Optimal Location of Exit Doors for Efficient Evacuation of Crowds at Gathering Places

This work deals with the optimal design for location of exit doors at meeting places (such as sports centers, public squares, street markets, transport stations, etc.) to guarantee a safer emergency evacuation in events sporting, social, entertainment or religious type. problem is stated an control nonlinear partial differential equations, where state system reformulation Hughes model (coupling eikonal equation density-weighted walking velocity pedestrians and continuity conservation pedestrian density), domain boundary (subject several geometric constraints), cost function related rate. We provide full numerical algorithm solving (a finite element technique discretization gradient-free procedure optimization), show results realistic case.