Particle swarm optimization (PSO) is a population-based optimization method and has been successfully applied to solve many real-world problems. This method belongs to the stochastic optimization method and is mainly driven by two random streams utilized in the stochastic search mechanism, namely, individual (cognition) and social randomness effects. To our best knowledge, no research work has been conducted about the manipulation of the random stream assignment for stochastic search mechanism in the PSO algorithm. In this work, the influences of controlling randomness in the searching scheme of PSO is studied by introducing different pseudo random number (PRN) assignment strategies. The order-1 and order-2 stability analyses for particle dynamics under different PRN assignment strategies are also conducted to understand the influences. Stability analysis is carried out using the stochastic process theory. Our results show that the correlation caused by PRN has no effect on the unbiasedness of the expectation of particle position, but it would reduce or increase the variance of particle dynamics. Second, the convergent conditions of the PSO system under different PRN assignment strategies and the corresponding parameter selection ranges are provided. Finally, an empirical analysis via experimental simulations evaluated by six common swarm diversity measures, eight benchmark test functions, and two parameter tuples is presented.

粒子群优化 (PSO) 是一种基于种群的优化方法，已成功应用于解决许多现实问题。该方法属于随机优化方法，主要由随机搜索机制中使用的两个随机流驱动，即个体（认知）和社会随机性效应。据我们所知，没有关于 PSO 算法中随机搜索机制的随机流分配操作的研究工作。在这项工作中，通过引入不同的伪随机数（PRN）分配策略来研究控制随机性对 PSO 搜索方案的影响。还进行了不同 PRN 分配策略下粒子动力学的 1 阶和 2 阶稳定性分析，以了解其影响。使用随机过程理论进行稳定性分析。我们的研究结果表明，PRN引起的相关性对粒子位置期望的无偏性没有影响，但会减少或增加粒子动力学的方差。其次，给出了 PSO 系统在不同 PRN 分配策略下的收敛条件和相应的参数选择范围。最后，通过六个常见的群体多样性度量、八个基准测试函数和两个参数元组评估了实验模拟的经验分析。其次，给出了 PSO 系统在不同 PRN 分配策略下的收敛条件和相应的参数选择范围。最后，通过六个常见的群体多样性度量、八个基准测试函数和两个参数元组评估了实验模拟的经验分析。其次，给出了 PSO 系统在不同 PRN 分配策略下的收敛条件和相应的参数选择范围。最后，通过六个常见的群体多样性度量、八个基准测试函数和两个参数元组评估了实验模拟的经验分析。