粒子群优化算法：任意系数分布下基于N-信息器的稳定性分析
Particle Swarm Optimization: Stability Analysis using N-Informers under Arbitrary Coefficient Distributions
摘要：
本文在最小建模假设下推导出一个简单易用的定理，用于获得一类常见粒子群优化（PSO）变体的阶- $1$和阶- $2$稳定性标准。具体来说，PSO的变种，可以重写为一个粒子的位置和群告密者之间的随机加权差向量的有限和覆盖的定理。此外，使用派生定理允许PSO从业者获得的稳定性标准，不包含人为的限制控制系数之间的关系。几乎所有以前的PSO稳定性的结果提供了社会和认知控制系数是相等的限制下的稳定性标准，这样的限制不存在时，使用推导出的定理。使用推导出的定理，作为其易用性的证明，稳定性准则推导出没有施加限制的控制系数之间的关系，为三个流行的PSO变种。
英文摘要：
This paper derives, under minimal modelling assumptions, a simple to use theorem for obtaining both order-$1$ and order-$2$ stability criteria for a common class of particle swarm optimization (PSO) variants. Specifically, PSO variants that can be rewritten as a finite sum of stochastically weighted difference vectors between a particle's position and swarm informers are covered by the theorem. Additionally, the use of the derived theorem allows a PSO practitioner to obtain stability criteria that contains no artificial restriction on the relationship between control coefficients. Almost all previous PSO stability results have provided stability criteria under the restriction that the social and cognitive control coefficients are equal; such restrictions are not present when using the derived theorem. Using the derived theorem, as demonstration of its ease of use, stability criteria are derived without the imposed restriction on the relation between the control coefficients for three popular PSO variants.
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