The Particle Swarm Optimisation (PSO) algorithm has undergone countless modifications and adaptations since its original formulation in 1995. Some of these have become mainstream whereas many others have not been adopted and faded away. Thus, a myriad of alternative formulations have been proposed to the extent that the question arises as to what the basic features of an algorithm must be to belong in the PSO family. The aim of this paper is to establish what defines a PSO algorithm and to attempt to formulate it in such a way that it encompasses many existing variants. Therefore, different versions of the method may be posed as settings within the proposed unified framework. In addition, the proposed formulation generalises, decouples and incorporates features to the method providing more flexibility to the behaviour of each particle. The closed forms of the trajectory difference equation are obtained, different types of behaviour are identified, stochasticity is decoupled, and traditionally global features such as sociometries and constraint-handling are re-defined as particle's attributes.

中文翻译：

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重新编排为统一灵活框架的“粒子群”

自1995年提出以来，粒子群优化（PSO）算法就进行了无数次修改和调整。其中一些算法已成为主流，而另一些算法尚未被采用并逐渐消失。因此，已经提出了无数替代公式，以至于出现一个问题，即算法的基本特征必须属于PSO系列。本文的目的是建立定义PSO算法的内容，并尝试以包含许多现有变体的方式来表述它。因此，可以在建议的统一框架内将方法的不同版本设置为设置。另外，所提出的配方概括，分离并结合了该方法的特征，从而为每个颗粒的行为提供了更大的灵活性。