Pedestrian Evacuation Optimization Dynamic Programming in Continuous Space and Time

Abstract

This paper deals with the optimal allocation of routes, destination, and departure times to members of a crowd, for instance in case of an evacuation or another hazardous situation in which the people need to leave the area as quickly as possible. The generic approach minimizes the evacuation times, considering the demand dependent waiting times at bottlenecks within the considered infrastructure. We present the mathematical optimization problem for both the optimal instructions, and the continuum model describing the pedestrian flow dynamics. The key contribution of the approach is that it solves the evacuation problem considering the entire solution space in a continuous manner (i.e. both the time dimension and the routing), implying that for each location and for each time instant the optimal path towards the most favorable exit is calculated, taking into consideration the traffic flow operations along the routes. The approach is generic in the sense that different network loading models can be used, and that a variety of components can be added to the optimization objective without loss of generality. Next to presenting the framework and the mathematical model, we propose an iterative numerical solver to compute the optimal instructions. We demonstrate the abilities and opportunities of this optimization framework with two case studies.