In this paper, we introduce a novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization (KBO) method with genetic dynamics (GKBO). The proposed method targets objective functions with multiple global minima, addressing a critical need in fields like engineering design, machine learning, and bioinformatics. By incorpo rating leader-follower dynamics and localized interactions, the algorithm efficiently navigates high-dimensional search spaces to detect multiple optimal solutions. After providing a binary description, a mean-field approximation is derived, and different numerical experiments are conducted to validate the results.

翻译：本文提出了一种新颖的多模态优化方法，通过将遗传动力学融入近期发展的基于动力学的优化方法中，构建了GKBO算法。该方法针对具有多个全局极小值的目标函数，满足了工程设计、机器学习和生物信息学等领域的关键需求。通过引入领导者-跟随者动力学机制和局部化交互策略，该算法能够高效探索高维搜索空间以检测多个最优解。在给出二元描述后，本文推导了平均场近似，并通过多种数值实验验证了结果的有效性。