Skip to main content

A column-generation approach for joint mobilization and evacuation planning

Abstract

Large-scale evacuations require authorities to decide and stage evacuation routes, mobilize resources, and issue evacuation orders under strict time constraints. These decisions must consider both the capacity of the road network and the evolution of the threat (e.g., a bushfire or a flood). This paper proposes, for the first time, an optimization model that jointly optimizes the mobilization and evacuation planning, taking into account the behavioral response of evacuees and the allocation of resources for communicating and implementing evacuation orders. From a technical standpoint, the model is solved by a column generation algorithm that jointly decides the evacuation route, evacuation time, and the resource allocation for each evacuated area in order to maximize the number of evacuees reaching safety and minimize the total duration of the evacuation.

This is a preview of subscription content, access via your institution.

References

  1. Alvelos, F., & Valério De Carvalho, J. (2000). Solving multicommodity flow problems with branch-and-price. Technical Report.

  2. Andreas, A.K., & Smith, J.C. (2009). Decomposition algorithms for the design of a nonsimultaneous capacitated evacuation tree network. Networks, 53(2), 91–103. doi:10.1002/net.20278.

    Article  MATH  MathSciNet  Google Scholar 

  3. Barnhart, C., Hane, C., & Vance, P. (1997). Integer multicommodity flow problems. Lecture Notes in Economics and Mathematical Systems, 450, 17–31.

    Article  MathSciNet  Google Scholar 

  4. Barnhart, C., Hane, C.A., & Vance, P.H. (2000). Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Operations Research, 48(2), 318–326. doi:10.1287/opre.48.2.318.12378.

    Article  Google Scholar 

  5. Bish, D.R., & Sherali, H.D. (2013). Aggregate-level demand management in evacuation planning. European Journal of Operational Research, 224(1), 79–92. doi:10.1016/j.ejor.2012.07.036.

    Article  MATH  MathSciNet  Google Scholar 

  6. Bretschneider, S., & Kimms, A. (2011). A basic mathematical model for evacuation problems in urban areas. Transportation Research Part A: Policy and Practice, 45(6), 523–539. doi:10.1016/j.tra.2011.03.008.

    Google Scholar 

  7. Bretschneider, S., & Kimms, A. (2012). Pattern-based evacuation planning for urban areas. European Journal of Operational Research, 216 (1), 57–69. doi:10.1016/j.ejor.2011.07.015.

    Article  MATH  MathSciNet  Google Scholar 

  8. Daganzo, C.F. (1994). The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B: Methodological, 28(4), 269–287. doi:10.1016/0191-2615(94)90002-7.

    Article  Google Scholar 

  9. Desaulniers, G., & Desrosiers, J. (2005). Column generation. In M.M. Solomon (Ed.) Mathematics of decision making. Springer.

  10. Even, C., Pillac, V., & Van Hentenryck, P. (2014). Nicta evacuation planner: Actionable evacuation plans with contraflows. In: Proceedings of the 20th European Conference on Artificial Intelligence (ECAI 2014), Frontiers in Artificial Intelligence and Applications, (Vol. 263, pp. 1143–1148). Amsterdam: IOS Press. doi:10.3233/978-1-61499-419-0-1143.

  11. Even, C., Pillac, V., & Van Hentenryck, P. (2015). Convergent plans for large-scale evacuations. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence (AAAI-15). In press.

  12. Hamacher, H.W., & Tjandra, S.A. (2002). Mathematical modelling of evacuation problems: A state of art. In M. Schreckenberger, & S. Sharma (Eds.) Pedestrian and evacuation dynamics (pp. 227–266). Springer Verlag.

  13. Holmberg, K., & Yuan, D. (2003). A multicommodity network-flow problem with side constraints on paths solved by column generation. INFORMS Journal on Computing, 15(1), 42–57. doi:10.1287/ijoc.15.1.42.15151.

    Article  MATH  MathSciNet  Google Scholar 

  14. Huibregtse, O., Hegyi, A., & Hoogendoorn, S. (2012). Blocking roads to increase the evacuation efficiency. Journal of Advanced Transportation, 46(3), 282–289. doi:10.1002/atr.210.

