
  volume =	{59},
  editor =	{D'Angelo, Gianlorenzo and Dollevoet, Twan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017.12},
  URN =		{urn:nbn:de:0030-drops-78924},
  doi =		{10.4230/OASIcs.ATMOS.2017.12},
  annote =	{Keywords: periodic timetabling, railway optimisation, modulo network simplex, periodic event scheduling problem}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2017.16
An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems

Authors: Trivikram Dokka and Marc Goerigk

Published in: OASIcs, Volume 59, 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

Abstract
Through the development of efficient algorithms, data structures and preprocessing techniques, real-world shortest path problems in street networks are now very fast to solve. But in reality, the exact travel times along each arc in the network may not be known. This led to the development of robust shortest path problems, where all possible arc travel times are contained in a so-called uncertainty set of possible outcomes. Research in robust shortest path problems typically assumes this set to be given, and provides complexity results as well as algorithms depending on its shape. However, what can actually be observed in real-world problems are only discrete raw data points. The shape of the uncertainty is already a modelling assumption. In this paper we test several of the most widely used assumptions on the uncertainty set using real-world traffic measurements provided by the City of Chicago. We calculate the resulting different robust solutions, and evaluate which uncertainty approach is actually reasonable for our data. This anchors theoretical research in a real-world application and gives an indicator which robust models should be the future focus of algorithmic development.
Cite as

Trivikram Dokka and Marc Goerigk. An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dokka_et_al:OASIcs.ATMOS.2017.16,
  author =	{Dokka, Trivikram and Goerigk, Marc},
  title =	{{An Experimental Comparison of Uncertainty Sets for Robust Shortest Path Problems}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{16:1--16:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-042-2},
  ISSN =	{2190-6807},
  year =	{2017},
  volume =	{59},
  editor =	{D'Angelo, Gianlorenzo and Dollevoet, Twan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017.16},
  URN =		{urn:nbn:de:0030-drops-79035},
  doi =		{10.4230/OASIcs.ATMOS.2017.16},
  annote =	{Keywords: robust shortest paths, uncertainty sets, real-world data, experimental study}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.ATMOS.2016
OASIcs, Volume 54, ATMOS'16, Complete Volume

Authors: Marc Goerigk and Renato Werneck

Published in: OASIcs, Volume 54, 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)

Abstract
OASIcs, Volume 54, ATMOS'16, Complete Volume
Cite as

16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016). Open Access Series in Informatics (OASIcs), Volume 54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@Proceedings{goerigk_et_al:OASIcs.ATMOS.2016,
  title =	{{OASIcs, Volume 54, ATMOS'16, Complete Volume}},
  booktitle =	{16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-021-7},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{54},
  editor =	{Goerigk, Marc and Werneck, Renato F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2016},
  URN =		{urn:nbn:de:0030-drops-66724},
  doi =		{10.4230/OASIcs.ATMOS.2016},
  annote =	{Keywords: Analysis of Algorithms and Problem Complexity, Optimization, Combinatorics, Graph Theory, Applications}
}
Document
Front Matter
DOI: 10.4230/OASIcs.ATMOS.2016.0
Front Matter, Table of Contents, Preface, Organization

Authors: Marc Goerigk and Renato F. Werneck

Published in: OASIcs, Volume 54, 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)

Abstract
Front Matter, Table of Contents, Preface, Organization
Cite as

16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016). Open Access Series in Informatics (OASIcs), Volume 54, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{goerigk_et_al:OASIcs.ATMOS.2016.0,
  author =	{Goerigk, Marc and Werneck, Renato F.},
  title =	{{Front Matter, Table of Contents, Preface, Organization}},
  booktitle =	{16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)},
  pages =	{0:i--0:x},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-021-7},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{54},
  editor =	{Goerigk, Marc and Werneck, Renato F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2016.0},
  URN =		{urn:nbn:de:0030-drops-65243},
  doi =		{10.4230/OASIcs.ATMOS.2016.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Organization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2013.1
Recoverable Robust Timetable Information

