A Nested Genetic Algorithm for Modeling Self-Organizing Rules in Collective Behaviors

In nature, the emergence of highly intelligent and flexible behaviors from large groups of simple individuals is a common phenomenon. To uncover the hidden self-organizing rules behind these collective behaviors, existing studies have modeled various self-organizing systems to replicate different swarm motion patterns, often based on biological or physical observations and specific assumptions. However, few studies have adopted a data-driven approach to model collective self-organization rules. In this paper, we leverage domain knowledge to propose a data-driven method to learn self-organization rules directly from collective motion data. We first construct a foundational collective model template that integrates existing domain knowledge and can represent various collective behaviors through different parameter configurations. Building on this template, we developed a bilevel nested evolutionary framework based on a genetic algorithm (GA), named BLGA, to optimize parameter combinations within the template. Using the template, we designed four distinct collective models for particle simulations, successfully replicating behaviors such as swarming and flocking, and collected corresponding motion data. The BLGA framework was then applied to learn from these data. Through interpreting evolutionary models, reproducing collective behaviors, and conducting a comparative analysis of evaluation metrics, our results demonstrate that the proposed method effectively captures the hidden self-organizing rules underlying the collective motion data.