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Annals of Operations Research

, Volume 254, Issue 1–2, pp 335–364 | Cite as

Efficient continuous contraflow algorithms for evacuation planning problems

  • Urmila PyakurelEmail author
  • Tanka Nath Dhamala
  • Stephan Dempe
Original Paper

Abstract

A productive research in the emerging field of disaster management plays a quite important role in relaxing this disastrous advanced society. The planning problem of saving affected areas and normalizing the situation after any kind of disasters is very challenging. For the optimal use of available road network, the contraflow technique increases the outward road capacities from the disastrous areas by reversing the arcs. Number of efficient algorithms and heuristics handle this issue with contraflow reconfiguration on particular networks but the problem with multiple sources and multiple sinks is NP-hard. This paper concentrates on analytical solutions of continuous time contraflow problem. We consider the value approximation earliest arrival transshipment contraflow for the arbitrary and zero transit times on each arcs. These problems are solved with pseudo-polynomial and polynomial time complexity, respectively. We extend the concept of dynamic contraflow to the more general setting where the given network is replaced by an abstract contraflow with a system of linearly ordered sets, called paths satisfying the switching property. We introduce the continuous maximum abstract contraflow problem and present polynomial time algorithms to solve its static and dynamic versions by reversing the direction of paths. Abstract contraflow approach not only increases the flow value but also eliminates the crossing at intersections. The flow value can be increased up to double with contraflow reconfiguration.

Keywords

Evacuation planning Contraflow Abstract flow Switching property 

Notes

Acknowledgements

The research is conducted under the Research Group Linkage Program entitled Optimization Models and Methods for Sustainable Development supported by Alexander von Humboldt Foundation. The second author acknowledges the support of DAAD under the partnership program, Graph Theory and Optimization with Applications in Industry and Society (GraTho), for the research stay at University of Kaiserslautern.

