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, Volume 16, Issue 4, pp 411–439 | Cite as

Generating constrained length personalized bicycle tours

  • P. StroobantEmail author
  • P. Audenaert
  • D. Colle
  • M. Pickavet
Research Paper
  • 136 Downloads

Abstract

In the context of recreational routing, the problem of finding a route which starts and ends in the same location (while achieving a length between specified upper and lower boundaries) is a common task, especially for tourists or cyclists who want to exercise. The topic of finding a tour between a specified starting and ending location while minimizing one or multiple criteria is well covered in literature. In contrast to this, the route planning task in which a pleasant tour with length between a maximum and a minimum boundary needs to be found is relatively underexplored. In this paper, we provide a formal definition of this problem, taking into account the existing literature on which route attributes influence cyclists in their route choice. We show that the resulting problem is NP-hard and devise a branch-and-bound algorithm that is able to provide a bound on the quality of the best solution in pseudo-polynomial time. Furthermore, we also create an efficient heuristic to tackle the problem and we compare the quality of the solutions that are generated by the heuristic with the bounds provided by the branch-and-bound algorithm. Also, we thoroughly discuss the complexity and running time of the heuristic.

Keywords

Constrained bicycle routing Branch-and-bound algorithm Reach-based routing 

Mathematics Subject Classification

Primary 05C38 Secondary 68R10 94C15 

Notes

Acknowledgements

We wish to thank the reviewers for their valuable comments and their constructive input in improving our work. Pieter Stroobant is funded by a Ph.D. grant of Ghent University, Special Research Fund (BOF). The authors wish to thank Ghent University–IMEC for their support and their funding through the IOP research project “Modelling uncertainty in hub location planning through interdisciplinary research”.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Alivand M, Hochmair HH (2015) Choice set generation for modeling scenic route choice behavior with geographic information systems. Trans Res Rec J Trans Res Board 2495:101–111.  https://doi.org/10.3141/2495-11, ISSN 0361-1981
  2. Alivand M, Hochmair H, Srinivasan S (2015) Analyzing how travelers choose scenic routes using route choice models. Comput Environ Urban Syst 50:41–52.  https://doi.org/10.1016/j.compenvurbsys.2014.10.004 CrossRefGoogle Scholar
  3. Bast H, Delling D, Goldberg A, Müller-Hannemann M, Thomas P, Peter S, Dorothea W, Werneck RF (2014) Route planning in transportation networks. Technical report, April 2015. http://arxiv.org/abs/1504.05140
  4. Dees J, Geisberger R, Sanders P, Bader R (2010) Defining and computing alternative routes in road networks. CoRR, abs/1002.4, February 2010. http://arxiv.org/abs/1002.4330
  5. Demeyer S, Audenaert P, Pickavet M, Demeester P (2014) Dynamic and stochastic routing for multimodal transportation systems. IET Intell Transp Syst 8(2):112–123.  https://doi.org/10.1049/iet-its.2012.0065, ISSN 1751-956X
  6. Fu ZJ, Hochmair H (2009) Web based bicycle trip planning for broward county, Florida. GIS Center, 31Google Scholar
  7. Geisberger R, Sanders P, Schultes D, Delling D (2008) Contraction hierarchies: faster and simpler hierarchical routing in road networks. In: Experimental algorithms, vol 5038 LNCS, pp 319–333. Springer, Berlin.  https://doi.org/10.1007/978-3-540-68552-4_24, ISBN 3540685480
  8. Gemsa A, Pajor T, Wagner D, Zündorf T (2013) Efficient computation of jogging routes. In: Lecture Notes in Computer Science, vol 7933 LNCS, pp 272–283.  https://doi.org/10.1007/978-3-642-38527-8_25, ISBN 9783642385261
  9. Gutman R (2004) Reach-based routing: a new approach to shortest path algorithms optimized for road networks. In: Proceedings 6th workshop on algorithm engineering and experiments, pp 100–111, Philadelphia, 2004. Society for Industrial and Applied Mathematics. http://www.siam.org/meetings/alenex04/abstacts/rgutman1.pdf, ISBN 0-89871-564-4
