This paper presents an extension of the state of the art theoretical model utilized for understanding the stability criteria of the particles in particle swarm optimization algorithms. Conditions for order-1 and order-2 stability are derived by modeling, in the simplest case, the expected value and variance of a particle’s personal and neighborhood best positions as convergent sequences of random variables. Furthermore, the condition that the expected value and variance of a particle’s personal and neighborhood best positions are convergent sequences is shown to be a necessary condition for order-1 and order-2 stability. The theoretical analysis presented is applicable to a large class of particle swarm optimization variants.

中文翻译：

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粒子群稳定性：使用非停滞分布假设的理论扩展

本文提出了用于理解粒子群优化算法中粒子稳定性标准的最新理论模型的扩展。在最简单的情况下，通过将粒子的个人和邻域最佳位置的期望值和方差建模为随机变量的收敛序列，可以得出1级和2级稳定性的条件。此外，表明粒子的个人和邻域最佳位置的期望值和方差是收敛序列的条件被证明是1级和2级稳定性的必要条件。提出的理论分析适用于一大类粒子群优化变量。