Journal of Combinatorial Optimization

, Volume 36, Issue 1, pp 280–306 | Cite as

Improved algorithms for the evacuation route planning problem

  • Gopinath Mishra
  • Subhra Mazumdar
  • Arindam Pal


Emergency evacuation is the process of movement of people away from the threat or actual occurrence of hazards such as natural disasters, terrorist attacks, fires and bombs. In this paper, we focus on evacuation from a building, but the ideas can be applied to city and region evacuation. We define the problem and show how it can be modeled using graphs. The resulting optimization problem can be formulated as an Integer Linear Program. Though this can be solved exactly, this approach does not scale well for graphs with thousands of nodes and several hundred thousands of edges. This is impractical for large graphs. First, we study a special case of this problem, where there is only a single source and a single sink. For this case, we give an improved algorithm Single Source Single Sink Evacuation Route Planner, whose evacuation time is always at most that of a famous algorithm Capacity Constrained Route Planner (CCRP), and whose running time is strictly less than that of CCRP. We prove this mathematically and give supporting results by extensive experiments. We also study randomized behavior model of people and prove some interesting results. We design the Multiple Sources Multiple Sinks Evacuation Route Planner (MSEP) algorithm to extend this for multiple sources and multiple sinks. We propose a randomized behavior model for MSEP and give a probabilistic analysis using ChernoffBounds.


Evacuation planning Graph algorithms Combinatorial optimization Randomized behavior models Probabilistic analysis 


  1. Ahmed N, Ghose A, Agrawal AK, Bhaumik C, Chandel V, Kumar A (2015) SmartEvacTrak: a people counting and coarse-level localization solution for efficient evacuation of large buildings. In: 2015 IEEE international conference on pervasive computing and communication workshops (PerCom Workshops), IEEE, pp 372–377Google Scholar
  2. Desmet A, Gelenbe E (2014) Capacity based evacuation with dynamic exit signs. In: 2014 IEEE international conference on pervasive computing and communications workshops (PERCOM Workshops), IEEE, pp 332–337Google Scholar
  3. Dressler D, Groß M, Kappmeier JP, Kelter T, Kulbatzki J, Plümpe D, Schlechter G, Schmidt M, Skutella M, Temme S (2010) On the use of network flow techniques for assigning evacuees to exits. Procedia Eng 3:205–215CrossRefGoogle Scholar
  4. Fleischer L, Tardos É (1998) Efficient continuous-time dynamic network flow algorithms. Oper Res Lett 23(3):71–80MathSciNetCrossRefMATHGoogle Scholar
  5. Gupta A, Sarda NL (2014) Efficient evacuation planning for large cities. In: Database and expert systems applications. Springer, New York, pp 211–225Google Scholar
  6. Hamacher HW, Tjandra SA (2001) Mathematical modelling of evacuation problems: a state of art. Fraunhofer-Institut für Techno-und Wirtschaftsmathematik, Fraunhofer (ITWM)Google Scholar
  7. Hausknecht M, Au TC, Stone P, Fajardo D, Waller T (2011) Dynamic lane reversal in traffic management. In: 2011 14th international IEEE conference on intelligent transportation systems (ITSC), IEEE, pp 1929–1934Google Scholar
  8. Hoppe B, Tardos É (1994) Polynomial time algorithms for some evacuation problems. In: Proceedings of the fifth annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and Applied Mathematics, pp 433–441Google Scholar
  9. Hoppe B, Tardos É (2000) The quickest transshipment problem. Math Oper Res 25(1):36–62MathSciNetCrossRefMATHGoogle Scholar
  10. Kim S, Shekhar S, Min M (2008) Contraflow transportation network reconfiguration for evacuation route planning. IEEE Trans Knowl Data Eng 20(8):1115–1129CrossRefGoogle Scholar
  11. Lin M, Jaillet P (2015) On the quickest flow problem in dynamic networks: a parametric min-cost flow approach. In: Proceedings of the twenty-sixth annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and Applied MathematicsGoogle Scholar
  12. Løvs GG (1998) Models of wayfinding in emergency evacuations. Eur J Oper Res 105(3):371–389CrossRefMATHGoogle Scholar
  13. Lu Q, George B, Shekhar S (2005) Capacity constrained routing algorithms for evacuation planning: a summary of results. In: Advances in spatial and temporal databases. Springer, New York, pp 291–307Google Scholar
  14. Min M (2012) Synchronized flow-based evacuation route planning. In Wireless algorithms, systems, and applications. Springer, New York, pp 411–422Google Scholar
  15. Min M, Lee J (2013) Maximum throughput flow-based contraflow evacuation routing algorithm. In: 2013 IEEE international conference on pervasive computing and communications workshops (PERCOM Workshops), IEEE, pp 511–516Google Scholar
  16. Min M, Lee J, Lim S (2014) Effective evacuation route planning algorithms by updating earliest arrival time of multiple paths. In: Proceedings of the 22nd ACM SIGSPATIAL international conference on advances in geographic information systemsGoogle Scholar
  17. Min M, Neupane BC (2011) An evacuation planner algorithm in flat time graphs. In: Proceedings of the 5th international conference on ubiquitous information management and communication, ACM, p 99Google Scholar
  18. Pillac V, Van Henetenryck P, Even C (2013) A conflict-based path-generation heuristic for evacuation planning. arXiv preprint arXiv:1309.2693
  19. Shahabi K, Wilson JP (2014) Casper: intelligent capacity-aware evacuation routing. Comput Environ Urban Syst 46:12–24CrossRefGoogle Scholar
  20. Skutella M (2009) An introduction to network flows over time. In: Research trends in combinatorial optimization. Springer, New York, pp 451–482Google Scholar
  21. Song X, Zhang Q, Sekimoto Y, Shibasaki R, Yuan NJ, Xie X (2015) A simulator of human emergency mobility following disasters: knowledge transfer from big disaster data. In AAAI conference on artificial intelligenceGoogle Scholar
  22. Wang JW, Wang HF, Zhang WJ, Ip WH, Furuta K (2013) Evacuation planning based on the contraflow technique with consideration of evacuation priorities and traffic setup time. IEEE Trans Intell Transp Syst 14(1):480–485CrossRefGoogle Scholar
  23. Wei Q, Wang L, Jiang B (2013) Tactics for evacuating from an affected area. Int J Mach Learn Comput 3(5):435CrossRefGoogle Scholar
  24. Yin D (2009) A scalable heuristic for evacuation planning in large road network. In: Proceedings of the second international workshop on computational transportation science, ACM, pp 19–24Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Advanced Computing and Microelectronics UnitIndian Statistical InstituteKolkataIndia
  2. 2.TCS ResearchTata Consultancy ServicesKolkataIndia

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