References

  1. Aronson, J. E. (1989). A survey of dynamic network flows. Annals of Operations Research, 20, 1–66.CrossRefGoogle Scholar
  2. Arulselvan, A. (2009). Network model for disaster management. Ph.D. Thesis, University of Florida.Google Scholar
  3. Baumann, N. (2007). Evacuation by earliest arrival flows. Ph.D. thesis, Department of Mathematics, University of Dortmund.Google Scholar
  4. Cova, T., & Johnson, J. P. (2003). A network flow model for lane-based evacuation routing. Transportation Research Part A: Policy and Practice, 37, 579–604.CrossRefGoogle Scholar
  5. Dhamala, T. N. (2015). A survey on models and algorithms for discrete evacuation planning network problems. Journal of Industrial and Management Optimization, 11, 265–289.CrossRefGoogle Scholar
  6. Dhamala, T. N., & Pyakurel, U. (2013). Earliest arrival contraflow problem on series-parallel graphs. International Journal of Operations Research, 10, 1–13.Google Scholar
  7. Dhamala, T. N., & Pyakurel, U. (2016). Significance of transportation network models in emergency planning of urban cities. International Journal of Cities, People and Places, 2, 58–76.Google Scholar
  8. Dhungana, R. C., Pyakurel, U. & Dhamala, T. N. (2016). Efficient algorithms on abstract contraflow for evacuation planning. International Journal of Operations Research (IJOR-TW) (under review).Google Scholar
  9. Fleischer, L. K., & Tardos, E. (1998). Efficient continuous-time dynamic network flow algorithms. Operations Research Letters, 23, 71–80.CrossRefGoogle Scholar
  10. Ford, F. R., & Fulkerson, D. R. (1956). Maximal flow through a network. Canadian Journal of Mathematics, 8, 399–404.CrossRefGoogle Scholar
  11. Ford, F. R., & Fulkerson, D. R. (1958). Constructing maximal dynamic flows from static flows. Operations Research, 6, 419–433.CrossRefGoogle Scholar
  12. Ford, F. R., & Fulkerson, D. R. (1962). Flows in networks. Princeton: Princeton University Press.Google Scholar
  13. Gross, M., Kappmeier, J-P. W., Schmidt, D. R. & Schmidt, M.(2012). Approximating earliest arrival flows in arbitrary networks. In L. Epstein and P. Ferragina (Eds.), Algorithms-ESA 2012, Lecture Notes in Computer Science (Vol. 7501, pp. 551–562).Google Scholar
  14. Hamacher, H. W. & Tjandra, S. A. (2002). Mathematical modeling of evacuation problems: A state of the art. In: M. Schreckenberger and S. D. Sharma (Eds.), Pedestrain and Evacuation Dynamics (pp. 227–266). Berlin: Springer.Google Scholar
  15. Hamacher, H. W., Heller, S., & Rupp, B. (2013). Flow location (FlowLoc) problems: Dynamic network flows and location models for evacuation planning. Annals of Operations Research, 207, 161–180.CrossRefGoogle Scholar
  16. Hamza-Lup, G., Hua, K. A., Le, M., & Peng, R. (2004). Enhancing intelligent transportation systems to improve and support homeland security. In Proceedings of the seventh IEEE international conference, intelligent transportation systems (ITSC), pp. 250–255.Google Scholar
  17. Hua, J., Ren, G., Cheng, Y., & Ran, B. (2014). An integrated contraflow strategy for multimodal evacuation. Hindawi Publishing Corporation Mathematical Problems in Engineering (Vol. 2014).Google Scholar
  18. Kappmeier, J-P. W. (2015). Generalizations of flows over time with application in evacuation optimization. Ph.D. Thesis, Technical University, Berlin.Google Scholar
  19. Kappmeier, J.-P. W., Matuschke, J., & Peis, B. (2014). Abstract flows over time: A first step towards solving dynamic packing problems. Theoretical Computer Sciences, 544, 74–83.CrossRefGoogle Scholar
  20. Kim, S., & Shekhar, S. (2005). Contraflow network reconfiguration for evacuation planning: A summary of results. In Proceedings of 13th ACM symposium on advances in geographic information systems (GIS 05), pp. 250–259.Google Scholar
  21. Kim, S., Shekhar, S., & Min, M. (2008). Contraflow transportation network reconfiguration for evacuation route planning. IEEE Transactions on Knowledge and Data Engineering, 20, 1–15.CrossRefGoogle Scholar
  22. Kotsireas, I. S., Nagurney, A. & Pardalos, P. M. (Eds.) (2015). Dynamics of disasters—key concepts, models, algorithms, and insights. Springer Proceedings in Mathematics and Statistics.Google Scholar
  23. Litman, T. (2006). Lessons from Katrina and Rita: What major disasters can teach transportation planners. Journal of Transportation Engineering, 132(1), 11–18.CrossRefGoogle Scholar
  24. Lv, N., Yan, X., Xu, K., & Wu, C. (2010). Bi-level programming based contraflow optimization for evacuation events. Kybernetes, 39(8), 1227–1234.CrossRefGoogle Scholar
  25. Matuschke, J. (2014). Network flows and network design in theory and practice. Ph.D. Thesis, Technical University, Berlin.Google Scholar
  26. McCormick, S. T. (1996). A polynomial algorithm for abstract maximum flow. Proceedings of the 7th Annual ACM-SIAM symposium on discrete algorithms, pp. 490–497.Google Scholar
  27. Min, M., & Lee, J. (2013). Maximum throughput flow-based contraflow evacuation routing algorithm. In Third international workshop on pervasive networks for emergency management, San Diego, pp. 511–516.Google Scholar
