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In this chapter, we discuss the mathematical modeling of egressingpedestrians in an unknown environment with multiple exits. We investigatedifferent control problems to enhance the evacuation time of a crowd of agents,by few informed individuals, named leaders. Leaders are not recognizable assuch and consist of two groups: a set of unaware leaders moving selfishlytoward a fixed target, whereas the rest is coordinated to improve theevacuation time introducing different performance measures. Follower-leaderdynamics is initially described microscopically by an agent-based model,subsequently a mean-field type model is introduced to approximate the largecrowd of followers. The mesoscopic scale is efficiently solved by a class ofnumerical schemes based on direct simulation Monte-Carlo methods. Optimizationof leader strategies is performed by a modified compass search method in thespirit of metaheuristic approaches. Finally, several virtual experiments arestudied for various control settings and environments.

Optimized leaders strategies for crowd evacuation in unknown environments with multiple exits