15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015), ATMOS 2015, September 17, 2015, Patras, Greece
ATMOS 2015
September 17, 2015
Patras, Greece
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
Giuseppe F.
Italiano
Giuseppe F. Italiano
Marie
Schmidt
Marie Schmidt
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
48
2015
978-3-939897-99-6
https://www.dagstuhl.de/dagpub/978-3-939897-99-6
Front Matter, Table of Contents, Preface, Organization
Front Matter, Table of Contents, Preface, Organization
Front Matter
Table of Contents
Preface
Organization
i-x
Front Matter
Giuseppe F.
Italiano
Giuseppe F. Italiano
Marie
Schmidt
Marie Schmidt
10.4230/OASIcs.ATMOS.2015.i
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode
Towards Realistic Pedestrian Route Planning
Pedestrian routing has its specific set of challenges, which are often neglected by state-of-the-art route planners. For instance, the lack of detailed sidewalk data and the inability to traverse plazas and parks in a natural way often leads to unappealing and suboptimal routes. In this work, we first propose to augment the network by generating sidewalks based on the street geometry and adding edges for routing over plazas and squares. Using this and further information, our query algorithm seamlessly handles node-to-node queries and queries whose origin or destination is an arbitrary location on a plaza or inside a park. Our experiments show that we are able to compute appealing pedestrian routes at negligible overhead over standard routing algorithms.
pedestrian routing
realistic model
shortest paths
speed-up technique
1-15
Regular Paper
Simeon
Andreev
Simeon Andreev
Julian
Dibbelt
Julian Dibbelt
Martin
Nöllenburg
Martin Nöllenburg
Thomas
Pajor
Thomas Pajor
Dorothea
Wagner
Dorothea Wagner
10.4230/OASIcs.ATMOS.2015.1
H. Alt and E. Welzl. Visibility Graphs and Obstacle-avoiding Shortest Paths. Zeitschrift für Operations Research, 32(3-4):145-164, 1988.
Simeon Danailov Andreev. Realistic Pedestrian Routing. Bachelor thesis, Karlsruhe Institute of Technology, November 2012.
Miquel Ginard Ballester, Maurici Ruiz Pérez, and John Stuiver. Automatic Pedestrian Network Generation. In Proceedings 14th AGILE International Conference on GIS, pages 1-13, 2011.
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 abs/1504.05140, ArXiv e-prints, 2015.
Jon Louis Bentley. Multidimensional Binary Search Trees Used for Associative Searching. Commun. ACM, 18(9):509-517, September 1975.
Raymond C. Browning, Emily A. Baker, Jessica A. Herron, and Rodger Kram. Effects of Obesity and Sex on the Energetic Cost and Preferred Speed of Walking. Journal of Applied Physiology, 100(2):390-398, 2006.
Francisc Bungiu, Michael Hemmer, John Hershberger, Kan Huang, and Alexander Kröller. Efficient Computation of Visibility Polygons. CoRR, abs/1403.3905, 2014.
Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. Computational Geometry: Algorithms and Applications. Springer, 3rd edition, 2008.
Daniel Delling, Andrew V. Goldberg, Thomas Pajor, and Renato F. Werneck. Customizable Route Planning in Road Networks. Transportation Science, 2015.
Daniel Delling, Andrew V. Goldberg, Ilya Razenshteyn, and Renato F. Werneck. Graph Partitioning with Natural Cuts. In 25th International Parallel and Distributed Processing Symposium (IPDPS'11), pages 1135-1146. IEEE Computer Society, 2011.
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Hassan A. Karimi and Piyawan Kasemsuppakorn. Pedestrian Network Map Generation Approaches and Recommendation. International Journal of Geographical Information Science, 27(5):947-962, 2013.
