40 Search Results for "Bornd�rfer, Ralf"

Document
Short Paper
DOI: 10.4230/OASIcs.ATMOS.2023.3
Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization (Short Paper)

Authors: Ralf Borndörfer, Fabian Danecker, and Martin Weiser

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.
Cite as

Ralf Borndörfer, Fabian Danecker, and Martin Weiser. Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization (Short Paper). In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 3:1-3:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2023.3,
  author =	{Bornd\"{o}rfer, Ralf and Danecker, Fabian and Weiser, Martin},
  title =	{{Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{3:1--3:6},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.3},
  URN =		{urn:nbn:de:0030-drops-187642},
  doi =		{10.4230/OASIcs.ATMOS.2023.3},
  annote =	{Keywords: shortest path, flight planning, free flight, optimal control, global optimization, Newton’s method}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2023.13
Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization

Authors: Boris Grimm, Ralf Borndörfer, and Julian Bushe

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
The fundamental task of every passenger railway operator is to offer an attractive railway timetable to the passengers while operating it as cost efficiently as possible. The available rolling stock has to be assigned to trips so that all trips are operated, operational requirements are satisfied, and the operating costs are minimum. This so-called Rolling Stock Rotation Problem (RSRP) is well studied in the literature. In this paper we consider an acyclic version of the RSRP that includes vehicle maintenance. As the latter is an important aspect, maintenance services have to be planned simultaneously to ensure the rotation’s feasibility in practice. Indeed, regular maintenance is important for the safety and reliability of the rolling stock as well as enforced by law in many countries. We present a new integer programming formulation that links a hyperflow to model vehicle compositions and their coupling decisions to a set of path variables that take care of the resource consumption of the individual vehicles. To solve the model we developed different column generation algorithms which are compared to each other as well as to the MILP flow formulation of [Ralf Borndörfer et al., 2016] on a test set of real world instances.
Cite as

Boris Grimm, Ralf Borndörfer, and Julian Bushe. Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{grimm_et_al:OASIcs.ATMOS.2023.13,
  author =	{Grimm, Boris and Bornd\"{o}rfer, Ralf and Bushe, Julian},
  title =	{{Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{13:1--13:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.13},
  URN =		{urn:nbn:de:0030-drops-187741},
  doi =		{10.4230/OASIcs.ATMOS.2023.13},
  annote =	{Keywords: Railway Rolling Stock Optimization, Integer Programming, Column Generation}
}
Document
Short Paper
DOI: 10.4230/OASIcs.ATMOS.2023.15
Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates (Short Paper)

Authors: Fabian Löbel, Ralf Borndörfer, and Steffen Weider

Published in: OASIcs, Volume 115, 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)

Abstract
The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems. Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear. In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized. Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic. We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.
Cite as

Fabian Löbel, Ralf Borndörfer, and Steffen Weider. Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates (Short Paper). In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 15:1-15:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lobel_et_al:OASIcs.ATMOS.2023.15,
  author =	{L\"{o}bel, Fabian and Bornd\"{o}rfer, Ralf and Weider, Steffen},
  title =	{{Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates}},
  booktitle =	{23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
  pages =	{15:1--15:6},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-302-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{115},
  editor =	{Frigioni, Daniele and Schiewe, Philine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2023.15},
  URN =		{urn:nbn:de:0030-drops-187765},
  doi =		{10.4230/OASIcs.ATMOS.2023.15},
  annote =	{Keywords: Electric Vehicle Scheduling, Battery Powered Vehicles, Charging Process, Non-linear Charging, Recharge Modeling, Dynamic Recharge Rate}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2022.1
An A* Algorithm for Flight Planning Based on Idealized Vertical Profiles

Authors: Marco Blanco, Ralf Borndörfer, and Pedro Maristany de las Casas

Published in: OASIcs, Volume 106, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)

Abstract
The Flight Planning Problem is to find a minimum fuel trajectory between two airports in a 3D airway network under consideration of the wind. We show that this problem is NP-hard, even in its most basic version. We then present a novel A* heuristic, whose potential function is derived from an idealized vertical profile over the remaining flight distance. This potential is, under rather general assumptions, both admissible and consistent and it can be computed efficiently. The method outperforms the state-of-the-art heuristic on real-life instances.
Cite as

