Efficient contraflow algorithms for quickest evacuation planning
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The optimization models and algorithms with their implementations on flow over time problems have been an emerging field of research because of largely increasing human-created and natural disasters worldwide. For an optimal use of transportation network to shift affected people and normalize the disastrous situation as quickly and Efficiently as possible, contraflow configuration is one of the highly applicable operations research (OR) models. It increases the outbound road capacities by reversing the direction of arcs towards the safe destinations that not only minimize the congestion and increase the flow but also decrease the evacuation time significantly. In this paper, we sketch the state of quickest flow solutions and solve the quickest contraflow problem with constant transit times on arcs proving that the problem can be solved in strongly polynomial time O(nm2(log n)2), where n and m are number of nodes and number of arcs, respectively in the network. This contraflow solution has the same computational time bound as that of the best min-cost flow solution. Moreover, we also introduce the contraflow approach with load dependent transit times on arcs and present an Efficient algorithm to solve the quickest contraflow problem approximately. Supporting the claim, our computational experiments on Kathmandu road network and on randomly generated instances perform very well matching the theoretical results. For sufficiently large number of evacuees, about double flow can be shifted with the same evacuation time and about half time is sufficient to push the given flow value with contraflow reconfiguration.
Keywordsevacuation planning contra flow flow over time quickest flow load dependent transit time
MSC(2010)90B10 90C27 68Q25 90B06 90B20
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This work was supported by Deutscher Akademischer Austauschdienst (German Academic Exchange Service) Partnership Program (with University of Kaiserslautern, Germany and Mindanao State University, Iligan Institute of Technology, Iligan, Philippines) and AvH Research Group Linkage Program (with Technische Universität Bergakademie Freiberg) in Graph Theory and Optimization at Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal. The first author was supported by the AvH Foundation for the Georg Forster Research Fellowship for post doctoral researchers at Technische Universität Bergakademic Freiberg Germany. The authors thank the anonymous referees for their valuable suggestions to improve the quality of this work.
- 3.Arulselvan A. Network model for disaster management. PhD Thesis. Gainesville: University of Florida, 2009Google Scholar
- 5.Berlin G N. The Use of Directed Routes for Assessing Escape Potential. Boston: National Fire Protection Association, 1979Google Scholar
- 19.Hamacher H W, Tjandra S A. Mathematical modeling of evacuation problems: A state of the art. In: Pedestrian and Evacuation Dynamics. New York: Springer, 2002, 227–266Google Scholar
- 21.Hung Y C, Chen G H. On the quickest path problem. In: Proceedings of International Conference on Computing and Information. Lecture Notes in Computer Science, vol. 497. Berlin: Springer-Verlag, 1991, 44–46Google Scholar
- 24.Kim S, Shekhar S. Contra flow network reconfiguration for evacuation planning: A summary of results. In: Proceedings of the 13th International ACM Symposium on Advances in Geographic Information Systems. New York: ACM, 2005, 250–259Google Scholar
- 28.Langkau K. Flows over time with flow-dependent transit times. PhD Thesis. Berlin: Technical University, 2003Google Scholar
- 34.Pyakurel U. Evacuation planning problem with contra flow approach. PhD Thesis. Kathmandu: Tribhuvan University, 2016Google Scholar
- 36.Pyakurel U, Dhamala T N. Continuous time dynamic contra flow models and algorithms. Adv Oper Res, 2016, 2016: Article ID 7902460Google Scholar
- 40.Pyakurel U, Hamacher H W, Dhamala T N. Generalized maximum dynamic contra flow on lossy network. Internat J Oper Res Nepal, 2014, 3: 27–44Google Scholar
- 44.Tjandra S A. Dynamic network flow optimization with application to the evacuation problem. PhD Thesis. Kaiserslautern: University of Kaiserslautern, 2003Google Scholar
- 48.Zhao X, Feng Z Y, Li Y, et al. Evacuation network optimization model with lane-based reversal and routing. Math Probl Eng, 2016, 2016: 1–12Google Scholar