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Speedups for Multi-Criteria Urban Bicycle Routing
Increasing the adoption of cycling is crucial for achieving more sustainable urban mobility. Navigating larger cities on a bike is, however, often challenging due to cities’ fragmented cycling infrastructure and/or complex terrain topology. Cyclists would thus benefit from intelligent route planning that would help them discover routes that best suit their transport needs and preferences. Because of the many factors cyclists consider in deciding their routes, employing multi-criteria route search is vital for properly accounting for cyclists’ route-choice criteria. Direct application of optimal multi-criteria route search algorithms is, however, not feasible due to their prohibitive computational complexity. In this paper, we therefore propose several heuristics for speeding up multi-criteria route search. We evaluate our method on a real-world cycleway network and show that speedups of up to four orders of magnitude over the standard multi-criteria label-setting algorithm are possible with a reasonable loss of solution quality. Our results make it possible to practically deploy bicycle route planners capable of producing high-quality route suggestions respecting multiple real-world route-choice criteria.
bicycle routing
multi-criteria shortest path
heuristic speedups
16-28
Regular Paper
Jan
Hrncir
Jan Hrncir
Pavol
Zilecky
Pavol Zilecky
Qing
Song
Qing Song
Michal
Jakob
Michal Jakob
10.4230/OASIcs.ATMOS.2015.16
H. Bast, D. Delling, A. Goldberg, M. Muller-Hannemann, T. Pajor, P. Sanders, D. Wagner, and R. Werneck. Route Planning in Transportation Networks. Technical report, Microsoft Research, 2014.
Hannah Bast, Mirko Brodesser, and Sabine Storandt. Result Diversity for Multi-Modal Route Planning. In Daniele Frigioni and Sebastian Stiller, editors, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, volume 33 of OpenAccess Series in Informatics (OASIcs), pages 123-136, Dagstuhl, Germany, 2013. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
J. Broach, J. Dill, and J. Gliebe. Where do cyclists ride? A route choice model developed with revealed preference GPS data. Transportation Research Part A: Policy and Practice, 46(10):1730 - 1740, 2012.
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B. C. Dean. Continuous-time dynamic shortest path algorithms. Master’s thesis, Massachusetts Institute of Technology, 1999.
D. Delling, J. Dibbelt, T. Pajor, D. Wagner, and R. F. Werneck. Computing and Evaluating Multimodal Journeys. Technical Report 2012-20, Faculty of Informatics, Karlsruhe Institut of Technology, 2012.
D. Delling, J. Dibbelt, T. Pajor, D. Wagner, and R. F. Werneck. Computing multimodal journeys in practice. In SEA, pages 260-271, 2013.
D. Delling and D. Wagner. Pareto paths with sharc. In Proceedings of the 8th International Symposium on Experimental Algorithms, volume 5526 of LNCS, pages 125-136. Springer, 2009.
D. Delling and D. Wagner. Time-dependent route planning. In Robust and Online Large-Scale Optimization, pages 207-230. Springer, 2009.
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V. Filler. (AUTO*MAT) Private communication, 2013. Why cycle route planners are important for cyclists.
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H. H. Hochmair and J. Fu. Web Based Bicycle Trip Planning for Broward County, Florida. In ESRI User Conference, 2009.
J. Hrncir, Q. Song, P. Zilecky, M. Nemet, and M. Jakob. Bicycle route planning with route choice preferences. In Prestigious Applications of Artificial Intelligence (PAIS), 2014.
P. L. Jacobsen. Safety in numbers: more walkers and bicyclists, safer walking and bicycling. Injury Prevention, 9(3):205-209, 2003.
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M. Muller-Hannemann and M. Schnee. Finding all attractive train connections by multi-criteria pareto search. In ATMOS, pages 246-263, 2004.
M. Müller-Hannemann and K. Weihe. On the cardinality of the pareto set in bicriteria shortest path problems. Annals of Operations Research, 147(1):269-286, 2006.
P. Perny and O. Spanjaard. Near admissible algorithms for multiobjective search. In Proceedings of the 2008 Conference on ECAI 2008: 18th European Conference on Artificial Intelligence, pages 490-494, Amsterdam, The Netherlands, 2008. IOS Press.
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Q. Song, P. Zilecky, M. Jakob, and J. Hrncir. Exploring pareto routes in multi-criteria urban bicycle routing. In Intelligent Transportation Systems (ITSC), 2014 IEEE 17th International Conference on, pages 1781-1787, Oct 2014.
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J. G. Su, M. Winters, M. Nunes, and M. Brauer. Designing a route planner to facilitate and promote cycling in Metro Vancouver, Canada. Transportation Research Part A: Policy and Practice, 44(7):495-505, 2010.