Marco Blanco, Ralf Borndörfer, and Pedro Maristany de las Casas. An A* Algorithm for Flight Planning Based on Idealized Vertical Profiles. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blanco_et_al:OASIcs.ATMOS.2022.1,
  author =	{Blanco, Marco and Bornd\"{o}rfer, Ralf and Maristany de las Casas, Pedro},
  title =	{{An A* Algorithm for Flight Planning Based on Idealized Vertical Profiles}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{1:1--1:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2022.1},
  URN =		{urn:nbn:de:0030-drops-171052},
  doi =		{10.4230/OASIcs.ATMOS.2022.1},
  annote =	{Keywords: shortest path problem, a-star algorithm, flight trajectory optimization, flight planning, heuristics}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2022.2
A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization

Authors: Ralf Borndörfer, Fabian Danecker, and Martin Weiser

Published in: OASIcs, Volume 106, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)

Abstract
We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.
Cite as

Ralf Borndörfer, Fabian Danecker, and Martin Weiser. A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2022.2,
  author =	{Bornd\"{o}rfer, Ralf and Danecker, Fabian and Weiser, Martin},
  title =	{{A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{2:1--2:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2022.2},
  URN =		{urn:nbn:de:0030-drops-171068},
  doi =		{10.4230/OASIcs.ATMOS.2022.2},
  annote =	{Keywords: shortest path, flight planning, free flight, discretization error bounds, optimal control, discrete optimization, global optimization}
}
Document
Short Paper
DOI: 10.4230/OASIcs.ATMOS.2021.17
Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation (Short Paper)

Authors: Güvenç Şahin, Amin Ahmadi Digehsara, and Ralf Borndörfer

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

Abstract
In order to plan and schedule a demand-responsive public transportation system, both temporal and spatial changes in demand should be taken into account even at the line planning stage. We study the multi-period line planning problem with integrated decisions regarding dynamic allocation of vehicles among the lines. Given the NP-hard nature of the line planning problem, the multi-period version is clearly difficult to solve for large public transit networks even with advanced solvers. It becomes necessary to develop algorithms that are capable of solving even the very-large instances in reasonable time. For instances which belong to real public transit networks, we present results of a heuristic local branching algorithm and an exact approach based on constraint propagation.
Cite as

Güvenç Şahin, Amin Ahmadi Digehsara, and Ralf Borndörfer. Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation (Short Paper). In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 17:1-17:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sahin_et_al:OASIcs.ATMOS.2021.17,
  author =	{\c{S}ahin, G\"{u}ven\c{c} and Ahmadi Digehsara, Amin and Bornd\"{o}rfer, Ralf},
  title =	{{Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation}},
  booktitle =	{21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)},
  pages =	{17:1--17:6},
  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.2021.17},
  URN =		{urn:nbn:de:0030-drops-148863},
  doi =		{10.4230/OASIcs.ATMOS.2021.17},
  annote =	{Keywords: public transportation, line planning, multi-period planning, local branching, constraint propagation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.27
Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs

Authors: Ralf Borndörfer, Katrin Casel, Davis Issac, Aikaterini Niklanovits, Stephan Schwartz, and Ziena Zeif