  10. Hochmair H (2004) Decision support for bicycle route planning in urban environments. In: Proceedings of the 7th AGILE conference on geographic information science, pp 697–706. Association of Geographic Information Laboratories in EuropeGoogle Scholar
  11. Hrncir J, Nemet M, Hrncir J, Song Q, Zilecky P, Nemet M, Jakob M (2014) Bicycle route planning with route choice preferences. In: Proceedings of the twenty-first European conference on artificial intelligence, pp 1149–1154. Elsevier and Springer.  https://doi.org/10.3233/978-1-61499-419-0-1149, ISBN 9781614994190
  12. Hrncir J, Zilecky P, Song Q, Jakob M (2015) Speedups for multi-criteria urban bicycle routing. OASIcs: OpenAccess Series in Informatics 48:28.  https://doi.org/10.4230/OASIcs.ATMOS.2015.16, ISSN 2190-6807. http://drops.dagstuhl.de/opus/volltexte/2015/5458/
  13. Karp RM (1978) A characterization of the minimum cycle mean in a digraph. Discrete Math 23(3):309–311.  https://doi.org/10.1016/0012-365X(78)90011-0, ISSN 0012365X. http://linkinghub.elsevier.com/retrieve/pii/0012365X78900110
  14. Kellerer H, Pferschy U, Pisinger D (2004) Knapsack problems, 1st edn. Springer, Berlin.  https://doi.org/10.1007/978-3-540-24777-7, ISBN 3642073115
  15. Lawler EL, Wood DE (1966) Branch-and-bound methods: a survey. Oper Res 14(4):699–719.  https://doi.org/10.1287/opre.14.4.699, ISSN 0030-364X
  16. Loiola EM, de Abreu NMM, Boaventura-Netto PO, Hahn P, Querido T (2007) A survey for the quadratic assignment problem. Eur J Oper Res 176(2):657–690.  https://doi.org/10.1016/j.ejor.2005.09.032, ISSN 03772217
  17. Paraskevopoulos A, Zaroliagis C (2013) Improved alternative route planning. In: 13th Workshop on algorithmic approaches for transportation modelling, optimization, and systems, vol 33, pp 108–122. Optimization and Systems, 2013. http://hal.archives-ouvertes.fr/hal-00871739/
  18. Pucher J, Buehler R, Merom D, Bauman A (2011) Walking and cycling in the United States, 2001–2009: evidence from the national household travel surveys. Am J Public Health 101(Suppl. 1):310–317.  https://doi.org/10.2105/AJPH.2010.300067, ISSN 00900036
  19. Rostami B, Chassein A, Hopf M, Frey D, Buchheim C, Malucelli F, Goerigk M (2016) The quadratic shortest path problem: complexity, approximability, and solution methods. Technical report, 2016. http://www.optimization-online.org/DB_HTML/2016/02/5341.html
  20. Schieferdecker D, Kobitzsch M, Radermacher M (2013) Evolution and evaluation of the penalty method for alternative graphs. In: Proceedings of the 13th workshop on algorithmic approaches for transportation modeling, optimization, and systems (ATMOS’13), vol 33, pp 94–107.  https://doi.org/10.4230/OASIcs.ATMOS.2013.94. http://drops.dagstuhl.de/opus/volltexte/2013/4247, ISBN 9783939897583
  21. Song Q, Zilecky P, Jakob M, Hrncir J (2014) Exploring pareto routes in multi-criteria urban bicycle routing. In: 17th international IEEE conference on intelligent transportation systems (ITSC), pp 1781. IEEE Intelligent Transportation Systems Society, 2014.  https://doi.org/10.1109/ITSC.2014.6957951, ISBN 2153-0009;21530009. http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6957951
  22. Storandt S (2012) Route planning for bicycles—exact constrained shortest paths made practical via contraction hierarchy. In: Proceedings of the twenty-second international conference on automated planning and scheduling, pp 234–242, ISBN 9781577355625Google Scholar
  23. Su JG, Winters M, Nunes M, Brauer M (2010) Designing a route planner to facilitate and promote cycling in Metro Vancouver, Canada. Transp Res A Policy Pract 44(7):495–505.  https://doi.org/10.1016/j.tra.2010.03.015, ISSN 09658564
  24. Turverey RJ, Cheng DD, Blair ON, Roth JT, Lamp GM (2010) Charlottesville bike route planner. In: 2010 IEEE systems and information engineering design symposium, SIEDS10, pp 68–72.  https://doi.org/10.1109/SIEDS.2010.5469679

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Information TechnologyGhent University, imec, IDLab, iGent TowerGhentBelgium

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