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M. Winters, G. Davidson, D. Kao, and K. Teschke. Motivators and deterrents of bicycling: comparing influences on decisions to ride. Transportation, 38(1):153-168, 2011.
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Routing of Electric Vehicles: Constrained Shortest Path Problems with Resource Recovering Nodes
We consider a constrained shortest path problem with the possibility to refill the resource at certain nodes. This problem is motivated by routing electric vehicles with a comparatively short cruising range due to the limited battery capacity. Thus, for longer distances the battery has to be recharged on the way. Furthermore, electric vehicles can recuperate energy during downhill drive. We extend the common constrained shortest path problem to arbitrary costs on edges and we allow regaining resources at the cost of higher travel time. We show that this yields not shortest paths but shortest walks that may contain an arbitrary number of cycles. We study the structure of optimal solutions and develop approximation algorithms for finding short walks under mild assumptions on charging functions. We also address a corresponding network flow problem that generalizes these walks.
routing of electric vehicles
constrained shortest paths
FPTAS
con- strained network flow
29-41
Regular Paper
Sören
Merting
Sören Merting
Christian
Schwan
Christian Schwan
Martin
Strehler
Martin Strehler
10.4230/OASIcs.ATMOS.2015.29
Georg Baier. Flows with Path Restrictions. PhD thesis, TU Berlin, 2003.
Georg Baier, Thomas Erlebach, Alexander Hall, Ekkehard Köhler, Heiko Schilling, and Martin Skutella. Length-bounded cuts and flows. In Automata, Languages and Programming, LNCS 4051, pages 679-690. Springer Berlin Heidelberg, 2006.
Moritz Baum, Julian Dibbelt, Lorenz Hübschle-Schneider, Thomas Pajor, and Dorothea Wagner. Speed-consumption tradeoff for electric vehicle route planning. In Proceedings of the 14th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’14), OpenAccess Series in Informatics (OASIcs), pages 138-151, 2014.
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.
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Mark Ziegelmann. Constrained shortest paths and related problems. Phd thesis, Universität des Saarlandes, Saarbrücken, 2001.
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Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows
We present heuristics to handle practical travelling salesman problems with multiple time windows per node, where the optimization goal is minimal tour duration, which is the time spent outside the depot node. We propose a dynamic programming approach which combines state labels by encoding intervals to handle the larger state space needed for this objective function. Our implementation is able to solve many practical instances in real-time and is used for heuristic search of near-optimal solutions for hard instances. In addition, we outline a hybrid genetic algorithm we implemented to cope with hard or unknown instances. Experimental evaluation proves the efficiency and suitability for practical use of our algorithms and even leads to improved upper bounds for yet unsolved instances from the literature.
TSPTW
minimum tour duration
dynamic programming
heuristics
42-55
Regular Paper
Niklas
Paulsen
Niklas Paulsen
Florian
Diedrich
Florian Diedrich
Klaus
Jansen
Klaus Jansen
10.4230/OASIcs.ATMOS.2015.42
Slim Belhaiza, Pierre Hansen, and Gilbert Laporte. A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows. Computers &Operations Research, 52:269-281, 2014.
Richard Bellman. Dynamic programming treatment of the travelling salesman problem. Journal of the ACM (JACM), 9(1):61-63, 1962.
Jacques Desrosiers, Yvan Dumas, Marius M Solomon, and François Soumis. Time constrained routing and scheduling. Handbooks in operations research and management science, 8:35-139, 1995.
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Michel Gendreau, Alain Hertz, Gilbert Laporte, and Mihnea Stan. A generalized insertion heuristic for the traveling salesman problem with time windows. Operations Research, 46(3):330-335, 1998.
David S Johnson. A theoretician’s guide to the experimental analysis of algorithms. Data structures, near neighbor searches, and methodology: fifth and sixth DIMACS implementation challenges, 59:215-250, 2002.
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Chryssi Malandraki and Robert B Dial. A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem. European Journal of Operational Research, 90(1):45-55, 1996.
Gilles Pesant, Michel Gendreau, Jean-Yves Potvin, and Jean-Marc Rousseau. On the flexibility of constraint programming models: From single to multiple time windows for the traveling salesman problem. European Journal of Operational Research, 117(2):253-263, 1999.