Authors: Marc Goerigk, Sacha Heße, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract
Timetable information is the process of determining a suitable travel route for a passenger. Due to delays in the original timetable, in practice it often happens that the travel route cannot be used as originally planned. For a passenger being already en route, it would hence be useful to know about alternatives that ensure that his/her destination can be reached. In this work we propose a recoverable robust approach to timetable information; i.e., we aim at finding travel routes that can easily be updated when delays occur during the journey. We present polynomial-time algorithms for this problem and evaluate the performance of the routes obtained this way on schedule data of the German train network of 2013 and simulated delay scenarios.
Cite as

Marc Goerigk, Sacha Heße, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel. Recoverable Robust Timetable Information. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{goerigk_et_al:OASIcs.ATMOS.2013.1,
  author =	{Goerigk, Marc and He{\ss}e, Sacha and M\"{u}ller-Hannemann, Matthias and Schmidt, Marie and Sch\"{o}bel, Anita},
  title =	{{Recoverable Robust Timetable Information}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{1--14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.1},
  URN =		{urn:nbn:de:0030-drops-42407},
  doi =		{10.4230/OASIcs.ATMOS.2013.1},
  annote =	{Keywords: timetable information, recoverable robustness, delay scenarios}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.76
The Price of Robustness in Timetable Information

Authors: Marc Goerigk, Martin Knoth, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
In timetable information in public transport the goal is to search for a good passenger's path between an origin and a destination. Usually, the travel time and the number of transfers shall be minimized. In this paper, we consider robust timetable information, i.e. we want to identify a path which will bring the passenger to the planned destination even in the case of delays. The classic notion of strict robustness leads to the problem of identifying those changing activities which will never break in any of the expected delay scenarios. We show that this is in general a strongly NP-hard problem. Therefore, we propose a conservative heuristic which identifies a large subset of these robust changing activities in polynomial time by dynamic programming and so allows us to find strictly robust paths efficiently. We also transfer the notion of light robustness, originally introduced for timetabling, to timetable information. In computational experiments we then study the price of strict and light robustness: How much longer is the travel time of a robust path than of a shortest one according to the published schedule? Based on the schedule of high-speed trains within Germany of 2011, we quantitatively explore the trade-off between the level of guaranteed robustness and the increase in travel time. Strict robustness turns out to be too conservative, while light robustness is promising: a modest level of guarantees is achievable at a reasonable price for the majority of passengers.
Cite as

Marc Goerigk, Martin Knoth, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel. The Price of Robustness in Timetable Information. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 76-87, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{goerigk_et_al:OASIcs.ATMOS.2011.76,
  author =	{Goerigk, Marc and Knoth, Martin and M\"{u}ller-Hannemann, Matthias and Schmidt, Marie and Sch\"{o}bel, Anita},
  title =	{{The Price of Robustness in Timetable Information}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{76--87},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.76},
  URN =		{urn:nbn:de:0030-drops-32680},
  doi =		{10.4230/OASIcs.ATMOS.2011.76},
  annote =	{Keywords: strict and light robustness, delay scenarios, experimental study}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2010.100
An Empirical Analysis of Robustness Concepts for Timetabling

Authors: Marc Goerigk and Anita Schöbel

Published in: OASIcs, Volume 14, 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10) (2010)

Abstract
Calculating timetables that are insensitive to disturbances has drawn considerable research efforts due to its practical importance on the one hand and its hard tractability by classical robustness concepts on the other hand. Many different robustness concepts for timetabling have been suggested in the literature, some of them very recently. In this paper we compare such concepts on real-world instances. We also introduce a new approach that is generically applicable to any robustness problem. Nevertheless it is able to adapt the special characteristics of the respective problem structure and hence generates solutions that fit to the needs of the respective problem.
Cite as

Marc Goerigk and Anita Schöbel. An Empirical Analysis of Robustness Concepts for Timetabling. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Open Access Series in Informatics (OASIcs), Volume 14, pp. 100-113, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{goerigk_et_al:OASIcs.ATMOS.2010.100,
  author =	{Goerigk, Marc and Sch\"{o}bel, Anita},
  title =	{{An Empirical Analysis of Robustness Concepts for Timetabling}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{100--113},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Erlebach, Thomas and L\"{u}bbecke, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2010.100},
  URN =		{urn:nbn:de:0030-drops-27537},
  doi =		{10.4230/OASIcs.ATMOS.2010.100},
  annote =	{Keywords: Timetabling, Robust Optimization, Algorithm Engineering}
}
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