Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle-based optimization methods, inspired by swarm intelligence principles, have shown effectiveness due to their ability to balance exploration and exploitation within the search space. In this work, we introduce a novel particle-based optimization algorithm where velocities are updated via random jumps, a strategy commonly used to enhance stochastic exploration. We formalize this approach by describing the dynamics through a kinetic modelling of BGK type, offering a unified framework that accommodates general noise distributions, including heavy-tailed ones like Cauchy. Under suitable parameter scaling, the model reduces to the Consensus-Based Optimization (CBO) dynamics. For non-degenerate Gaussian noise in bounded domains, we prove propagation of chaos and convergence towards minimizers. Numerical results on benchmark problems validate the approach and highlight its connection to CBO.

翻译：元启发式算法是全局优化的强大工具，尤其适用于精确方法往往不切实际的非凸与不可微问题。基于粒子的优化方法受群体智能原理启发，因其在搜索空间内平衡探索与开发的能力而展现出卓越效能。本研究提出一种新型粒子优化算法，其速度通过随机跳跃进行更新——这是一种常用于增强随机探索的策略。我们通过BGK型动力学建模描述该动态过程，从而形式化该方法，提供了一个可容纳一般噪声分布（包括柯西分布等重尾分布）的统一框架。在适当的参数缩放条件下，该模型可简化为基于共识的优化（CBO）动力学。针对有界域中的非退化高斯噪声，我们证明了混沌传播特性及向最小化器的收敛性。在基准问题上的数值结果验证了该方法的有效性，并揭示了其与CBO的内在关联。