Jean-Yves Potvin and Samy Bengio. The vehicle routing problem with time windows part II: genetic search. INFORMS journal on Computing, 8(2):165-172, 1996.
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Martin WP Savelsbergh. The vehicle routing problem with time windows: Minimizing route duration. ORSA journal on computing, 4(2):146-154, 1992.
Hiroaki Sengoku and Ikuo Yoshihara. A fast TSP solver using GA on Java. In Third International Symposium on Artificial Life, and Robotics (AROB III’98), pages 283-288, 1998.
Christian Tilk and Stefan Irnich. Dynamic programming for the minimum tour duration problem. Technical Report LM-2014-04, Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Mainz, Germany, 2014.
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Single Source Shortest Paths for All Flows with Integer Costs
We consider a shortest path problem for a directed graph with edges labeled with a cost and a capacity. The problem is to push an unsplittable flow $f$ from a specified source to all other vertices with the minimum cost for all f values. Let G = (V, E) with |V| = n and |E| = m. If there are t different capacity values, we can solve the single source shortest path problem t times for all f in O(tm + tn log n) time, which is O(m^2) when t = m. We improve this time to O(min{t, cn}m + cn^2), which is less than O(cmn) if edge costs are non-negative integers bounded by c. Our algorithm performs better for denser graphs.
information sharing
shortest path problem for all flows
priority queue
limited edge cost
transportation network
56-67
Regular Paper
Tadao
Takaoka
Tadao Takaoka
10.4230/OASIcs.ATMOS.2015.56
Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, 1993.
N. Alon, Z. Galil, and O. Margalit. On the exponent of the all pairs shortest path problems. JCSS 54, 255-262, 1997.
Amit Chakrabarti, Chandra Chekuri, Anupam Gupta, and Amit Kumar. Approximation algorithms for the unsplittable flow problem. Algorithmica 47(1): 53-78, 2007.
B. V. Cherkassky, A. V. Goldberg, and T. Radzik. Shortest paths algorithms: Theory and experimental evaluation. Mathematical Programming 73, 129-174, 1996.
Thomas F. Coleman and Jorge J. More. Estimation of sparse jacobian matrices and graph coloring problems. SIAM Journal on Numerical Analysis 20 (1): 187-209, 1983.
E. V. Denardo and B. L. Fox. Shortest-route methods: I. reaching, pruning, and buckets. Operations Research 27, 161-186, 1979.
R. B. Dial. Algorithm 360: Shortest path forest with topological ordering. CACM 12, 632-633, 1969.
E. W. Dijkstra. A note on two problems in connexion with graphs. Numer. Math. 1, 269-271, 1959.
Y. N. Dinits, N. Garg Y, and N. Goemans. On the single-source unsplittable flow problem. Combinatorica, Springer, 19(1), 17-41, 1999.
Ran Duan and Seth Pettie. Fast algorithms for (max, min)-matrix multiplication and bottleneck shortest paths. Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '09), pp. 384–391, 2009.
Matthias Ehrgott. Multicriteria Optimization. Springer-Verlag, 2005.
M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Jour. ACM 34, 596-615, 1987.
Harold N. Gabow and Robert E. Tarjan. Algorithms for two bottleneck optimization problems. Journal of Algorithms 9 (3): 411–417, 1988.
Tong-Wook Shinn and Tadao Takaoka. Combining all pairs shortest paths and all pairs bottleneck paths problems. LATIN 2014: 226-237, 2014.
Tong-Wook Shinn and Tadao Takaoka. Combining the shortest paths and the bottleneck paths problems. ACSC 2014: 13-18, 2014.
Tong-Wook Shinn and Tadao Takaoka. Some extensions of the bottleneck paths problem. WALCOM 2014: 176-187, 2014.
Tadao Takaoka. Subcubic cost algorithms for the all pairs shortest path problem. Algorithmica 20(3): 309-318, 1998.
Tadao Takaoka. Sharing information for the all pairs shortest path problem. Theor. Comput. Sci. 520: 43-50, 2014.
M. Thorup. Integer priority queues with decrease key in constant time and the single source shortest paths problem. STOC03, 149-158, 2003.
U. Zwick. All pairs shortest paths using bridging sets and rectangular matrix multiplication. Jour. ACM, 49, 3, 289-317, 2002.
