14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2014, September 11, 2014, Wrocław, Poland
ATMOS 2014
September 11, 2014
Wrocław, Poland
Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems
ATMOS
http://atmos-workshop.org/
https://dblp.org/db/conf/atmos
Open Access Series in Informatics
OASIcs
https://www.dagstuhl.de/dagpub/2190-6807
https://dblp.org/db/series/oasics
2190-6807
Stefan
Funke
Stefan Funke
Matús
Mihalák
Matús Mihalák
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
42
2014
978-3-939897-75-0
https://www.dagstuhl.de/dagpub/978-3-939897-75-0
Frontmatter, Table of Contents, Preface, Workshop Organization
Frontmatter, Table of Contents, Preface, Workshop Organization
Frontmatter
Table of Contents
Preface
Workshop Organization
i-ix
Front Matter
Stefan
Funke
Stefan Funke
Matús
Mihalák
Matús Mihalák
10.4230/OASIcs.ATMOS.2014.i
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Delay-Robust Journeys in Timetable Networks with Minimum Expected Arrival Time
We study the problem of computing delay-robust routes in timetable
networks. Instead of a single path we compute a decision graph containing all stops and trains/vehicles that might be relevant. Delays are formalized using a stochastic model. We show how to compute a decision graph that minimizes the expected arrival time while bounding the latest arrival time over all sub-paths. Finally we show how the information contained within a decision graph can compactly be represented to the user. We experimentally evaluate our algorithms and show that the running times allow for interactive usage on a realistic train network.
Algorithms
Optimization
Delay-robustness
Route planning
Public transportation
1-14
Regular Paper
Julian
Dibbelt
Julian Dibbelt
Ben
Strasser
Ben Strasser
Dorothea
Wagner
Dorothea Wagner
10.4230/OASIcs.ATMOS.2014.1
Hannah Bast, Daniel Delling, Andrew V. Goldberg, Matthias Müller-Hannemann, Thomas Pajor, Peter Sanders, Dorothea Wagner, and Renato F. Werneck. Route planning in transportation networks. Technical Report MSR-TR-2014-4, Microsoft Research, 2014.
Hannah Bast, Jonas Sternisko, and Sabine Storandt. Delay-robustness of transfer patterns in public transportation route planning. In Proceedings of the 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'13), OpenAccess Series in Informatics (OASIcs), pages 42-54, September 2013.
Hannah Bast and Sabine Storandt. Flow-based guidebook routing. In Proceedings of the 16th Meeting on Algorithm Engineering and Experiments (ALENEX'14), pages 155-165. SIAM, 2014.
Annabell Berger, Andreas Gebhardt, Matthias Müller-Hannemann, and Martin Ostrowski. Stochastic delay prediction in large train networks. In Proceedings of the 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'11), volume 20 of OpenAccess Series in Informatics (OASIcs), pages 100-111, 2011.
Kateřina Böhmová, Matúš Mihalák, Tobias Pröger, Rastislav Šrámek, and Peter Widmayer. Robust routing in urban public transportation: How to find reliable journeys based on past observations. In Proceedings of the 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'13), OpenAccess Series in Informatics (OASIcs), pages 27-41, September 2013.
Daniel Delling, Thomas Pajor, and Renato F. Werneck. Round-based public transit routing. In Proceedings of the 14th Meeting on Algorithm Engineering and Experiments (ALENEX'12), pages 130-140. SIAM, 2012.
Julian Dibbelt, Thomas Pajor, Ben Strasser, and Dorothea Wagner. Intriguingly simple and fast transit routing. In Proceedings of the 12th International Symposium on Experimental Algorithms (SEA'13), volume 7933 of Lecture Notes in Computer Science, pages 43-54. Springer, 2013.
Yann Disser, Matthias Müller-Hannemann, and Mathias Schnee. Multi-criteria shortest paths in time-dependent train networks. In Proceedings of the 7th Workshop on Experimental Algorithms (WEA'08), volume 5038 of Lecture Notes in Computer Science, pages 347-361. Springer, June 2008.
Donatella Firmani, Giuseppe F. Italiano, Luigi Laura, and Federico Santaroni. Is timetabling routing always reliable for public transport? In Proceedings of the 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'13), OpenAccess Series in Informatics (OASIcs), pages 15-26, September 2013.
Marc Goerigk, Sascha Heße, Matthias Müller-Hannemann, and Marie Schmidt. Recoverable robust timetable information. In Proceedings of the 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'13), OpenAccess Series in Informatics (OASIcs), pages 1-14, September 2013.
Marc Goerigk, Martin Knoth, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel. The price of robustness in timetable information. In Proceedings of the 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'11), volume 20 of OpenAccess Series in Informatics (OASIcs), pages 76-87, 2011.
Ben Strasser and Dorothea Wagner. Connection scan accelerated. In Proceedings of the 16th Meeting on Algorithm Engineering and Experiments (ALENEX'14), pages 125-137. SIAM, 2014.
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Shortest Path with Alternatives for Uniform Arrival Times: Algorithms and Experiments
The Shortest Path with Alternatives (SPA) policy differs from classical shortest path routing in the following way: instead of providing an exact list of means of transportation to follow, this policy gives such a list for each stop, and the traveler is supposed to pick the first option from this list when waiting at some stop. First, we show that an optimal policy of this type can be computed in polynomial time for uniform arrival times under reasonable assumptions. A similar result was so far only known for Poisson arrival times, which are less realistic for frequency-based public transportation systems. Second, we experimentally evaluate such policies. In this context, our main finding is that SPA policies are surprisingly competitive compared to traditional shortest paths, and moreover yield a significant reduction of waiting times, and therefore improvement of user experience, compared to similar greedy approaches. Specifically, for roughly 25% of considered cases, we could decrease the expected waiting time by at least 20%. To run our experiments, we also describe a tool-chain to derive the necessary information from the popular GTFS-format, therefore allowing the application of SPA policies to a wide range of public transportation systems.
