2021/08/27 by Albi, Giacomo, Ferrarese, Federica, Segala, Chiara · 4 citations
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2108.12231
In this chapter, we discuss the mathematical modeling of egressing pedestrians in an unknown environment with multiple exits. We investigate different control problems to enhance the evacuation time of a crowd of agents, by few informed individuals, named leaders. Leaders are not recognizable as such and consist of two groups: a set of unaware leaders moving selfishly toward a fixed target, whereas the rest is coordinated to improve the evacuation time introducing different performance measures. Follower-leader dynamics is initially described microscopically by an agent-based model, subsequently a mean-field type model is introduced to approximate the large crowd of followers. The mesoscopic scale is efficiently solved by a class of numerical schemes based on direct simulation Monte-Carlo methods. Optimization of leader strategies is performed by a modified compass search method in the spirit of metaheuristic approaches. Finally, several virtual experiments are studied for various control settings and environments.