论文标题
从粒子群优化到基于共识的优化：随机建模和平均场极限
From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limit
论文作者
论文摘要
在本文中，我们考虑了基于流行粒子群优化（PSO）过程的随机微分方程（PSO）过程，以解决全局优化问题，并在大粒子中得出基于Vlasov-fokker-planck-type方程的相应均值近似值。通过引入一个附加的微分方程来描述局部最佳的演变，克服了存储局部最佳位置所引起的记忆效应的缺点。全球最佳允许正式允许的正规化过程可以正式得出相应的均值描述。随后，在较小的惯性极限中，我们计算了相关的宏观流体动力学方程，这些方程阐明了与最近引入的基于共识的优化（CBO）方法的联系。几个数值示例说明了平均野外过程，小惯性限制以及这种全局优化方法的一般类别的潜力。
In this paper we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the corresponding mean-field approximation based on Vlasov-Fokker-Planck-type equations. The disadvantage of memory effects induced by the need to store the local best position is overcome by the introduction of an additional differential equation describing the evolution of the local best. A regularization process for the global best permits to formally derive the respective mean-field description. Subsequently, in the small inertia limit, we compute the related macroscopic hydrodynamic equations that clarify the link with the recently introduced consensus based optimization (CBO) methods. Several numerical examples illustrate the mean field process, the small inertia limit and the potential of this general class of global optimization methods.
