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 ac-cumulative 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 per-formance 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.

中文翻译：

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基于共识的全局优化与个人最佳

在本文中，我们提出了一种基于共识的全局优化（CBO）方法的变体，该方法使用个人最佳信息来计算非凸局部Lipschitz连续函数的全局最小值。提出的方法受原始粒子群算法的启发，其中粒子相对于个人最佳，当前全局最佳和某些加性噪声来调整其位置。借助加权平均值，可以包含沿着单个轨迹的个人最佳信息。由于其加权累积结构，因此可以非常有效地计算该加权平均值。它通过附加的漂移项进入动力学。我们通过一个玩具示例来说明性能，分别分析与内存相关的随机系统，并将性能与原始CBO进行逐项噪声比较，以解决几个基准问题。所提出的方法对于具有较小粒子数的计算实验具有较高的成功率，并且相对于全局最小值而言，初始粒子分布不利。