Shortest Path
Stochastic Optimization
Public Transportation
15-24
Regular Paper
Tim
Nonner
Tim Nonner
Marco
Laumanns
Marco Laumanns
10.4230/OASIcs.ATMOS.2014.15
Utku Günay Acer, Paolo Giaccone, David Hay, Giovanni Neglia, and Saed Tarapiah. Timely data delivery in a realistic bus network. IEEE Transactions on Vehicular Technology, 61(3):1251-1265, 2012.
Hannah Bast, Daniel Delling, Andrew Goldberg, Matthias Müller-Hannemann, Thomas Pajor, Peter Sanders, Dorothea Wagner, and Renato Werneck. Route planning in transportation networks. Technical Report MSR-TR-2014-4, Microsoft Research, January 2014.
Hannah Bast and Sabine Storandt. Flow-based guidebook routing. In Proceedings of the 16th Workshop on Algorithm Engineering and Experiments (ALENEX'14), pages 155-165, 2014.
Dimitri P. Bertsekas and John N. Tsitsiklis. An analysis of stochastic shortest path problems. Math. Oper. Res., 16:580-595, August 1991.
Justin Boyan and Michael Mitzenmacher. Improved results for route planning in stochastic transportation. In Proceedings of the 12th annual ACM-SIAM Symposium on Discrete Algorithms (SODA'01), pages 895-902, 2001.
Mayur Datar and Abhiram G. Ranade. Commuting with delay prone buses. In Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'00), pages 22-29, 2000.
Julian Dibbelt, Thomas Pajor, Ben Strasser, and Dorothea Wagner. Intriguingly simple and fast transit routing. In Proceedings of the 12th International Symposium on Experimental Algorithms (SEA'13), pages 43-54, 2013.
Evdokia Nikolova, Jonathan A Kelner, Matthew Brand, and Michael Mitzenmacher. Stochastic shortest paths via quasi-convex maximization. In Proceedings of the 14th Annual European Symposium on Algorithms (ESA'06), pages 552-563. Springer, 2006.
Tim Nonner. Polynomial-time approximation schemes for shortest path with alternatives. In Proceedings of the 20th Annual European Symposium on Algorithms (ESA'12), pages 755-765, 2012.
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Locating Battery Charging Stations to Facilitate Almost Shortest Paths
We study a facility location problem motivated by requirements pertaining to the distribution of charging stations for electric vehicles: Place a minimum number of battery charging stations at a subset of nodes of a network, so that battery-powered electric vehicles will be able to move between destinations using "t-spanning" routes, of lengths within a factor t > 1 of the length of a shortest path, while having sufficient charging stations along the way. We give constant-factor approximation algorithms for minimizing the number of charging stations, subject to the t-spanning constraint. We study two versions of the problem, one in which the stations are required to support a single ride (to a single destination), and one in which the stations are to support multiple rides through a sequence of destinations, where the destinations are revealed one at a time.
approximation algorithms; geometric spanners; transportation networks
25-33
Regular Paper
Esther M.
Arkin
Esther M. Arkin
Paz
Carmi
Paz Carmi
Matthew J.
Katz
Matthew J. Katz
Joseph S. B.
Mitchell
Joseph S. B. Mitchell
Michael
Segal
Michael Segal
10.4230/OASIcs.ATMOS.2014.25
Prosenjit Bose, Paz Carmi, Lilach Chaitman-Yerushalmi, Sébastien Collette, Matthew J. Katz, and Stefan Langerman. Stable roommates spanner. Computational Geometry, 46(2):120-130, 2013.
Xiuzhen Cheng, Xiao Huang, Deying Li, Weili Wu, and Ding-Zhu Du. A polynomial-time approximation scheme for the minimum-connected dominating set in ad hoc wireless networks. Networks, 42(4):202-208, 2003.
Brent N. Clark, Charles J. Colbourn, and David S. Johnson. Unit disk graphs. Discrete Mathematics, 86(1-3):165-177, 1990.
Stefan Funke, Alexander Kesselman, Ulrich Meyer, and Michael Segal. A simple improved distributed algorithm for minimum cds in unit disk graphs. ACM Trans. Sen. Netw., 2(3):444-453, 2006.
Xiaofeng Gao, Yuexuan Wang, Xianyue Li, and Weili Wu. Analysis on theoretical bounds for approximating dominating set problems. Discrete Mathematics, Algorithms and Applications, 1(1):71-84, 2009.
J. Mark Keil and Carl A. Gutwin. Classes of graphs which approximate the complete euclidean graph. Discrete &Computational Geometry, 7(1):13-28, 1992.
Minming Li, Peng-Jun Wan, and Frances Yao. Tighter approximation bounds for minimum CDS in wireless ad hoc networks. In International Symposium on Algorithms and Computation (ISAAC), pages 699-709. 2009.
M. V. Marathe, H. Breu, H. B. Hunt, S. S. Ravi, and D. J. Rosenkrantz. Simple heuristics for unit disk graphs. Networks, 25(2):59-68, 1995.
Giri Narasimhan and Michiel Smid. Geometric spanner networks. Cambridge University Press, 2007.
Srinivasan Parthasarathy and Rajiv Gandhi. Distributed algorithms for coloring and domination in wireless ad hoc networks. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), pages 447-459. 2005.
Sabine Storandt and Stefan Funke. Enabling e-mobility: Facility location for battery loading stations. In 27th Conference on Artificial Intelligence (AAAI), 2013.
Alireza Vahdatpour, Foad Dabiri, Maryam Moazeni, and Majid Sarrafzadeh. Theoretical bound and practical analysis of connected dominating set in ad hoc and sensor networks. In 22nd International Symposium on Distributed Computing (DISC), pages 481-495, 2008.
Peng-Jun Wan, K.M. Alzoubi, and O. Frieder. Distributed construction of connected dominating set in wireless ad hoc networks. In 21st IEEE International Conference on Computer Communications (INFOCOM), volume 3, pages 1597-1604, 2002.
Peng-Jun Wan, Lixin Wang, and F. Yao. Two-phased approximation algorithms for minimum CDS in wireless ad hoc networks. In 28th International Conference on Distributed Computing Systems (ICDCS), pages 337-344, 2008.
