Efficient computation of evacuation routes on a three-dimensional geometric network

•We define a real-time emergency evacuation problem that seeks for rapid evacuation routes in buildings.•We formulate the stochastic routing problem as a non-linear routing problem subject to node-wise constraints.•We prove the problem to be NP-hard.•We suggest the exact dynamic programming algorith...

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Published in:	Computers & industrial engineering Vol. 76; pp. 231 - 242
Main Authors:	Tang, Huajun, Elalouf, Amir, Levner, Eugene, Cheng, T.C.E.
Format:	Journal Article
Language:	English
Published:	New York Elsevier Ltd 01.10.2014 Pergamon Press Inc
Subjects:	Algorithms Approximation Computer networks Construction Dynamic programming Evacuation Evacuations & rescues Fully polynomial-time approximately feasible scheme Fully polynomial-time approximation scheme Geometry Mathematical models Mathematical problems Networks No-notice building evacuation Random variables Real time Real-time emergency routing Route optimization Routing (telecommunications) Studies Three dimensional Fully polynomial-time approximation scheme Real-time emergency routing Dynamic programming Fully polynomial-time approximately feasible scheme No-notice building evacuation
ISSN:	0360-8352, 1879-0550
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Abstract	•We define a real-time emergency evacuation problem that seeks for rapid evacuation routes in buildings.•We formulate the stochastic routing problem as a non-linear routing problem subject to node-wise constraints.•We prove the problem to be NP-hard.•We suggest the exact dynamic programming algorithm and two polynomial time approximation algorithms.•We present and discuss a case study and results of computational experiments. We consider a real-time emergency evacuation problem that seeks to compute a set of rapid evacuation routes in a building. Given a three-dimensional geometric structure of the evacuation network, an emergency evacuation route is a sequence of movements of people away from the threat or actual occurrence of a hazard (such as a fire, a hidden bomb) to a safe exit in the network. In such a network each room/crossing/exit in the building is designated as a node and the corridors/staircases/links between the rooms are edges. The evacuation times assigned to the edges are normally distributed random variables. This stochastic routing problem subject to deadline constraints is NP-hard. We provide a new pseudo-polynomial-time dynamic programming algorithm to solve this problem. Based on this algorithm, we construct two types of approximation algorithm, namely a fully polynomial-time approximation scheme providing “almost-optimal” solutions and a fully polynomial-time approximately feasible scheme yielding a best “almost feasible” solution. We present a case study and results of computational experiments to illustrate the working and efficacy of the proposed solution methods, respectively.
AbstractList	We consider a real-time emergency evacuation problem that seeks to compute a set of rapid evacuation routes in a building. Given a three-dimensional geometric structure of the evacuation network, an emergency evacuation route is a sequence of movements of people away from the threat or actual occurrence of a hazard (such as a fire, a hidden bomb) to a safe exit in the network. In such a network each room/crossing/exit in the building is designated as a node and the corridors/staircases/links between the rooms are edges. The evacuation times assigned to the edges are normally distributed random variables. This stochastic routing problem subject to deadline constraints is NP-hard. We provide a new pseudo-polynomial-time dynamic programming algorithm to solve this problem. Based on this algorithm, we construct two types of approximation algorithm, namely a fully polynomial-time approximation scheme providing "almost-optimal" solutions and a fully polynomial-time approximately feasible scheme yielding a best "almost feasible" solution. We present a case study and results of computational experiments to illustrate the working and efficacy of the proposed solution methods, respectively. •We define a real-time emergency evacuation problem that seeks for rapid evacuation routes in buildings.•We formulate the stochastic routing problem as a non-linear routing problem subject to node-wise constraints.•We prove the problem to be NP-hard.•We suggest the exact dynamic programming algorithm and two polynomial time approximation algorithms.•We present and discuss a case study and results of computational experiments. We consider a real-time emergency evacuation problem that seeks to compute a set of rapid evacuation routes in a building. Given a three-dimensional geometric structure of the evacuation network, an emergency evacuation route is a sequence of movements of people away from the threat or actual occurrence of a hazard (such as a fire, a hidden bomb) to a safe exit in the network. In such a network each room/crossing/exit in the building is designated as a node and the corridors/staircases/links between the rooms are edges. The evacuation times assigned to the edges are normally distributed random variables. This stochastic routing problem subject to deadline constraints is NP-hard. We provide a new pseudo-polynomial-time dynamic programming algorithm to solve this problem. Based on this algorithm, we construct two types of approximation algorithm, namely a fully polynomial-time approximation scheme providing “almost-optimal” solutions and a fully polynomial-time approximately feasible scheme yielding a best “almost feasible” solution. We present a case study and results of computational experiments to illustrate the working and efficacy of the proposed solution methods, respectively.
Author	Elalouf, Amir Levner, Eugene Cheng, T.C.E. Tang, Huajun
Author_xml	– sequence: 1 givenname: Huajun surname: Tang fullname: Tang, Huajun organization: School of Business, Macau University of Science and Technology, Macau, China – sequence: 2 givenname: Amir surname: Elalouf fullname: Elalouf, Amir organization: Department of Management, Bar Ilan University, Ramat Gan, Israel – sequence: 3 givenname: Eugene surname: Levner fullname: Levner, Eugene email: levner@hit.ac.il organization: School of Economics, Ashkelon Academic College, Ashkelon, Israel – sequence: 4 givenname: T.C.E. surname: Cheng fullname: Cheng, T.C.E. organization: Faculty of Business, The Hong Kong Polytechnic University, Hong Kong, China
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Snippet	•We define a real-time emergency evacuation problem that seeks for rapid evacuation routes in buildings.•We formulate the stochastic routing problem as a... We consider a real-time emergency evacuation problem that seeks to compute a set of rapid evacuation routes in a building. Given a three-dimensional geometric...
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SubjectTerms	Algorithms Approximation Computer networks Construction Dynamic programming Evacuation Evacuations & rescues Fully polynomial-time approximately feasible scheme Fully polynomial-time approximation scheme Geometry Mathematical models Mathematical problems Networks No-notice building evacuation Random variables Real time Real-time emergency routing Route optimization Routing (telecommunications) Studies Three dimensional
Title	Efficient computation of evacuation routes on a three-dimensional geometric network
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