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Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past
Given an urban public transportation network and historic delay information, we consider the problem of computing reliable journeys. We propose new algorithms based on our recently presented solution concept (Böhmová et al., ATMOS 2013), and perform an experimental evaluation using real-world delay data from Zürich, Switzerland. We compare these methods to natural approaches as well as to our recently proposed method which can also be used to measure typicality of past observations. Moreover, we demonstrate how this measure relates to the predictive quality of the individual methods. In particular, if the past observations are typical, then the learning-
based methods are able to produce solutions that perform well on typical days, even in the presence of large delays.
public transportation
route planning
robustness
optimization
experiments
68-81
Regular Paper
Katerina
Böhmová
Katerina Böhmová
Matúš
Mihalák
Matúš Mihalák
Peggy
Neubert
Peggy Neubert
Tobias
Pröger
Tobias Pröger
Peter
Widmayer
Peter Widmayer
10.4230/OASIcs.ATMOS.2015.68
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, 2014.
Hannah Bast, Jonas Sternisko, Sabine Storandt, et al. Delay-robustness of transfer patterns in public transportation route planning. In ATMOS, pages 42-54, 2013.
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 ATMOS, pages 27-41, 2013.
Justin Boyan and Michael Mitzenmacher. Improved results for route planning in stochastic transportation. In SODA, pages 895-902, 2001.
Joachim M. Buhmann, Matúš Mihalák, Rastislav Šrámek, and Peter Widmayer. Robust optimization in the presence of uncertainty. In ITCS, pages 505-514, 2013.
Julian Dibbelt, Thomas Pajor, Ben Strasser, and Dorothea Wagner. Intriguingly simple and fast transit routing. In SEA, pages 43-54, 2013.
Julian Dibbelt, Ben Strasser, and Dorothea Wagner. Delay-robust journeys in timetable networks with minimum expected arrival time. In ATMOS, pages 1-14, 2014.
Yann Disser, Matthias Müller-Hannemann, and Mathias Schnee. Multi-criteria shortest paths in time-dependent train networks. In WEA, pages 347-361, 2008.
Donatella Firmani, Giuseppe F. Italiano, Luigi Laura, and Federico Santaroni. Is timetabling routing always reliable for public transport? In ATMOS, pages 15-26, 2013.
H Frank. Shortest paths in probabilistic graphs. Operations Research, 17(4):583-599, 1969.
Marc Goerigk, Sacha Heße, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel. Recoverable robust timetable information. In ATMOS, pages 1-14, 2013.
Marc Goerigk, Martin Knoth, Matthias Müller-Hannemann, Marie Schmidt, and Anita Schöbel. The price of robustness in timetable information. In ATMOS, pages 76-87, 2011.
Sejoon Lim, Christian Sommer, Evdokia Nikolova, and Daniela Rus. Practical route planning under delay uncertainty: Stochastic shortest path queries. In Robotics: Science and Systems VIII, 2012.
Matthias Müller-Hannemann and Mathias Schnee. Efficient timetable information in the presence of delays. In Robust and Online Large-Scale Optimization, pages 249-272. Springer, 2009.
Evdokia Nikolova, Jonathan A Kelner, Matthew Brand, and Michael Mitzenmacher. Stochastic shortest paths via quasi-convex maximization. In ESA, pages 552-563, 2006.
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Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks
Based on time-dependent travel times for N past days, we consider the computation of robust routes according to the min-max relative regret criterion. For this method we seek a path minimizing its maximum weight in any one of the N days, normalized by the weight of an optimum for the respective day. In order to speed-up this computationally demanding approach, we observe that its output belongs to the Pareto front of the network with time-dependent
multi-criteria edge weights. We adapt a well-known algorithm for computing Pareto fronts in time-dependent graphs and apply the bi-directional search technique to it. We also show how to parametrize this algorithm by a value K to compute a K-approximate Pareto front. An experimental evaluation for the cases N = 2 and N = 3 indicates a considerable speed-up of the bi-directional search over the uni-directional.
shortest path
time-dependent
bi-criteria
bi-directional search
min-max relative regret
82-94
Regular Paper
Matúš
Mihalák
Matúš Mihalák
Sandro
Montanari
Sandro Montanari
10.4230/OASIcs.ATMOS.2015.82
H. Aissi, C. Bazgan, and D. Vanderpooten. Min-max and min-max regret versions of combinatorial optimization problems: A survey. European Journal of Operational Research, 197(2):427-438, 2009.