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. In these settings, it is often desirable to partition into a fixed number of parts of roughly of the same size or weight. The resulting computational problem is called Balanced Connected Partition (BCP). The two classical objectives for BCP are to maximize the weight of the smallest, or minimize the weight of the largest component. We study BCP on c-claw-free graphs, the class of graphs that do not have K_{1,c} as an induced subgraph, and present efficient (c-1)-approximation algorithms for both objectives. In particular, for 3-claw-free graphs, also simply known as claw-free graphs, we obtain a 2-approximation. Due to the claw-freeness of line graphs, this also implies a 2-approximation for the edge-partition version of BCP in general graphs. A harder connected partition problem arises from demanding a connected partition into k parts that have (possibly) heterogeneous target weights w₁,…,w_k. In the 1970s Győri and Lovász showed that if G is k-connected and the target weights sum to the total size of G, such a partition exists. However, to this day no polynomial algorithm to compute such partitions exists for k > 4. Towards finding such a partition T₁,…, T_k in k-connected graphs for general k, we show how to efficiently compute connected partitions that at least approximately meet the target weights, subject to the mild assumption that each w_i is greater than the weight of the heaviest vertex. In particular, we give a 3-approximation for both the lower and the upper bounded version i.e. we guarantee that each T_i has weight at least (w_i)/3 or that each T_i has weight most 3w_i, respectively. Also, we present a both-side bounded version that produces a connected partition where each T_i has size at least (w_i)/3 and at most max({r,3}) w_i, where r ≥ 1 is the ratio between the largest and smallest value in w₁, … , w_k. In particular for the balanced version, i.e. w₁ = w₂ = , … , = w_k, this gives a partition with 1/3w_i ≤ w(T_i) ≤ 3w_i.
Cite as

Ralf Borndörfer, Katrin Casel, Davis Issac, Aikaterini Niklanovits, Stephan Schwartz, and Ziena Zeif. Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{borndorfer_et_al:LIPIcs.APPROX/RANDOM.2021.27,
  author =	{Bornd\"{o}rfer, Ralf and Casel, Katrin and Issac, Davis and Niklanovits, Aikaterini and Schwartz, Stephan and Zeif, Ziena},
  title =	{{Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.27},
  URN =		{urn:nbn:de:0030-drops-147200},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.27},
  annote =	{Keywords: connected partition, Gy\H{o}ri-Lov\'{a}sz, balanced partition, approximation algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2019.1
A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance

Authors: Boris Grimm, Ralf Borndörfer, Markus Reuther, and Thomas Schlechte

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

Abstract
For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
Cite as

Boris Grimm, Ralf Borndörfer, Markus Reuther, and Thomas Schlechte. A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 1:1-1:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{grimm_et_al:OASIcs.ATMOS.2019.1,
  author =	{Grimm, Boris and Bornd\"{o}rfer, Ralf and Reuther, Markus and Schlechte, Thomas},
  title =	{{A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{1:1--1:12},
  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.2019.1},
  URN =		{urn:nbn:de:0030-drops-114136},
  doi =		{10.4230/OASIcs.ATMOS.2019.1},
  annote =	{Keywords: Railway Operations Research, Integer Programming, Infeasible Path Cuts, Cut Separation, Rolling Stock Rotation Problem}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2019.12
A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks

Authors: Ricardo Euler and Ralf Borndörfer

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

Abstract
We present a novel framework to mathematically describe the fare systems of local public transit companies. The model allows the computation of a provably cheapest itinerary even if prices depend on a number of parameters and non-linear conditions. Our approach is based on a ticket graph model to represent tickets and their relation to each other. Transitions between tickets are modeled via transition functions over partially ordered monoids and a set of symbols representing special properties of fares (e.g. surcharges). Shortest path algorithms rely on the subpath optimality property. This property is usually lost when dealing with complicated fare systems. We restore it by relaxing domination rules for tickets depending on the structure of the ticket graph. An exemplary model for the fare system of Mitteldeutsche Verkehrsbetriebe (MDV) is provided. By integrating our framework in the multi-criteria RAPTOR algorithm we provide a price-sensitive algorithm for the earliest arrival problem and assess its performance on data obtained from MDV. We discuss three preprocessing techniques that improve run times enough to make the algorithm applicable for real-time queries.
Cite as

Ricardo Euler and Ralf Borndörfer. A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{euler_et_al:OASIcs.ATMOS.2019.12,
  author =	{Euler, Ricardo and Bornd\"{o}rfer, Ralf},
  title =	{{A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{12:1--12:15},
  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.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.12},
  URN =		{urn:nbn:de:0030-drops-114243},
  doi =		{10.4230/OASIcs.ATMOS.2019.12},
  annote =	{Keywords: shortest path, public transit, optimization, price-sensitive, raptor, fare, operations research}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.ATMOS.2018
OASIcs, Volume 65, ATMOS'18, Complete Volume

