A Matrix Translation Model for Evacuation Path Optimization

In order to make the optimization of evacuation efficient enough for application, a Matrix Translation Model (MTM) has been developed. In MTM, a building is represented by using a network and the matrices attached to the network, and the crowd movement is simulated by translating matrices along the network. The performance of MTM was evaluated by comparison with a widely used commercial evacuation simulator, Pathfinder. The results showed that with accurate reproduction of the evacuation processes, MTM ran 10-15 times and 29-37 times faster than Pathfinder's flow-based (SFPE) and agent-based (Steering) modes, respectively. Furthermore, an evacuation path optimization method based on MTM is proposed by balancing the use of different exits. When run on a laptop, the path optimization of a building with 21 rooms and 944 occupants took less than 3 s. The optimized path was verified by Pathfinder, showing that approximately 50 s of the evacuation time was saved. MTM provides a new framework for evacuation simulation, i.e., the network defines the path connection, the matrix represents the spatial state, the macroscopic rules drive the matrix translation, and the microscopic rules limit the element transfer between the matrices. The path optimization algorithm developed based on the new framework offers new possibilities for real-time evacuation optimization of large buildings.