  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.
