Min-Max-Flow Based Algorithm for Evacuation Network Planning in Restricted Spaces

  • Yi HongEmail author
  • Jiandong Liu
  • Chuanwen Luo
  • Deying Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)


Recently, emergency evacuation management, which is a social work around the world, has been getting lots of attentions due to its importance and necessity. The primary task of emergency evacuation management is evacuation route planning. Considering the particularity of restrict space scenarios, it is more important to guarantee the security and promptness of evacuation routes than that in open space scenarios. In this paper, we introduce a new evacuation route planning problem in restricted spaces, namely Congestion-Avoidable Evacuation Route Network Planning (CA-ERNP) problem. Based on the minimum cost maximum flow (Min-Max Flow) problem, we propose a batch scheduling algorithm based on node-slitting transformation. In addition, we evaluate the average performance of the algorithms via simulation and the results indicate the proposed algorithm outperforms the existing alternatives in terms of efficiency and time cost.


Evacuation route planning Restrict space Min-max flow Batch scheduling 



This research was supported in part by Beijing Natural Science Foundation (4174090), Program of Beijing Excellent Talents Training for Young Scholar (2016000020124G056).


  1. 1.
    Evans, J.: Optimization Algorithms for Networks and Graphs, 2nd edn. Marcel Dekker, New York (1992)Google Scholar
  2. 2.
    Cherkassky, B.V., Goldberg, A.V., Radzik, T.: Shortest paths algorithms: theory and experimental evaluation. Math. Program. 73(2), 129–174 (1996)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Jalali, S.E., Noroozi, M.: Determination of the optimal escape routes of underground mine networks in emergency cases. Saf. Sci. 47, 1077–1082 (2009)CrossRefGoogle Scholar
  4. 4.
    Martins, E.D.Q.V., Queir, E., Dos Santos, J.L.E., Martins, V., Margarida, M., Pascoal, M.M.B.: A new algorithm for ranking loopless paths. Technical report, Univ. de Coimbra (1997)Google Scholar
  5. 5.
    Eppstein, D.: Finding the k shortest paths. SIAM J. Comput. 28(2), 652–673 (1998)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jin, W., Chen, S., Jiang, H.: Finding the K shortest paths in a time-schedule network with constraints on arcs. Comput. Oper. Res. 40, 2975–2982 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Sever, D., Dellaert, N., Van Woensel, T., De Kok, T.: Dynamic shortest path problems: hybrid routing policies considering network disruptions. Comput. Oper. Res. 40, 2852–2863 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hong, Y., Li, D., Wu, Q., Xu, H. Dynamic route network planning problem for emergency evacuation in restricted space scenarios. J. Adv. Transp. Article ID 4295419, 13 p. (2018)Google Scholar
  9. 9.
    Hong, Y., Li, D., Wu, Q., Xu, H.: Priority-oriented route network planning for evacuation in constrained space scenarios. J. Optim. Theory Appl. (2018).
  10. 10.
    Vogiatzis, C., Walteros, J.L., Pardalos, P.M.: Evacuation through clustering techniques. In: Goldengorin, B., Kalyagin, V., Pardalos, P. (eds.) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol. 32, pp. 185–198. Springer, New York (2013). Scholar
  11. 11.
    Lujak, M., Giordani, S.: Centrality measures for evacuation: finding agile evacuation routes. Futur. Gener. Comput. Syst. 83, 401–412 (2018)CrossRefGoogle Scholar
  12. 12.
    Vogiatzis, C., Pardalos, P.M.: Evacuation modeling and betweenness centrality. In: Kotsireas, I., Nagurney, A., Pardalos, P. (eds.) DOD 2015 2016. Springer Proceedings in Mathematics & Statistics, vol. 185, pp. 345–359. Springer, Cham (2016). Scholar
  13. 13.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Inc., Upper Saddle River (1993). ISBN 0-13-617549-XzbMATHGoogle Scholar
  14. 14.
    Klein, M.: A primal method for minimal cost flows with applications to the assignment and transportation problems. Manag. Sci. 14, 205–220 (1967)CrossRefGoogle Scholar
  15. 15.
    Goldberg, A.V., Tarjan, R.E.: Finding minimum-cost circulations by canceling negative cycles. J. ACM 36(4), 873–886 (1989)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. J. ACM 19(2), 248–264 (1972)CrossRefGoogle Scholar
  17. 17.
    Orlin, J.B.: A polynomial time primal network simplex algorithm for minimum cost flows. Math. Program. 78, 109–129 (1997)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Tanka Nath Dhamala: A survey on models and algorithms for discrete evacuation planning network problems. J. Ind. Manag. Optim. 11(1), 265–289 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Choi, W., Hamacher, H.W., Tufekci, S.: Modeling of building evacuation problems by network flows with side constraints. Eur. J. Oper. Res. 35(1), 98–110 (1988)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu, Y., Chang, G.L., Liu, Y., Lai, X.: Corridor-based emergency evacuation system for Washington, DC: system development and case study. Transp. Res. Rec.: J. Transp. Res. Board 2041, 58–67 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Yi Hong
    • 1
    Email author
  • Jiandong Liu
    • 1
  • Chuanwen Luo
    • 2
  • Deying Li
    • 2
  1. 1.Information Engineering CollegeBeijing Institute of Petrochemical TechnologyBeijingPeople’s Republic of China
  2. 2.School of InformationRenmin University of ChinaBeijingPeople’s Republic of China

Personalised recommendations