Weili Wu, Hongwei Du, Xiaohua Jia, Yingshu Li, and Scott C.-H. Huang. Minimum connected dominating sets and maximal independent sets in unit disk graphs. Theoretical Computer Science, 352(1-3):1-7, 2006.
Andrew Chi-Chih Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM Journal on Computing, 11(4):721-736, 1982.
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Online Train Shunting
At the occasion of ATMOS 2012, Tim Nonner and Alexander Souza defined a new train shunting problem that can roughly be described as follows. We are given a train visiting stations in a given order and cars located at some source stations. Each car has a target station. During the trip of the train, the cars are added to the train at their source stations and removed from it at their target stations. An addition or a removal of a car in the strict interior of the train incurs a cost higher than when the operation is performed at the end of the train. The problem consists in minimizing the total cost, and thus, at each source station of a car, the position the car takes in the train must be carefully decided. Among other results, Nonner and Souza showed that this problem is polynomially solvable by reducing the problem to the computation of a minimum independent set in a bipartite graph. They worked in the offline setting, i.e. the sources and the targets of all cars are known before the trip of the train starts. We study the online version of the problem, in which cars become known at their source stations. We derive a 2-competitive algorithm and prove than no better ratios are achievable. Other related questions are also addressed.
Bipartite graph
competitive analysis
online algorithm
train shunting problem
vertex cover
34-45
Regular Paper
Vianney
Boeuf
Vianney Boeuf
Frédéric
Meunier
Frédéric Meunier
10.4230/OASIcs.ATMOS.2014.34
Katharina Beygang, Florian Dahms, and Sven O. Krumke. Train marshalling problem: Algorithms and bounds. Technical report, 2010.
Markus Bohlin, Florian Dahms, Holger Flier, and Sara Gestrelius. Optimal freight train classification using column generation. In Proceedings of the 12th workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'12), volume 25, pages 10-22, 2012.
Nils Boysen, Malte Fliedner, Florian Jaehn, and Erwin Pesch. Shunting yard operations: Theoretical aspects and applications. European Journal of Operational Research, 220:1-14, 2012.
Alberto Ceselli, Michael Gatto, Marco E. Lübbecke, Marc Nunkesser, and Heiko Schilling. Optimizing the cargo express service of Swiss federal railways. Transportation Science, 42:450-465, 2008.
Elias Dahlhaus, Peter Horák, Mirka Miller, and Joseph F. Ryan. The train marshalling problem. Discrete Applied Mathematics, 103:41-54, 2000.
Marc Demange and Vangelis T. Paschos. On-line vertex-covering. Theoretical Computer Science, 332:83-108, 2005.
Gabriele Di Stefano and Magnus Love Koci. A graph theoretical approach to the shunting problem. Electronic Notes in Theoretical Computer Science, 92:16-33, 2004.
Andrew L. Dulmage and Nathan S. Mendelsohn. Coverings of bipartite graphs. Canadian Journal of Mathematics, 10:517-534, 1958.
Michael Gatto, Jens Maue, Matús Mihalák, and Peter Widmayer. Robust and Online Large-Scale Optimization, chapter Shunting for dummies: An introductory algorithmic survey, pages 310-337. Springer, 2009.
Riko Jacob, Peter Marton, Jens Maue, and Marc Nunkesser. Multistage methods for freight train classification. Networks, 57:87-105, 2011.
Tim Nonner and Alexander Souza. Optimal algorithms for train shunting and relaxed list update problems. In Proceedings of the 12th workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'12), volume 25, pages 97-107, 2012.
Marc Nunkesser, Michael Gatto, and Riko Jacob. Optimization of a railway hub-and-spoke system: routing and shunting. In Proceedings of WEA 2005, 2005.
Alexandrer Schrijver. Combinatorial Optimization. Springer, 2003.
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Engineering Graph-Based Models for Dynamic Timetable Information Systems
Many efforts have been done in the last years to model public transport timetables in order to find optimal routes. The proposed models can be classified into two types: those representing the timetable as an array, and those representing it as a graph. The array-based models have been shown to be very effective in terms of query time, while the graph-based models usually answer queries by computing shortest paths, and hence they are suitable to be used in combination with speed-up techniques developed for road networks.
In this paper, we focus on the dynamic behavior of graph-based models considering the case where transportation systems are subject to delays with respect to the given timetable. We make three contributions: (i) we give a simplified and optimized update routine for the well-known time-expanded model along with an engineered query algorithm; (ii) we propose a new graph-based model tailored for handling dynamic updates; (iii) we assess the effectiveness of the proposed models and algorithms by an experimental study, which shows that both models require negligible update time and a query time which is comparable to that required by some array-based models.
Timetabling
dynamic updates
queries
shortest paths
46-61
Regular Paper
Alessio
Cionini
Alessio Cionini
Gianlorenzo
D'Angelo
Gianlorenzo D'Angelo
Mattia
D'Emidio
Mattia D'Emidio
Daniele
Frigioni
Daniele Frigioni
Kalliopi
Giannakopoulou
Kalliopi Giannakopoulou
Andreas
Paraskevopoulos
Andreas Paraskevopoulos
Christos
Zaroliagis
Christos Zaroliagis
10.4230/OASIcs.ATMOS.2014.46
Hannah Bast, Erik Carlsson, Arno Eigenwillig, Robert Geisberger, Chris Harrelson, Veselin Raychev, and Fabien Viger. Fast routing in very large public transportation networks using transfer patterns. In 18th Annual European Symposium on Algorithms (ESA 2010), volume 6346 of LNCS, pages 290-301. Springer, 2010.
Hannah Bast, Daniel Delling, Andrew Goldberg, Matthias Mueller-Hannemann, Thomas Pajor, Peter Sanders, Dorothea Wagner, and Renato Werneck. Route planning in transportation networks. Technical Report MSR-TR-2014-4, Microsoft Research, 2014.
Hannah Bast, Jonas Sternisko, and Sabine Storandt. Delay-Robustness of Transfer Patterns in Public Transportation Route Planning. In 13th Work. on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS), pages 42-54. Schloss Dagstuhl, 2013.
