  In this paper we propose a variant of a consensus-based global optimization
(CBO) method that uses personal best information in order to compute the global
minimum of a non-convex, locally Lipschitz continuous function. The proposed
approach is motivated by the original particle swarming algorithms, in which
particles adjust their position with respect to the personal best, the current
global best, and some additive noise. The personal best information along an
individual trajectory is included with the help of a weighted mean. This
weighted mean can be computed very efficiently due to its accumulative
structure. It enters the dynamics via an additional drift term. We illustrate
the performance with a toy example, analyze the respective memory-dependent
stochastic system and compare the performance with the original CBO with
component-wise noise for several benchmark problems. The proposed method has a
higher success rate for computational experiments with a small particle number
and where the initial particle distribution is disadvantageous with respect to
the global minimum.
