The building evacuation problem with shared information

Abstract

Abstract:In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP-hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real-world network representing a four-story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided.

Mathematical Models for Evacuation Planning in Urban Areas

“…for building evacuation , Choi et al 1988or Chen and Miller-Hooks 2008. for building evacuation , Choi et al 1988or Chen and Miller-Hooks 2008.…”

“…for building evacuation , Choi et al 1988or Chen and Miller-Hooks 2008. Chen and Miller-Hooks (2008) incorporate "shared information" (modeled with binary variables on arcs and in every point in time) in their building evacuation problem that updates the evacuation routes in every point in time. Using the "triple optimization result" proven by the considered problem solves also the maximization of the total number of evacuees as well as the minimization of the total evacuation time.…”

Hierarchical multi-objective evacuation routing in stadium using ant colony optimization approach

“…In addition, several objectives, including minimization of average evacuation time, maximization of the total number of surviving evacuees and minimization of congestion on road links were identified by Lin et al (2008). Currently, some optimization algorithms or techniques, including game theory (Lo et al, 2006), agent (Shi et al, 2009), non-dominated sorting genetic algorithm (NSGA-II; Saadatseresht et al, 2009), Benders' decomposition algorithm (Chen and Miller-Hooks, 2008), linear programming relaxation (Tayfur and Taaffe, 2009), cellular automation (Fang et al, 2010) and the Fletcher-Reeves technique (Tavares and Galea, 2009), have been used in attempts to solve routing optimization problems in evacuation. The majority of these approaches are designed to calculate a single optimal evacuation routing plan.…”

Optimal Traffic Planning for Efficient Evacuation

“…Another variant with time dependent flow uses tree structure network to evacuate from common buildings. Moreover, time dependent case updates the evacuation routes in every time period [2]. A variant of the problem evacuates through a single route.…”