G. V. Batz, R. Geisberger, P. Sanders, and C. Vetter. Minimum time-dependent travel times with contraction hierarchies. ACM Journal of Experimental Algorithmics, 18, 2013.
G. V. Batz and P. Sanders. Time-dependent route planning with generalized objective functions. In ESA, pages 169-180, 2012.
J. M. Buhmann, M. Mihalák, R. Šrámek, and P. Widmayer. Robust optimization in the presence of uncertainty. In ITCS, pages 505-514, 2013.
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D. Delling. Time-dependent SHARC-routing. Algorithmica, 60(1):60-94, 2011.
D. Delling and D. Wagner. Pareto paths with SHARC. In SEA, pages 125-136, 2009.
S. Demeyer, J. Goedgebeur, P. Audenaert, M. Pickavet, and P. Demeester. Speeding up Martins' algorithm for multiple objective shortest path problems. 4OR, 11(4):323-348, 2013.
S. Erb, M. Kobitzsch, and P. Sanders. Parallel bi-objective shortest paths using weight-balanced B-trees with bulk updates. In SEA, pages 111-122, 2014.
L. Foschini, J. Hershberger, and S. Suri. On the complexity of time-dependent shortest paths. Algorithmica, 68(4):1075-1097, 2014.
S. Funke and S. Storandt. Polynomial-time construction of contraction hierarchies for multi-criteria objectives. In ALENEX, pages 41-54, 2013.
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R. Geisberger, M. Kobitzsch, and P. Sanders. Route planning with flexible objective functions. In ALENEX, pages 124-137, 2010.
A. V. Goldberg and C. Harrelson. Computing the shortest path: A* search meets graph theory. In SODA, pages 156-165, 2005.
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A Mixed Integer Linear Program for the Rapid Transit Network Design Problem with Static Modal Competition (Short Paper)
We present a mixed integer linear program for the rapid transit network design problem with static modal competition. Previous discrete formulations cannot handle modal competition for realistic size instances because of the complexity of modeling alternatives for each flow in the network. We overcome this difficulty by exploiting a pre-assigned topological configuration. Results of a case study will be presented at the conference.
metro network design
multi-objective optimization
modal competition
95-96
Short Paper
Gabriel
Gutiérrez-Jarpa
Gabriel Gutiérrez-Jarpa
Gilbert
Laporte
Gilbert Laporte
Vladimir
Marianov
Vladimir Marianov
Luigi
Moccia
Luigi Moccia
10.4230/OASIcs.ATMOS.2015.95
G. Bruno and G. Laporte. An interactive decision support system for the design of rapid public transit networks. INFOR, 40(2):111-118, 2002.
D. Canca, A. De-Los-Santos, G. Laporte, and J. A. Mesa. A general rapid network design, line planning and fleet investment integrated model. Annals of Operations Research, In Press:1-18, 2014.
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G. Gutiérrez-Jarpa, C. Obreque, G. Laporte, and V. Marianov. Rapid transit network design for optimal cost and origin-destination demand capture. Computers &Operations Research, 40(12):3000-3009, 2013.
G. Laporte, A. Marín, J. A. Mesa, and F. Perea. Designing robust rapid transit networks with alternative routes. Journal of Advanced Transportation, 45(1):54-65, 2011.
G. Laporte and J. A. Mesa. The design of rapid transit networks. In G. Laporte, S. Nickel, and F. Saldanha da Gama, editors, Location Science, pages 581-594. Springer, Berlin, Heidelberg, 2015.
G. Laporte, J. A. Mesa, F. A. Ortega, and I. Sevillano. Maximizing trip coverage in the location of a single rapid transit alignment. Annals of Operations Research, 136(1):49-63, 2005.
Á. Marín and R. García-Ródenas. Location of infrastructure in urban railway networks. Computers &Operations Research, 36(5):1461-1477, 5 2009.
