Abstract

In this work we present a new strategy, employing optimal control techniques of partial differential equations, to automate the optimization of locations for a given number of exit doors at gathering places, so that the evacuation of crowds takes place in a safer and faster way. Once given a detailed mathematical formulation of the problem, in order to solve the constrained optimal control problem numerically, we propose its full discretization, with a space semi-discretization via the finite element method over a family of triangular meshes of the domain under study, and a time semi-discretization via the Euler algorithm. Finally, for the resulting discretized minimization problem, we try its optimization by means of a derivative-free algorithm. Numerical examples, corresponding to different scenarios for a real-world study case posed on “Plaza de la Liberación” (Guadalajara, Mexico), are presented and discussed to assess the effectiveness of our approach.