Reinhard Bauer, Daniel Delling, Peter Sanders, Dennis Schieferdecker, Dominik Schultes, and Dorothea Wagner. Combining hierarchical and goal-directed speed-up techniques for dijkstra’s algorithm. ACM J. Exp. Alg., 15:Article 2.3, 2010.
Reinhard Bauer, Daniel Delling, and Dorothea Wagner. Experimental study of speed up techniques for timetable information systems. Networks, 57(1):38-52, 2011.
F. Bruera, S. Cicerone, G. D'Angelo, G. Di Stefano, and D. Frigioni. Dynamic multi-level overlay graphs for shortest paths. Math. Comp. Sc., 1(4):709-736, 2008.
Serafino Cicerone, Gianlorenzo D'Angelo, Gabriele Di Stefano, Daniele Frigioni, and Alfredo Navarra. Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases. Journal of Combinatorial Optimization, 18(3):229-257, 2009.
Serafino Cicerone, Gianlorenzo D'Angelo, Gabriele Di Stefano, Daniele Frigioni, Alfredo Navarra, Michael Schachtebeck, and Anita Schöbel. Recoverable robustness in shunting and timetabling. In Robust and Online Large-Scale Opt., volume 5868 of LNCS, pages 28-60. Springer, 2009.
Gianlorenzo D'Angelo, Mattia D'Emidio, and Daniele Frigioni. Fully dynamic update of arc-flags. Networks, 63(3):243-259, 2014.
D. Delling and D. Wagner. Landmark-based routing in dynamic graphs. In 6th Work. on Experimental Algorithms, LNCS, pages 52-65. Springer, 2007.
Daniel Delling, Kalliopi Giannakopoulou, Dorothea Wagner, and Christos Zaroliagis. Timetable Information Updating in Case of Delays: Modeling Issues. Technical Report ARRIVAL-TR-0133, ARRIVAL Project, 2008.
Daniel Delling, Thomas Pajor, and Dorothea Wagner. Engineering time-expanded graphs for faster timetable information. In Robust and Online Large-Scale Optimization, volume 5868 of LNCS, pages 182-206. Springer, 2009.
Daniel Delling, Thomas Pajor, and Renato F. Werneck. Round-Based Public Transit Routing, pages 130-140. SIAM, 2012.
Daniel Delling and Renato F. Werneck. Faster customization of road networks. In 12th Symp. Exp. Alg. (SEA), volume 7933 of LNCS, pages 30-42. Springer, 2013.
Julian Dibbelt, Thomas Pajor, Ben Strasser, and Dorothea Wagner. Intriguingly simple and fast transit routing. In 12th Symp. Exp. Alg. (SEA), volume 7933 of LNCS, pages 43-54. Springer, 2013.
Julian Dibbelt, Ben Strasser, and Dorothea Wagner. Customizable contraction hierarchies. In 13th Int. Symp. on Exp. Alg. (SEA), volume 8504 of LNCS, pages 271-282. Springer, 2014.
Alexandros Efentakis and Dieter Pfoser. Optimizing landmark-based routing and preprocessing. In 6th ACM SIGSPATIAL Int. Work. on Computational Transp. Science. ACM, 2013.
Donatella Firmani, Giuseppe F. Italiano, Luigi Laura, and Federico Santaroni. Is Timetabling Routing Always Reliable for Public Transport? In 13th Work. on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS), pages 15-26. Schloss Dagstuhl, 2013.
Matteo Fischetti, Domenico Salvagnin, and Arrigo Zanette. Fast approaches to improve the robustness of a railway timetable. Transportation Science, 43(3):321-335, 2009.
A. Goldberg and C. Harrelson. Computing the shortest path: A* search meets graph theory. In ACM-SIAM Symposium on Discrete Algorithms (SODA05), pages 156-165. SIAM, 2005.
HaCon - Ingenieurgesellschaft mbH. http://www.hacon.de, 2008.
http://www.hacon.de
U. Lauther. An extremely fast, exact algorithm for finding shortest paths. Static Networks with Geographical Background, 22:219-230, 2004.
Christian Liebchen, Michael Schachtebeck, Anita Schöbel, Sebastian Stiller, and André Prigge. Computing delay resistant railway timetables. Computers & OR, 37(5):857-868, 2010.
Georgia Mali, Panagiotis Michail, Andreas Paraskevopoulos, and Christos Zaroliagis. A new dynamic graph structure for large-scale transportation networks. In 8th Int. Conf. on Algorithms and Complexity (CIAC), volume 7878 of LNCS, pages 312-323. Springer, 2013.
Matthias Müller-Hannemann and Mathias Schnee. Efficient timetable information in the presence of delays. In Robust and Online Large-Scale Optimization, volume 5868 of LNCS, pages 249-272. Springer Berlin Heidelberg, 2009.
Evangelia Pyrga, Frank Schulz, Dorothea Wagner, and Christos Zaroliagis. Efficient models for timetable information in public transportation systems. ACM J Exp Alg, 12(2.4):1-39, 2008.
Michael Schachtebeck and Anita Schöbel. To wait or not to wait - and who goes first? delay management with priority decisions. Transportation Sc., 44(3):307-321, 2010.
D. Schultes and P. Sanders. Dynamic highway-node routing. In 6th Workshop on Experimental Algorithms (WEA), LNCS, pages 66-79. Springer, 2007.
Dorothea Wagner, Thomas Willhalm, and Christos D. Zaroliagis. Geometric containers for efficient shortest-path computation. ACM J. Exp. Alg., 10(1.3):1-30, 2005.
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Local Search for the Resource Constrained Assignment Problem
The resource constrained assignment problem (RCAP) is to find a minimal cost cycle partition in a directed graph such that a resource constraint is fulfilled. The RCAP has its roots in an application that deals with the covering of a railway timetable by rolling stock vehicles. Here, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes several variants of vehicle routing problems. We contribute a local search algorithm for this problem that is derived from an exact algorithm which is similar to the Hungarian method for the standard assignment problem. Our algorithm can be summarized as a k-OPT heuristic, exchanging k arcs of an alternating cycle of the incumbent solution in each improvement step. The alternating cycles are found by dual arguments from linear programming. We present computational results for instances from our railway application at Deutsche Bahn Fernverkehr AG as well as for instances of the vehicle routing problem from the literature.