Authors: Ralf Borndörfer and Sabine Storandt

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

Abstract
OASIcs, Volume 65, ATMOS'18, Complete Volume
Cite as

18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{borndorfer_et_al:OASIcs.ATMOS.2018,
  title =	{{OASIcs, Volume 65, ATMOS'18, Complete Volume}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018},
  URN =		{urn:nbn:de:0030-drops-97272},
  doi =		{10.4230/OASIcs.ATMOS.2018},
  annote =	{Keywords: Theory of computation, Design and analysis of algorithms, Mathematics of computing, Discrete mathematics, Mathematics of computing, Combinatorics}
}
Document
Front Matter
DOI: 10.4230/OASIcs.ATMOS.2018.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Ralf Borndörfer and Sabine Storandt

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

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

18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2018.0,
  author =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{0:i--0:x},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.0},
  URN =		{urn:nbn:de:0030-drops-97050},
  doi =		{10.4230/OASIcs.ATMOS.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2018.1
Reformulations for Integrated Planning of Railway Traffic and Network Maintenance

Authors: Tomas Lidén

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

Abstract
This paper addresses the capacity planning problem of coordinating train services and network maintenance windows for a railway system. We present model reformulations, for a mixed integer linear optimization model, which give a mathematically stronger model and substantial improvements in solving performance - as demonstrated with computational experiments on a set of synthetic test instances. As a consequence, more instances can be solved to optimality within a given time limit and the optimality gap can be reduced quicker.
Cite as

Tomas Lidén. Reformulations for Integrated Planning of Railway Traffic and Network Maintenance. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 1:1-1:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{liden:OASIcs.ATMOS.2018.1,
  author =	{Lid\'{e}n, Tomas},
  title =	{{Reformulations for Integrated Planning of Railway Traffic and Network Maintenance}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{1:1--1:10},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.1},
  URN =		{urn:nbn:de:0030-drops-97065},
  doi =		{10.4230/OASIcs.ATMOS.2018.1},
  annote =	{Keywords: Railway scheduling, Maintenance planning, Optimization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2018.2
Large Scale Railway Renewal Planning with a Multiobjective Modeling Approach

Authors: Nuno Sousa, Luis Alçada-Almeida, and João Coutinho-Rodrigues

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

Abstract
A multiobjective modeling approach for managing large scale railway infrastructure asset renewal is presented. An optimized intervention project schedule is obtained considering operational constraints in a three objectives model: evenly spreading investment throughout multiple years, minimizing total cost, minimizing work start postponements on higher priority railway sections. The MILP model was based on a real world case study; the objectives and constraints specified by an infrastructure management company. Results show that investment spreading greatly influences the other objectives and that total cost fluctuations depend on the overall condition of the railway infrastructure. The model can produce exact efficient solutions in reasonable time, even for very large-sized instances (a test network of similar size to the USA railway network, the largest in the world). The modeling approach is therefore a very useful, practical methodology, for generating optimized solutions and analyzing trade-offs among objectives, easing the task of ultimately selecting a solution and produce the works schedule for field implementation.
Cite as

Nuno Sousa, Luis Alçada-Almeida, and João Coutinho-Rodrigues. Large Scale Railway Renewal Planning with a Multiobjective Modeling Approach. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{sousa_et_al:OASIcs.ATMOS.2018.2,
  author =	{Sousa, Nuno and Al\c{c}ada-Almeida, Luis and Coutinho-Rodrigues, Jo\~{a}o},
  title =	{{Large Scale Railway Renewal Planning with a Multiobjective Modeling Approach}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{2:1--2:9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.2},
  URN =		{urn:nbn:de:0030-drops-97071},
  doi =		{10.4230/OASIcs.ATMOS.2018.2},
  annote =	{Keywords: Rail infrastructure, Renewal maintenance, Multiobjective modeling}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2018.3
How to Measure the Robustness of Shunting Plans