  28. Moriarty, K. D., Ni, D., & Collura, J. (2007). Modeling traffic flow under emergency evacuation situations: Current practice and future directions. 86th Transportation Research Board Annual Meeting, Washington, D.C. http://works.bepress.com/daiheng_ni/24.
  29. Pascoal, M. M. B., Captivo, M. E. V., & Climaco, J. C. N. (2006). A comprehensive survey on the quickest path problem. Annals of Operations Research, 147(1), 5–21.CrossRefGoogle Scholar
  30. Pyakurel, U. (2016). Evacuation planning problem with contraflow approach. Ph.D. Thesis, IOST, Tribhuvan University, Nepal.Google Scholar
  31. Pyakurel, U., & Dhamala, T. N. (2014b). Earliest arrival contraflow model for evacuation planning. Neural, Parallel, and Scientific Computations, 22, 287–294.Google Scholar
  32. Pyakurel, U., & Dhamala, T. N. (2015). Models and algorithms on contraflow evacuation planning network problems. International Journal of Operations Research, 12, 36–46.CrossRefGoogle Scholar
  33. Pyakurel, U., & Dhamala, T. N. (2016a). Evacuation planning by earliest arrival contraflow. Journal of Industrial and Management Optimization, 487–501. doi: 10.3934/jimo.2016028.
  34. Pyakurel, U. & Dhamala, T. N. (2016b). Continuous time dynamic contraflow models and algorithms. Advance in Operations Research; Article ID 368587, pp. 1–7.Google Scholar
  35. Pyakurel, U. & Dhamala, T. N. (2016c). Continuous dynamic contraflow approach for evacuation planning. Annals of Operation Research (pp. 1–26). doi: 10.1007/s10479-016-2302-5.
  36. Pyakurel, U., Hamacher, H. W., & Dhamala, T. N. (2014). Generalized maximum dynamic contraflow on lossy network. International Journal of Operations Research Nepal, 3, 27–44.Google Scholar
  37. Rebennack, S., Arulselvan, A., Elefteriadou, L., & Pardalos, P. M. (2010). Complexity analysis for maximum flow problems with arc reversals. Journal of Combinatorial Optimization, 19, 200–216.CrossRefGoogle Scholar
  38. Tuydes, H. & Ziliaskopoulos, A. (2004). Network re-design to optimize evacuation contraflow. In Proceedings 83rd Annual Meeting of the Transportation Research Board.Google Scholar
  39. Tuydes, H. & Ziliaskopoulos, A. (2006). Tabu-based heuristic for optimization of network evacuation contraflow. In Proceedings, 85th annual meeting of the transportation research board.Google Scholar
  40. Vogiatzis, C., Yoshida, R., Aviles-Spadoni, I., Imamoto, S., & Pardalos, P. M. (2013). Livestock evacuation planning for natural and man-made emergencies. International Journal of Mass Emergencies and Disasters, 31(1), 25–37.Google Scholar
  41. Vogiatzis, C., Walteros, J. L. & Pardalos, P. M. (2012). Evacuation through clustering techniques. In Models, algorithms, and technologies for network analysis, Proceedings in Mathematics and Statistics. Springer (vol. 32, pp. 185–198).Google Scholar
  42. Wang, J. W., Ip, W. H., & Zhang, W. J. (2010). An integrated road construction and resource planning approach to the evacuation of victims from single source to multiple destinations. IEEE Transactions on Intelligent Transportation Systems, 11(2), 277–289.CrossRefGoogle Scholar
  43. Wang, J. W., Wang, H. F., Zhang, W. J., Ip, W. H., & Furuta, K. (2013). Evacuation planning based on the contraflow technique with consideration of evacuation priorities and traffic setup time. IEEE Transactions on Intelligent Transportation Systems, 14(1), 480–485.CrossRefGoogle Scholar
  44. Williamson, D. P., & Shmoys, D. B. (2011). The design of approximation algorithms (1st ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  45. Wolshon, B., Urbina, E. & Levitan, M. (2002). National review of hurricane evacuation plans and policies. Technical Report, Hurricane Center, Louisiana State University, Baton Rouge, Louisiana.Google Scholar
  46. Xie, C., & Turnquist, M. A. (2011). Lane-based evacuation network optimization: An integrated Lagrangian relaxation and tabu search approach. Transportation Research Part C, 19(1), 40–63.CrossRefGoogle Scholar
  47. Xie, C., Lin, D. Y., & Waller, S. T. (2010). A dynamic evacuation network optimization problem with lane reversal and crossing elimination strategies. Transportation Research Part E, 46(3), 295–316.CrossRefGoogle Scholar
  48. Yusoff, M., Ariffin, J., & Mohamed, A. (2008). Optimization approaches for macroscopic emergency evacuation planning: A survey. In Information technology, ITSim, international symposium, IEEE, vol. 3, no. 26–28, pp. 1–7.Google Scholar
  49. Zhao, X., Feng, Z.-Y., Li, Y., & Bernard, A. (2016). Evacuation network optimization model with lane-based reversal and routing. Mathematical Problems in Engineering, 1273508, 1–12.Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Urmila Pyakurel
    • 1
    • 2
    Email author
  • Tanka Nath Dhamala
    • 1
  • Stephan Dempe
    • 3
  1. 1.Central Department of MathematicsTribhuvan UniversityKathmanduNepal
  2. 2.TU Bergakademie FreibergFreibergGermany
  3. 3.TU Bergakademie Freiberg, Fakultät für Mathematik und InformatikFreibergGermany

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