Assignment Problem
Local Search
Rolling Stock Rotation Problem
Vehicle Routing Problem
62-78
Regular Paper
Markus
Reuther
Markus Reuther
10.4230/OASIcs.ATMOS.2014.62
M. L. Balinski and R. E. Gomory. A primal method for the assignment and transportation problems. Management Science, 10(3):578-593, 1964.
Timo Berthold. Rens - the optimal rounding. Technical Report 12-17, ZIB, Takustr.7, 14195 Berlin, 2012.
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Emilie Danna, Edward Rothberg, and Claude Le Pape. Exploring relaxation induced neighborhoods to improve mip solutions. Mathematical Programming, 102(1):71-90, 2005.
I. Dumitrescu. Constrained Path and Cycle Problems. University of Melbourne, Department of Mathematics and Statistics, 2002.
Matteo Fischetti and Andrea Lodi. Local branching. Mathematical Programming, 98(1-3):23-47, 2003.
Chris Groër, Bruce Golden, and Edward Wasil. A library of local search heuristics for the vehicle routing problem. Mathematical Programming Computation, 2(2):79–-101, 2010.
Keld Helsgaun. An effective implementation of k-opt moves for the linkernighan tsp heuristic. Technical report, Roskilde University, 2006.
Keld Helsgaun. General k-opt submoves for the Lin–Kernighan TSP heuristic. Mathematical Programming Computation, 1(2-3):119–-163, 2009.
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H. W. Kuhn. The hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1-2):83-97, 1955.
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Karl Nachtigall and Jens Opitz. Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations. In ATMOS'08, volume 9 of OpenAccess Series in Informatics (OASIcs), Dagstuhl, Germany, 2008. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
Luigi Di Puglia Pugliese and Francesca Guerriero. A survey of resource constrained shortest path problems: Exact solution approaches. Networks, 62(3):183-200, 2013.
T. Ralphs. Branch cut and price resource web (http://www.branchandcut.org), June 2014.
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Markus Reuther, Ralf Borndörfer, Thomas Schlechte, and Steffen Weider. Integrated optimization of rolling stock rotations for intercity railways. In Proceedings of RailCopenhagen, Copenhagen, Denmark, May 2013.
Edward Rothberg. An evolutionary algorithm for polishing mixed integer programming solutions. INFORMS Journal on Computing, 19(4):534-541, 2007.
Paolo Toth and Daniele Vigo, editors. The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001.
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A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem
We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.
Coarse-To-Fine Linear Programming
Rolling Stock Rotation Problem
79-91
Regular Paper
Ralf
Borndörfer
Ralf Borndörfer
Markus
Reuther
Markus Reuther
Thomas
Schlechte
Thomas Schlechte
10.4230/OASIcs.ATMOS.2014.79
Andreas Bärmann, Frauke Liers, Alexander Martin, Maximilian Merkert, Christoph Thurner, and Dieter Weninger. Solving network design problems via iterative aggregation. Technical report, Department Mathematik, 2013.
Jacques Desrosiers, Jean Bertrand Gauthier, and Marco E. Lübbecke. Row-reduced column generation for degenerate master problems. European Journal of Operational Research, 236(2):453 - 460, 2014.
Issmail Elhallaoui, Abdelmoutalib Metrane, François Soumis, and Guy Desaulniers. Multi-phase dynamic constraint aggregation for set partitioning type problems. Mathematical Programming, 123(2):345-370, 2010.
Olga Heismann. The Hypergraph Assignment Problem. PhD thesis, Technische Universität Berlin, 2014.
M.E. Lübbecke and J. Desrosiers. Selected topics in column generation. Oper. Res., 53(6):1007-1023, 2005.
C. Raphael. Coarse-to-fine dynamic programming. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(12):1379-1390, 2001.
Markus Reuther, Ralf Borndoerfer, Thomas Schlechte, and Steffen Weider. Integrated optimization of rolling stock rotations for intercity railways. In Proceedings of the 5th International Seminar on Railway Operations Modelling and Analysis (RailCopenhagen), Copenhagen, Denmark, May 2013.
Markus Reuther, Ralf Borndörfer, and Thomas Schlechte. A coarse-to-fine approach to the railway rolling stock rotation problem. Technical Report 14-26, ZIB, Takustr.7, 14195 Berlin, 2014.
David F. Rogers, Robert D. Plante, Richard T. Wong, and James R. Evans. Aggregation and disaggregation techniques and methodology in optimization. Operations Research, 39(4):553-582, 1991.
Thomas Schlechte, Ralf Borndörfer, Berkan Erol, Thomas Graffagnino, and Elmar Swarat. Micro-Macro Transformation of Railway Networks. Journal of Rail Transport Planning & Management, 1(1):38-48, 2011.
J. Tang, S. MacLachlan, R. Nabben, and C. Vuik. A comparison of two-level preconditioners based on multigrid and deflation. SIAM Journal on Matrix Analysis and Applications, 31(4):1715-1739, 2010.
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Mathematical programming models for scheduling locks in sequence
We investigate the scheduling of series of consecutive locks. This setting occurs naturally along canals and waterways. We describe a problem that generalizes different models that have been studied in literature. Our contribution is to (i) provide two distinct mathematical programming formulations, and compare them empirically, (ii) show how these models allow for minimizing emission by having the speed of a ship as a decision variable, (iii) to compare, on realistic instances, the optimum solution found by solving the models with the outcome of a decentralized heuristic.
Mixed Integer Programming
Inland Waterways
Lock Scheduling
92-106
Regular Paper
Ward
Passchyn
Ward Passchyn
Dirk
Briskorn
Dirk Briskorn
Frits C.R.
Spieksma
Frits C.R. Spieksma
10.4230/OASIcs.ATMOS.2014.92
A. Caris, G. Janssens, and C. Macharis. A simulation approach to the analysis of intermodal freight transport networks. In ESM'2007 Proceedings. EUROSIS, 2007.
S. Coene, W. Passchyn, F.C.R. Spieksma, G. Vanden Berghe, D. Briskorn, and J.L. Hurink. The lockmaster’s problem. under review, 2013.