Authors: Roel van den Broek, Han Hoogeveen, and Marjan van den Akker

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

Abstract
The general problem of scheduling activities subject to temporal and resource constraints as well as a deadline emerges naturally in numerous application domains such as project management, production planning, and public transport. The schedules often have to be implemented in an uncertain environment, where disturbances cause deviations in the duration, release date or deadline of activities. Since these disruptions are not known in the planning phase, we must have schedules that are robust, i.e., capable of absorbing the disturbances without large deteriorations of the solution quality. Due to the complexity of computing the robustness of a schedule directly, many surrogate robustness measures have been proposed in literature. In this paper, we propose new robustness measures, and compare these and several existing measures with the results of a simulation study to determine which measures can be applied in practice to obtain good approximations of the true robustness of a schedule with deadlines. The experiments are performed on schedules generated for real-world scheduling problems at the shunting yards of the Dutch Railways (NS).
Cite as

Roel van den Broek, Han Hoogeveen, and Marjan van den Akker. How to Measure the Robustness of Shunting Plans. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 3:1-3:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vandenbroek_et_al:OASIcs.ATMOS.2018.3,
  author =	{van den Broek, Roel and Hoogeveen, Han and van den Akker, Marjan},
  title =	{{How to Measure the Robustness of Shunting Plans}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{3:1--3:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.3},
  URN =		{urn:nbn:de:0030-drops-97081},
  doi =		{10.4230/OASIcs.ATMOS.2018.3},
  annote =	{Keywords: robustness, resource-constrained project scheduling, partial order schedule, uncertainty, Monte Carlo simulation, train shunting}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2018.4
Robustness as a Third Dimension for Evaluating Public Transport Plans

Authors: Markus Friedrich, Matthias Müller-Hannemann, Ralf Rückert, Alexander Schiewe, and Anita Schöbel

Published in: OASIcs, Volume 65, 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)

Abstract
Providing attractive and efficient public transport services is of crucial importance due to higher demands for mobility and the need to reduce air pollution and to save energy. The classical planning process in public transport tries to achieve a reasonable compromise between service quality for passengers and operating costs. Service quality mostly considers quantities like average travel time and number of transfers. Since daily public transport inevitably suffers from delays caused by random disturbances and disruptions, robustness also plays a crucial role. While there are recent attempts to achieve delay-resistant timetables, comparably little work has been done to systematically assess and to compare the robustness of transport plans from a passenger point of view. We here provide a general and flexible framework for evaluating public transport plans (lines, timetables, and vehicle schedules) in various ways. It enables planners to explore several trade-offs between operating costs, service quality (average perceived travel time of passengers), and robustness against delays. For such an assessment we develop several passenger-oriented robustness tests which can be instantiated with parameterized delay scenarios. Important features of our framework include detailed passenger flow models, delay propagation schemes and disposition strategies, rerouting strategies as well as vehicle capacities. To demonstrate possible use cases, our framework has been applied to a variety of public transport plans which have been created for the same given demand for an artificial urban grid network and to instances for long-distance train networks. As one application we study the impact of different strategies to improve the robustness of timetables by insertion of supplement times. We also show that the framework can be used to optimize waiting strategies in delay management.
Cite as

Markus Friedrich, Matthias Müller-Hannemann, Ralf Rückert, Alexander Schiewe, and Anita Schöbel. Robustness as a Third Dimension for Evaluating Public Transport Plans. In 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018). Open Access Series in Informatics (OASIcs), Volume 65, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{friedrich_et_al:OASIcs.ATMOS.2018.4,
  author =	{Friedrich, Markus and M\"{u}ller-Hannemann, Matthias and R\"{u}ckert, Ralf and Schiewe, Alexander and Sch\"{o}bel, Anita},
  title =	{{Robustness as a Third Dimension for Evaluating Public Transport Plans}},
  booktitle =	{18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2018)},
  pages =	{4:1--4:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-096-5},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{65},
  editor =	{Bornd\"{o}rfer, Ralf and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2018.4},
  URN =		{urn:nbn:de:0030-drops-97097},
  doi =		{10.4230/OASIcs.ATMOS.2018.4},
  annote =	{Keywords: robustness, timetabling, vehicle schedules, delays}
}
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