Abstract: Considering new experiment points fall into the local optimum because of the greedy of expected improvement strategy and Kriging model is well-suited to parallelize optimization,a new parallel surrogate optimization method based on Kriging model and Bayesian expected improvement control strategy was proposed,which made full use of the predictive uncertainty measurement capability of the Kriging model.The first experimental points were selected by classic expected improvement strategy and were taken as the control reference points.Then,the Bayesian expected improvement control strategy was updated by the control function,and the new experiment points were taken as the control reference points for the next experiment point.The proposed strategies could enhance the ability of global exploration and ensure that new experiment points had good spatial distribution characteristics.In addition,two extended Bayesian expected improvement control strategies were constructed by using the control function adjustment method.Numerical examples and simulation cases showed that the Bayesian expected improvement control strategy was more efficient than single point infill strategy and the proposed parallel surrogate-based optimization method had better robustness and faster convergence speed under the same precision conditions.

Key words: expected improvement strategy, Bayesian expected improvement control, control function, Kriging model, parallel surrogate-based optimization method

摘要： 针对经典期望改进策略因过于贪婪而易于陷入局部最优,以及Kriging模型十分适用于并行优化的特点,提出了基于Kriging模型和Bayesian期望改进控制的并行代理优化方法。实现过程中,Kriging模型在小样本条件下,建立输入与输出见的近似函数关系。所提出的Bayesian期望改进控制策略充分利用Kriging模型对未试验点预测不确定性的度量能力,首先利用经典期望改进策略选取第一个试验点,并将其作为控制参考点;然后,借助所构造的控制函数更新贝叶斯期望改进控制策略,并将新增加试验点作为下个试验点选取的控制参考点。所提策略可以在提升全局探索能力的同时,使新试验点具有良好的空间分布特性。此外,借助控制函数调整方法,构建了两种拓展的Bayesian期望改进控制策略。数值算例及仿真案例结果表明:相比单点填充,Bayesian期望改进控制策略更高效;所提并行代理优化方法在同等精度条件下具有更好的稳健性及更快的收敛速度。

关键词: 期望改进策略, Bayesian期望改进控制, 控制函数, Kriging模型, 并行代理优化方法