    Article  Google Scholar 

  15. Huibregtse, O.L., Bliemer, M.C., & Hoogendoorn, S.P. (2010). Analysis of near-optimal evacuation instructions. Procedia Engineering, 3, 189–203. 1st Conference on Evacuation Modeling and Management.

    Article  Google Scholar 

  16. Huibregtse, O.L., Hoogendoorn, S.P., Hegyi, A., & Bliemer, M. C. J. (2011). A method to optimize evacuation instructions. OR Spectrum, 33(3), 595–627. doi:10.1007/s00291-011-0245-4.

    Article  MATH  MathSciNet  Google Scholar 

  17. Lim, G.J., Zangeneh, S., Baharnemati, M.R., & Assavapokee, T. (2012). A capacitated network flow optimization approach for short notice evacuation planning. European Journal of Operational Research, 223(1), 234–245. doi:10.1016/j.ejor.2012.06.004.

    Article  MATH  Google Scholar 

  18. Lin, P., Lo, S., Huang, H., & Yuen, K. (2008). On the use of multi-stage time-varying quickest time approach for optimization of evacuation planning. Fire Safety Journal, 43(4), 282–290. doi:10.1016/j.firesaf.2007.08.005.

    Article  Google Scholar 

  19. Lindell, M., & Prater, C. (2007). Critical behavioral assumptions in evacuation time estimate analysis for private vehicles: Examples from hurricane research and planning. Journal of Urban Planning and Development, 133(1), 18–29. doi:10.1061/(ASCE)0733-9488(2007)133:1(18).

    Article  Google Scholar 

  20. Liu, H.X., He, X., & Ban, X. (2007). A cell-based many-to-one dynamic system optimal model and its heuristic solution method for emergency evacuation. In Proceedings 86th annual meeting transportation res. board (pp. 1–20).

  21. Lu, Q., George, B., & Shekhar, S. (2005). Capacity constrained routing algorithms for evacuation planning: A summary of results In C. Bauzer Medeiros, M. Egenhofer, & E. Bertino (Eds.), Advances in spatial and temporal databases, lecture notes in computer science (Vol. 3633, pp. 291–307). Berlin Heidelberg: Springer. doi:10.1007/11535331_17.

  22. Lu, Q., Huang, Y., & Shekhar, S. (2003). Evacuation planning: A capacity constrained routing approach. In H. Chen, R. Miranda, D. Zeng, C. Demchak, J. Schroeder, & T. Madhusudan (Eds.) Intelligence and security informatics, lecture notes in computer science (Vol. 2665, pp. 111–125). Berlin Heidelberg: Springer. doi:10.1007/3-540-44853-5_9.

  23. Lübbecke, M., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, 53(6), 1007–1023.

    Article  MATH  MathSciNet  Google Scholar 

  24. Opper, S. (2004). The application of timelines to evacuation planning. Tech. rep., NSW State Emergency Service.

  25. Pel, A.J., Bliemer, M. C. J., & Hoogendoorn, S.P. (2012). A review on travel behaviour modelling in dynamic traffic simulation models for evacuations. Transportation, 39(1), 97–123. doi:10.1007/s11116-011-9320-6.

    Article  Google Scholar 

  26. Pillac, V., Even, C., & Van Hentenryck, P. (2013). A conflict-based path-generation heuristic for evacuation planning: Technical Report VRL-7393, NICTA. ArXiv:1309.2693, submitted for publication.

  27. Pillac, V., Van Hentenryck, P., & Even, C. (2014). A path-generation matheuristic for large scale evacuation planning. In M. Blesa, C. Blum, & S. Voss (Eds.) Hybrid metaheuristics, lecture notes in computer science, 9th International Workshop on Hybrid Metaheuristics (Vol. 8457, pp. 71–84). Springer.

  28. Richter, K.F., Shi, M., Gan, H.S., & Winter, S. (2013). Decentralized evacuation management. Transportation Research Part C: Emerging Technologies, 31, 1–17. doi:10.1016/j.trc.2013.02.013.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pascal Van Hentenryck.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pillac, V., Cebrian, M. & Van Hentenryck, P. A column-generation approach for joint mobilization and evacuation planning. Constraints 20, 285–303 (2015). https://doi.org/10.1007/s10601-015-9189-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10601-015-9189-7

Keywords

  • Evacuation planning
  • Column generation
  • Behavioral operations research