This article presents Underdamped Particle Swarm Optimization (UEPS), a novel metaheuristic inspired by both the Particle Swarm Optimization (PSO) algorithm and the dynamic behavior of an underdamped system. The underdamped motion acts as an intermediate solution between undamped systems, which oscillate indefinitely, and overdamped systems, which stabilize without oscillation. In the context of optimization, this type of motion allows particles to explore the search space dynamically, alternating between exploration and exploitation, with the ability to overshoot the optimal solution to explore new regions and avoid getting trapped in local optima. First, we review the concept of damped vibrations, an essential physical principle that describes how a system oscillates while losing energy over time, behaving in an underdamped, overdamped, or critically damped manner. This understanding forms the foundation for applying these concepts to optimization, ensuring a balanced management of exploration and exploitation. Furthermore, the classical PSO algorithm is discussed, highlighting its fundamental features and limitations, providing the necessary context to understand how the underdamped behavior improves PSO performance. The proposed metaheuristic is evaluated using benchmark functions and classic engineering problems, demonstrating its high robustness and efficiency.

翻译：本文提出了一种新颖的元启发式算法——欠阻尼粒子群优化算法（UEPS），其灵感来源于粒子群优化（PSO）算法以及欠阻尼系统的动态行为。欠阻尼运动介于无阻尼系统（无限振荡）与过阻尼系统（无振荡稳定）之间，作为一种折中方案。在优化背景下，此类运动使粒子能够动态探索搜索空间，在探索与利用之间交替进行，并具备超越最优解以探索新区域、避免陷入局部最优的能力。首先，我们回顾了阻尼振动的概念，这是一个描述系统如何随时间耗散能量而振荡的基本物理原理，表现为欠阻尼、过阻尼或临界阻尼行为。这一理解构成了将这些概念应用于优化的基础，确保了对探索与利用的平衡管理。此外，本文讨论了经典PSO算法，重点阐述了其基本特征与局限性，为理解欠阻尼行为如何提升PSO性能提供了必要的背景。所提出的元启发式算法通过基准函数与经典工程问题进行了评估，结果证明了其高度的鲁棒性与高效性。