We propose novel particle swarm optimization (PSO) variants incorporated with deep neural networks (DNNs) for particles to pursue globally optimal positions in dynamic environments. PSO is a heuristic approach for solving complex optimization problems. However, canonical PSO and its variants struggle to adapt efficiently to dynamic environments, in which the global optimum moves over time, and to track them accurately. Many PSO algorithms improve convergence by increasing the swarm size beyond potential optima, which are global/local optima but are not identified until they are discovered. Additionally, in dynamic environments, several methods use multiple sub-population and re-diversification mechanisms to address outdated memory and local optima entrapment. To track the global optimum in dynamic environments with smaller swarm sizes, the DNNs in our methods determine particle movement by learning environmental characteristics and adapting dynamics to pursue moving optimal positions. This enables particles to adapt to environmental changes and predict the moving optima. We propose two variants: a swarm with a centralized network and distributed networks for all particles. Our experimental results show that both variants can track moving potential optima with lower cumulative tracking error than those of several recent PSO-based algorithms, with fewer particles than potential optima.

翻译：我们提出了融合深度神经网络（DNN）的新型粒子群优化（PSO）变体，使粒子能够在动态环境中追踪全局最优位置。PSO是一种解决复杂优化问题的启发式方法。然而，标准PSO及其变体难以高效适应全局最优点随时间移动的动态环境，并实现精确追踪。许多PSO算法通过将种群规模扩大至超出潜在极值点（全局/局部最优，但在发现前无法识别）来提升收敛性。此外，在动态环境中，多种方法采用多重子种群和再多样化机制以应对记忆过时与局部极值陷阱问题。为在较小种群规模下追踪动态环境中的全局最优值，我们的方法通过DNN学习环境特征并适应动态变化，从而指导粒子移动以追踪移动最优位置。这使得粒子能够适应环境变化并预测移动中的最优点。我们提出了两种变体：集中式网络群与全粒子分布式网络群。实验结果表明，与近期多种基于PSO的算法相比，这两种变体均能以更少粒子（少于潜在极值点数量）追踪移动潜在极值点，且累积追踪误差更低。