Efficient computation of evacuation routes on a three-dimensional geometric network - Tang, Huajun; Elalouf, Amir; Levner, Eugene; Cheng, T.C.E. (Computers & industrial engineering, 2014)
•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.