A. Perugia, J.-F. Cordeau, G. Laporte, and L. Moccia. Designing a home-to-work bus service in a metropolitan area. Transportation Research Part B: Methodological, 45(10):1710-1726, 2011.
C. Roth, S. M. Kang, M. Batty, and M. Barthelemy. A long-time limit for world subway networks. Journal of the Royal Society Interface, 9(75):2540-2550, 2012.
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Ordering Constraints in Time Expanded Networks for Train Timetabling Problems
The task of the train timetabling problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. This kind of problem has proven to be very challenging and numerous solution approaches have been proposed. One of the most successful approaches is based on time discretized network models. However, one of the major weaknesses of these models is that fractional solutions tend to change the order of trains along some track, which is not allowed for integer solutions, leading to poor relaxations. In this paper, we present an extension for these kind of models, which aims at overcoming these problems. By exploiting a configuration based formulation, we propose to extend the model with additional ordering constraints. These constraints enforce compatibility of orderings along a sequence of tracks and greatly improve the quality of the relaxations. We show in some promising preliminary computational experiments that our approach indeed helps to resolve many of the invalid overtaking problems of relaxations
for the standard models.
combinatorial optimization
train timetabling
Lagrangian relaxation
ordering constraints
97-110
Regular Paper
Frank
Fischer
Frank Fischer
10.4230/OASIcs.ATMOS.2015.97
Ralf Borndörfer, Andreas Löbel, Markus Reuther, Thomas Schlechte, and Steffen Weider. Rapid branching. Public Transport, 5(1-2):1-21, 2013. URL: http://dx.doi.org/10.1007/s12469-013-0066-8.
http://dx.doi.org/10.1007/s12469-013-0066-8
Ralf Borndörfer and Thomas Schlechte. Models for railway track allocation. In Christian Liebchen, Ravindra K. Ahuja, and Juan A. Mesa, editors, ATMOS 2007 - 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems, Dagstuhl Seminar Proceedings. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany, 2007. URL: http://dx.doi.org/10.4230/OASIcs.ATMOS.2007.1170.
http://dx.doi.org/10.4230/OASIcs.ATMOS.2007.1170
U. Brännlund, P. O. Lindberg, A. Nõu, and J. E. Nilsson. Railway timetabling using Lagrangian relaxation. Transportation Science, 32(4):358-369, 1998.
Valentina Cacchiani, Fabio Furini, and Martin Philip Kidd. Approaches to a real-world train timetabling problem in a railway node. Omega, 58:97-110, 2016. URL: http://dx.doi.org/10.1016/j.omega.2015.04.006.
http://dx.doi.org/10.1016/j.omega.2015.04.006
Valentina Cacchiani and Paolo Toth. Nominal and robust train timetabling problems. European Journal of Operational Research, 219(3):727-737, 2012. URL: http://dx.doi.org/10.1016/j.ejor.2011.11.003.
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Alberto Caprara, Matteo Fischetti, and Paolo Toth. Modeling and solving the train timetabling problem. Operations Research, 50(5):851-861, 2002.
Frank Fischer. Dynamic Graph Generation and an Asynchronous Parallel Bundle Method Motivated by Train Timetabling. PhD thesis, Chemnitz University of Technology, 2013. URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-118358.
http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-118358
Frank Fischer. DynG Dynamic Graph Generation library, 2014. URL: http://www.mathematik.uni-kassel.de/~fifr/fossils/dyng.
http://www.mathematik.uni-kassel.de/~fifr/fossils/dyng
Frank Fischer and Christoph Helmberg. Dynamic graph generation for the shortest path problem in time expanded networks. Mathematical Programming A, 143(1-2):257-297, 2014. URL: http://dx.doi.org/10.1007/s10107-012-0610-3.
http://dx.doi.org/10.1007/s10107-012-0610-3
Frank Fischer and Christoph Helmberg. A parallel bundle framework for asynchronous subspace optimization of nonsmooth convex functions. SIAM Journal on Optimization, 24(2):795-822, 2014. URL: http://dx.doi.org/10.1137/120865987.
http://dx.doi.org/10.1137/120865987
Frank Fischer, Christoph Helmberg, Jürgen Janßen, and Boris Krostitz. Towards solving very large scale train timetabling problems by Lagrangian relaxation. In Matteo Fischetti and Peter Widmayer, editors, ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems, Dagstuhl, Germany, 2008. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany. URL: http://dx.doi.org/10.4230/OASIcs.ATMOS.2008.1585.
http://dx.doi.org/10.4230/OASIcs.ATMOS.2008.1585
Christoph Helmberg. ConicBundle 0.3.11. Fakultät für Mathematik, Technische Universität Chemnitz, 2012. URL: http://www.tu-chemnitz.de/~helmberg/ConicBundle.