E. Günther, M. E. Lübbecke, and R. H. Möhring. Ship Traffic Optimization for the Kiel Canal. In TRISTAN VII Book of Extended Abstracts, 2010.
M. Kunst. Organisation of vessel traffic management centres of the future. In Smart Rivers Conference 2013 Abstract Booklet, Liege, Belgium, 2013.
M. Luy. Ship lock scheduling. http://sourceforge.net/projects/lockscheduling/, November 2012.
http://sourceforge.net/projects/lockscheduling/
E.R. Petersen and A.J. Taylor. An optimal scheduling system for the Welland Canal. Transportation Science, 22:173-185, august 1988.
J. Qian and R. Eglese. Finding least fuel emission paths in a network with time-varying speeds. Networks, 63(1):96-106, 2014.
L. D. Smith, D. C. Sweeney, and J. F. Campbell. Simulation of alternative approaches to relieving congestion at locks in a river transportation system. Journal of the Operational Research Society, 60:519-533, 2009.
C. Ting and P. Schonfeld. Effects of speed control on tow travel costs. Journal of waterway, port, coastal, and ocean engineering, 125(4):203-206, 1999.
C. Ting and P. Schonfeld. Control alternatives at a waterway lock. Journal of waterway, port, coastal, and ocean engineering, 127(2):89-96, 2001.
J. Verstichel, P. De Causmaecker, and G. Vanden Berghe. The Lock Scheduling Problem. PhD thesis, KU Leuven, 2013.
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Simultaneous frequency and capacity setting for rapid transit systems with a competing mode and capacity constraints
The railway planning problem consists of several consecutive phases: network design, line planning, timetabling, personnel assignment and rolling stocks planning. In this paper we will focus on the line planning process. Traditionally, the line planning problem consists of determining a set of lines and their frequencies optimizing a certain objective. In this work we will focus on the line planning problem context taking into account aspects related to rolling stock and crew operating costs. We assume that the number of possible vehicles is limited, that is, the problem that we are considering is a capacitated problem and the line network can be a crowding network. The main novelty in this paper is the consideration of the size of vehicles and frequencies as variables as well as the inclusion of a congestion function measuring the level of in-vehicle crowding. Concretely, we present the problem and an algorithm to solve it, which are tested via a computational experience.
Line planning
railway
capacity
frequency
congestion
107-121
Regular Paper
Alicia
De-Los-Santos
Alicia De-Los-Santos
Gilbert
Laporte
Gilbert Laporte
Juan A.
Mesa
Juan A. Mesa
Federico
Perea
Federico Perea
10.4230/OASIcs.ATMOS.2014.107
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Timing of Train Disposition: Towards Early Passenger Rerouting in Case of Delays
Passenger-friendly train disposition is a challenging, highly complex online optimization problem with uncertain and incomplete information about future delays. In this paper we focus on the timing within the disposition process. We introduce three different classification schemes to predict as early as possible the status of a transfer: whether it will almost surely break, is so critically delayed that it requires manual disposition, or can be regarded as only slightly uncertain or as being safe. The three approaches use lower bounds on travel times, historical distributions of delay data, and fuzzy logic, respectively. In experiments with real delay data we achieve an excellent classification rate. Furthermore, using realistic passenger flows we observe that there is a significant potential to reduce the passenger delay if an early rerouting strategy is applied.
train delays
event-activity model
timing of decisions
passenger flows
passenger rerouting
122-137
Regular Paper
Martin
Lemnian
Martin Lemnian
Ralf
Rückert
Ralf Rückert
Steffen
Rechner
Steffen Rechner
Christoph
Blendinger
Christoph Blendinger
Matthias
Müller-Hannemann
Matthias Müller-Hannemann
10.4230/OASIcs.ATMOS.2014.122
L. Anderegg, P. Penna, and P. Widmayer. Online train disposition: to wait or not to wait? ATMOS'02, ICALP 2002 Satellite Workshop on Algorithmic Methods and Models for Optimization of Railways, Electronic Notes in Theoretical Computer Science, 66(6), 2002.
R. Bauer and A. Schöbel. Rules of thumb - practical online strategies for delay management. Technical report, NAM Report, Göttingen, 2012.
M. Bender, S. Büttner, and S.O. Krumke. Online delay management on a single train line: beyond competitive analysis. Public Transport, 5:243-266, 2013.
A. Berger, C. Blaar, A. Gebhardt, M. Müller-Hannemann, and M. Schnee. Passenger flow-oriented train disposition. In C. Demetrescu and M. M. Halldórsson, editors, Proceedings of the 19th Annual European Symposium on Algorithms (ESA), volume 6942 of Lecture Notes in Computer Science, pages 227-238. Springer, 2011.
A. Berger, A. Gebhardt, M. Müller-Hannemann, and M. Ostrowski. Stochastic delay prediction in large train networks. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS), volume 20 of OpenAccess Series in Informatics (OASIcs), pages 100-111. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2011.
A. Berger, R. Hoffmann, U. Lorenz, and S. Stiller. Online railway delay management: Hardness, simulation and computation. Simulation, 87(7):616-629, 2011.
C. Biederbick. Computergestützte Disposition im schienengebundenen Personentransport: ein kundenorientierter Ansatz. PhD thesis, Universität Paderborn, 2006.
C. Biederbick and L. Suhl. Decision support tools for customer-oriented dispatching. In F. Geraets, L.G. Kroon, A. Schoebel, D. Wagner, and C. Zaroliagis, editors, Algorithmic Methods for Railway Optimization, volume 4359 of Lecture Notes in Computer Science, pages 171-183. Springer, 2007.
S. Cicerone, G. Di Stefano, M. Schachtebeck, and A. Schöbel. Multi-stage recovery robustness for optimization problems: A new concept for planning under disturbances. Information Sciences, 190:107-126, 2012.
A. D'Ariano. Improving Real-Time Train Dispatching: Models, Algorithms and Applications. PhD thesis, Technische Universiteit Delft, 2008.
