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Силинская А. А., Bogomolov A. S., Kushnikov V. A. A mathematical model of social group evacuation from buildings with multiple exits. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 2, pp. 302-311. DOI: 10.18500/1816-9791-2026-26-2-302-311, EDN: UEEHGG
A mathematical model of social group evacuation from buildings with multiple exits
This paper introduces a computational model for simulating multi-agent evacuation dynamics based on the Multi-Agent Proximal Policy Optimization (MAPPO) algorithm. The proposed framework incorporates multiple evacuation exits with varying opening times, heterogeneous agent types, panic-induced behavioral modifications, and social interactions of the leader – follower type. A hybrid action space is employed, combining discrete exit selection with continuous movement control. Training is performed under a curriculum learning paradigm, gradually increasing the number of agents to enhance generalization and adaptability to different population sizes. Several methodological refinements were implemented to improve training stability and efficiency: dropout layers to mitigate overfitting, exponential exploration decay to enable a smooth shift toward precise actions, and reward normalization to stabilize policy updates. Simulations were conducted in a $15\times20$ m environment with three exits (each 1.5 m wide, opening sequentially every 6 seconds). The model also incorporates mechanisms of information dissemination: leaders are aware of all exits from the start of the simulation, while individual agents detect exits within a 5 m radius and propagate this knowledge to neighbors within 2 m. Social groups follow predefined behavioral rules, such as granting elderly agents a speed adjustment and assigning leaders strategic decision-making roles. Computational experiments with scenarios involving 50 agents demonstrated that the presence of social groups and leaders significantly accelerates evacuation, particularly benefiting elderly agents. Optimal performance was observed in settings with two leaders, whereas scenarios with a single leader led to bottlenecks, longer evacuation times, and higher levels of panic. These findings highlight the potential of reinforcement learning–based approaches for analyzing and optimizing evacuation processes in complex indoor environments. The developed mathematical model is intended for use in the creation of digital twins for simulating and optimizing human flow processes, as well as for conducting computational experiments to calculate efficient evacuation times and routes.
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