Advertisement

A Column-Generation Algorithm for Evacuation Planning with Elementary Paths

  • Mohd. Hafiz HasanEmail author
  • Pascal Van Hentenryck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10416)

Abstract

Evacuation planning algorithms are critical tools for assisting authorities in orchestrating large-scale evacuations while ensuring optimal utilization of resources. To be deployed in practice, these algorithms must include a number of constraints that dramatically increase their complexity. This paper considers the zone-based non-preemptive evacuation planning problem in which each evacuation zone is assigned a unique evacuation path to safety and the flow of evacuees over time for a given zone follows one of a set of specified response curves. The starting point of the paper is the recognition that the first and only optimization algorithm previously proposed for zone-based non-preemptive evacuation planning may produce non-elementary paths, i.e., paths that visit the same node multiple times over the course of the evacuation. Since non-elementary paths are undesirable in practice, this paper proposes a column-generation algorithm where the pricing subproblem is a least-cost path under constraints. The paper investigates a variety of algorithms for solving the subproblem as well as their hybridization. Experimental results on a real-life case study show that the new algorithm produces evacuation plans with elementary paths of the same quality as the earlier algorithm in terms of the number of evacuees reaching safety and the completion time of the evacuation, at the expense of a modest increase in CPU time.

Keywords

Column generation Evacuation planning k-shortest paths Mixed-integer programming Constraint programming 

References

  1. 1.
    Bish, D.R., Sherali, H.D., Hobeika, A.G.: Optimal evacuation planning using staging and routing. J. Oper. Res. Soc. 65(1), 124–140 (2014)CrossRefGoogle Scholar
  2. 2.
    Bish, D.R., Sherali, H.D.: Aggregate-level demand management in evacuation planning. Eur. J. Oper. Res. 224(1), 79–92 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bretschneider, S., Kimms, A.: Pattern-based evacuation planning for urban areas. Eur. J. Oper. Res. 216(1), 57–69 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cova, T.J., Johnson, J.P.: A network flow model for lane-based evacuation routing. Transp. Res. Part A: Policy Pract. 37(7), 579–604 (2003)Google Scholar
  5. 5.
    Desaulniers, G., Desrosiers, J., Solomon, M.M.: Column Generation, vol. 5. Springer Science & Business Media, Berlin (2006)zbMATHGoogle Scholar
  6. 6.
    Desrochers, M., Desrosiers, J., Solomon, M.: A new optimization algorithm for the vehicle routing problem with time windows. Oper. Res. 40(2), 342–354 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Even, C., Pillac, V., Van Hentenryck, P.: Convergent plans for large-scale evacuations. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, pp. 1121–1127. AAAI Press (2015)Google Scholar
  8. 8.
    Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. In: Desaulniers, G., Desrosiers, J., Solomon, M.M. (eds.) Column Generation, pp. 33–65. Springer, Boston (2005). doi: 10.1007/0-387-25486-2_2 CrossRefGoogle Scholar
  9. 9.
    Jiménez, V.M., Marzal, A.: Computing the K shortest paths: a new algorithm and an experimental comparison. In: Vitter, J.S., Zaroliagis, C.D. (eds.) WAE 1999. LNCS, vol. 1668, pp. 15–29. Springer, Heidelberg (1999). doi: 10.1007/3-540-48318-7_4 CrossRefGoogle Scholar
  10. 10.
    Lim, G.J., Zangeneh, S., Baharnemati, M.R., Assavapokee, T.: A capacitated network flow optimization approach for short notice evacuation planning. Eur. J. Oper. Res. 223(1), 234–245 (2012)CrossRefzbMATHGoogle Scholar
  11. 11.
    Miller-Hooks, E., Sorrel, G.: Maximal dynamic expected flows problem for emergency evacuation planning. Transp. Res. Record: J. Transp. Res. Board 2089, 26–34 (2008)CrossRefGoogle Scholar
  12. 12.
    Pel, A.J., Bliemer, M.C.J., Hoogendoorn, S.P.: A review on travel behaviour modelling in dynamic traffic simulation models for evacuations. Transportation 39(1), 97–123 (2012)CrossRefGoogle Scholar
  13. 13.
    Pillac, V., Cebrian, M., Van Hentenryck, P.: A column-generation approach for joint mobilization and evacuation planning. Constraints 20(3), 285–303 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Pillac, V., Van Hentenryck, P., Even, C.: A conflict-based path-generation heuristic for evacuation planning. Transp. Res. Part B 83, 136–150 (2016)CrossRefGoogle Scholar
  15. 15.
    Romanski, J., Van Hentenryck, P.: Benders decomposition for large-scale prescriptive evacuations. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, pp. 3894–3900. AAAI Press (2016)Google Scholar
  16. 16.
    Xie, C., Lin, D.Y., Waller, S.T.: A dynamic evacuation network optimization problem with lane reversal and crossing elimination strategies. Transp. Res. Part E: Logist. Transp. Rev. 46(3), 295–316 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of MichiganAnn ArborUSA

Personalised recommendations