A. D'Ariano, F. Corman, D. Pacciarelli, and M. Pranzo. Reordering and local rerouting strategies to manage train traffic in real time. Transportation Science, 42(4):405-419, 2008.
T. Dollevoet and D. Huisman. Fast heuristics for delay management with passenger rerouting. Public Transport, 2013. URL: http://link.springer.com/article/10.1007%2Fs12469-013-0076-6#page-1.
http://link.springer.com/article/10.1007%2Fs12469-013-0076-6#page-1
T. Dollevoet, D. Huisman, M. Schmidt, and A. Schöbel. Delay management with re-routing of passengers. In J. Clausen and G. Di Stefano, editors, 9th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS), OpenAccess Series in Informatics (OASIcs). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2009.
M. Gatto, B. Glaus, R. Jacob, L. Peeters, and P. Widmayer. Railway delay management: Exploring its algorithmic complexity. In T. Hagerup and J. Katajainen, editors, Proceedings of 9th Scandinavian Workshop on Algorithm Theory (SWAT), volume 3111 of Lecture Notes in Computer Science, pages 199-211. Springer, 2004.
M. Gatto, R. Jacob, L. Peeters, and A. Schöbel. The computational complexity of delay management. In D. Kratsch, editor, Graph-Theoretic Concepts in Computer Science: 31st International Workshop (WG 2005), volume 3787 of Lecture Notes in Computer Science. Springer, 2005.
M. Gatto, R. Jacob, L. Peeters, and P. Widmayer. On-line delay management on a single train line. In F. Geraets, L.G. Kroon, A. Schoebel, D. Wagner, and C. Zaroliagis, editors, Algorithmic Methods for Railway Optimization, volume 4359 of Lecture Notes in Computer Science, pages 306-320. Springer, 2007.
J. Jespersen-Groth, D. Potthoff, J. Clausen, D. Huisman, L.G. Kroon, G. Maróti, and M.N. Nielsen. Disruption management in passenger railway transportation. In R. Ahuja, R.-H. Möhring, and C. Zaroliagis, editors, Robust and Online Large-Scale Optimization, volume 5868 of Lecture Notes in Computer Science, pages 399-421. Springer, Heidelberg, 2009.
P. Kecman, F. Corman, A. D'Ariano, and R. Goverde. Rescheduling models for railway traffic management in large-scale networks. Public Transport, 5:95-123, 2013.
P. Kecman and R. M. P. Goverde. Adaptive, data-driven, online prediction of train event times. In 16th IEEE Annual Conference on Intelligent Transportation Systems (ITCS 2013), 2013.
N. Kliewer and L. Suhl. A note on the online nature of the railway delay management problem. Networks, 57:28-37, 2011.
S.O. Krumke, C. Thielen, and C. Zeck. Extensions to online delay management on a single train line: new bounds for delay minimization and profit maximization. Mathematical Methods of Operations Research, 74(1):53-75, 2011.
S. Kurby. Makroskopisches Echtzeitdispositionsmodell zur Lösung von Anschlusskonflikten im Eisenbahnbetrieb. PhD thesis, Fakultät Verkehrswissenschaften "Friedrich List", Technische Universität Dresden, 2012.
M. Müller-Hannemann and M. Schnee. Finding all attractive train connections by multi-criteria Pareto search. In F. Geraets, L. Kroon, A. Schoebel, D. Wagner, and C. Zaroliagis, editors, Proceedings of the 4th Dagstuhl conference on algorithmic approaches for transportation modelling, optimization, and systems (ATMOS), volume 4359 of Lecture Notes in Computer Science, pages 246-263. Springer Verlag, 2007.
M. Müller-Hannemann and M. Schnee. Efficient timetable information in the presence of delays. In R. Ahuja, R.-H. Möhring, and C. Zaroliagis, editors, Robust and Online Large-Scale Optimization, volume 5868 of Lecture Notes in Computer Science, pages 249-272. Springer, 2009.
M. Schachtebeck and A. Schöbel. To wait or not to wait and who goes first? Delay management with priority decisions. Transportation Science, 44(3):307-321, 2010.
T. Schaer, J. Jacobs, S. Scholl, S. Kurby, A. Schöbel, S. Güttler, and N. Bissantz. DisKon - Laborversion eines flexiblen, modularen und automatischen Dispositionsassistenzsystems. Eisenbahntechnische Rundschau (ETR), 45:809-821, 2005.
M. Schmidt. Simultaneous optimization of delay management decisions and passenger routes. Public Transport, 5:125-147, 2013.
A. Schöbel. A model for the delay management problem based on mixed-integer programming. Electronic Notes in Theoretical Computer Science, 50(1), 2001.
A. Schöbel. Customer-oriented optimization in public transportation. Springer, Berlin, 2006.
A. Schöbel. Integer programming approaches for solving the delay management problem. In F. Geraets, L. Kroon, A. Schoebel, D. Wagner, and C. Zaroliagis, editors, Algorithmic Methods for Railway Optimization, volume 4359 of Lecture Notes in Computer Science, pages 145-170. Springer, 2007.
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Speed-Consumption Tradeoff for Electric Vehicle Route Planning
We study the problem of computing routes for electric vehicles (EVs) in road networks. Since their battery capacity is limited, and consumed energy per distance increases with velocity, driving the fastest route is often not desirable and may even be infeasible. On the other hand, the energy-optimal route may be too conservative in that it contains unnecessary detours or simply takes too long. In this work, we propose to use multicriteria optimization to obtain Pareto sets of routes that trade energy consumption for speed. In particular, we exploit the fact that the same road segment can be driven at different speeds within reasonable intervals. As a result, we are able to provide routes with low energy consumption that still follow major roads, such as freeways.
Unfortunately, the size of the resulting Pareto sets can be too large to be practical. We therefore also propose several nontrivial techniques that can be applied on-line at query time in order to speed up computation and filter insignificant solutions from the Pareto sets.