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Richard M. Lusby, Jesper Larsen, Matthias Ehrgott, and David Ryan. Railway track allocation: models and methods. OR Spectrum, 33(4):843-883, oct 2011. URL: http://dx.doi.org/10.1007/s00291-009-0189-0.
http://dx.doi.org/10.1007/s00291-009-0189-0
RAS Problem Solving Competition 2012, 2012. URL: https://www.informs.org/Community/RAS/Problem-Solving-Competition/2012-RAS-Problem-Solving-Competition.
https://www.informs.org/Community/RAS/Problem-Solving-Competition/2012-RAS-Problem-Solving-Competition
Thomas Schlechte. Railway Track Allocation: Models and Algorithms. PhD thesis, TU Berlin, 2012.
Steffen Weider. Integration of Vehicle and Duty Scheduling in Public Transport. PhD thesis, TU Berlin, 2007. URL: http://opus.kobv.de/tuberlin/volltexte/2007/1624/.
http://opus.kobv.de/tuberlin/volltexte/2007/1624/
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Regional Search for the Resource Constrained Assignment Problem
The resource constrained assignment problem (RCAP) is to find a minimal cost partition of the nodes of a directed graph into cycles such that a resource constraint is fulfilled. The RCAP has its roots in rolling stock rotation optimization where a railway timetable has to be covered by rotations, i.e., cycles. In that context, the resource constraint corresponds to maintenance constraints for rail vehicles. Moreover, the RCAP generalizes variants of the vehicle routing problem (VRP). The paper contributes an exact branch and bound algorithm for the RCAP and, primarily, a straightforward algorithmic concept that we call regional search (RS). As a symbiosis of a local and a global search algorithm, the result of an RS is a local optimum for a combinatorial optimization problem. In addition, the local optimum must be globally optimal as well if an instance of a problem relaxation is computed. In order to present the idea for a standardized setup we introduce an RS for binary programs. But the proper contribution of the paper is an RS that turns the Hungarian method into a powerful heuristic for the resource constrained assignment problem by utilizing the exact branch and bound. We present computational results for RCAP instances from an industrial cooperation with Deutsche Bahn Fernverkehr AG as well as for VRP instances from the literature. The results show that our RS provides a solution quality of 1.4 % average gap w.r.t. the best known solutions of a large test set. In addition, our branch and bound algorithm can solve many RCAP instances to proven optimality, e.g., almost all asymmetric traveling salesman and capacitated vehicle routing problems that we consider.
assignment problem
local search
branch and bound
rolling stock rota- tion problem
vehicle routing problem
111-129
Regular Paper
Ralf
Borndörfer
Ralf Borndörfer
Markus
Reuther
Markus Reuther
10.4230/OASIcs.ATMOS.2015.111
Tobias Achterberg. Constraint Integer Programming. PhD thesis, Technische Universität Berlin, 2009.
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Approximation Algorithms for Mixed, Windy, and Capacitated Arc Routing Problems
We show that any alpha(n)-approximation algorithm for the n-vertex metric asymmetric Traveling Salesperson problem yields O(alpha(C))-approximation algorithms for various mixed, windy, and capacitated arc routing problems. Herein, C is the number of weakly-connected components in the subgraph induced by the positive-demand arcs, a number that can be expected to be small in applications. In conjunction with known results, we derive constant-factor approximations if C is in O(log n) and O(log(C)/log(log(C)))-approximations in general.
vehicle routing
transportation
Rural Postman
Chinese Postman
NP- hard problem
parameterized algorithm
combinatorial optimization
130-143
Regular Paper
René
van Bevern
René van Bevern
Christian
Komusiewicz
Christian Komusiewicz
Manuel
Sorge
Manuel Sorge
10.4230/OASIcs.ATMOS.2015.130
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