Our extensive experimental study, which uses a real-world energy consumption model, reveals that we are able to compute diverse sets of alternative routes on continental networks that closely resemble the exact Pareto set in just under a second---several orders of magnitude faster than the exhaustive algorithm.
electric vehicles
shortest paths
route planning
bicriteria optimization
algorithm engineering
138-151
Regular Paper
Moritz
Baum
Moritz Baum
Julian
Dibbelt
Julian Dibbelt
Lorenz
Hübschle-Schneider
Lorenz Hübschle-Schneider
Thomas
Pajor
Thomas Pajor
Dorothea
Wagner
Dorothea Wagner
10.4230/OASIcs.ATMOS.2014.138
Andreas Artmeier, Julian Haselmayr, Martin Leucker, and Martin Sachenbacher. The Shortest Path Problem Revisited: Optimal Routing for Electric Vehicles. In Proceedings of the 33rd Annual German Conference on Advances in Artificial Intelligence, volume 6359 of Lecture Notes in Computer Science, pages 309-316. Springer, 2010.
Hannah Bast, Daniel Delling, Andrew V. Goldberg, Matthias Müller-Hannemann, Thomas Pajor, Peter Sanders, Dorothea Wagner, and Renato F. Werneck. Route Planning in Transportation Networks. Technical Report MSR-TR-2014-4, Microsoft Research, 2014.
Lucas S. Batista, Felipe Campelo, Frederico G. Guimarães, and Jaime A. Ramírez. A Comparison of Dominance Criteria in Many-Objective Optimization Problems. In IEEE Congress on Evolutionary Computation, pages 2359-2366. IEEE, 2011.
Moritz Baum, Julian Dibbelt, Thomas Pajor, and Dorothea Wagner. Energy-Optimal Routes for Electric Vehicles. In Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 54-63. ACM Press, 2013.
Richard Bellman. On a Routing Problem. Quarterly of Applied Mathematics, 16:87-90, 1958.
Lee R. Dice. Measures of the Amount of Ecologic Association between Species. Ecology, 26(3):297-302, 1945.
Edsger W. Dijkstra. A Note on Two Problems in Connexion with Graphs. Numerische Mathematik, 1:269-271, 1959.
Yann Disser, Matthias Müller-Hannemann, and Mathias Schnee. Multi-Criteria Shortest Paths in Time-Dependent Train Networks. In Proceedings of the 7th Workshop on Experimental Algorithms (WEA'08), volume 5038 of Lecture Notes in Computer Science, pages 347-361. Springer, 2008.
Jochen Eisner, Stefan Funke, and Sabine Storandt. Optimal Route Planning for Electric Vehicles in Large Network. In Proceedings of the 25th AAAI Conference on Artificial Intelligence. AAAI Press, 2011.
Stephan Erb, Moritz Kobitzsch, and Peter Sanders. Parallel Bi-objective Shortest Paths Using Weight-Balanced B-trees with Bulk Updates. In Proceedings of the 13th International Symposium on Experimental Algorithms (SEA'14), volume 8504 of Lecture Notes in Computer Science, pages 111-122. Springer, 2014.
Martin Ester, Hans-Peter Kriegel, Jörg Sander, and Xiaowei Xu. A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining (KDD'96), pages 226-231. AAAI Press, 1996.
Stefan Funke and Sabine Storandt. Polynomial-Time Construction of Contraction Hierarchies for Multi-criteria Objectives. In Proceedings of the 15th Meeting on Algorithm Engineering and Experiments (ALENEX'13), pages 31-54. SIAM, 2013.
Michael R. Garey and David S. Johnson. Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, 1979.
Robert Geisberger, Moritz Kobitzsch, and Peter Sanders. Route Planning with Flexible Objective Functions. In Proceedings of the 12th Workshop on Algorithm Engineering and Experiments (ALENEX'10), pages 124-137. SIAM, 2010.
Pierre Hansen. Bricriteria Path Problems. In Multiple Criteria Decision Making - Theory and Application -, pages 109-127. Springer, 1979.
Peter E. Hart, Nils Nilsson, and Bertram Raphael. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics, 4:100-107, 1968.
Stefan Hausberger, Martin Rexeis, Michael Zallinger, and Raphael Luz. Emission Factors from the Model PHEM for the HBEFA Version 3. Technical Report I-20/2009, University of Technology, Graz, 2009.
Lorenz Hübschle-Schneider. Speed-Consumption Trade-Off for Electric Vehicle Routing. Bachelor thesis, Karlsruhe Institute of Technology, 2013.
Enrique Machuca and Lawrence Mandow. Multiobjective Heuristic Search in Road Maps. Expert Systems with Applications, 39(7):6435-6445, 2012.
Lawrence Mandow and José-Luis Pérez-de-la-Cruz. Multiobjective A* Search with Consistent Heuristics. Journal of the ACM, 57(5):27:1-27:24, 2010.
Ernesto Queiros Martins. On a Multicriteria Shortest Path Problem. European Journal of Operational Research, 26(3):236-245, 1984.
Matthias Müller-Hannemann and Karsten Weihe. Pareto Shortest Paths is Often Feasible in Practice. In Proceedings of the 5th International Workshop on Algorithm Engineering (WAE'01), volume 2141 of Lecture Notes in Computer Science, pages 185-197. Springer, 2001.
Martin Sachenbacher, Martin Leucker, Andreas Artmeier, and Julian Haselmayr. Efficient Energy-Optimal Routing for Electric Vehicles. In Proceedings of the 25th AAAI Conference on Artificial Intelligence. AAAI Press, 2011.
Peter Sanders and Lawrence Mandow. Parallel Label-Setting Multi-Objective Shortest Path Search. In Proceedings of the 27th International Parallel and Distributed Processing Symposium (IPDPS'13), pages 215-224. IEEE Computer Society, 2013.
Sabine Storandt. Quick and Energy-Efficient Routes: Computing Constrained Shortest Paths for Electric Vehicles. In Proceedings of the 5th ACM SIGSPATIAL International Workshop on Computational Transportation Science, pages 20-25. ACM Press, 2012.
Chi Tung Tung and Kim Lin Chew. A multicriteria Pareto-optimal path algorithm. European Journal of Operational Research, 62(2):203-209, 1992.
Eckart Zitzler and Lothar Thiele. Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. Evolutionary Computation, IEEE Transactions on, 3(4):257-271, 1999.
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