摘要
针对传统Kriging模型在多变量(高维)输入全局优化中因超参数过多而引发收敛速度慢,精度低,建模效率不高问题,提出了基于偏最小二乘变换技术和Kriging模型的有效全局优化方法.首先,构造偏最小二乘高斯核函数;其次,借助差分进化算法寻找满足期望改进准则最大化条件的新样本点;然后,将不同核函数和期望改进准则组合,构建四种有效全局优化算法并进行比较;最后,数值算例结果表明,基于偏最小二乘变换的Kriging全局优化方法在解决高维全局优化问题方面相比于标准的全局优化算法在收敛精度及收敛速度方面更具优势.
Kriging models are widely applied in analysis of computer experiments,but it less efficient in multivariate(high-dimensional) problems.Considering above problems,an efficient global algorithm based Kriging model and partial least squares is proposed.Firstly,the partial least squares Gaussian kernel function is constructed.Secondly,the new sample points satisfying the maximization condition of the expected improvement criterion are found by the differential evolution algorithm.Then,the different kernel functions and the expected improvement criteria are combined to construct four effective global optimization algorithms.In the end,numerical examples show that the Kriging global optimization method based on partial least squares transform has advantages in solving high-dimensional global optimization problems compared with standard global optimization algorithms in terms of convergence accuracy and convergence speed.
作者
林成龙
马义中
刘丽君
LIN Cheng-long;Ma Yi-zhong;LIU Li-jun(School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China)
出处
《数学的实践与认识》
北大核心
2020年第8期158-168,共11页
Mathematics in Practice and Theory
基金
国家自然科学基金(71931006,71871119,71702072)。
关键词
偏最小二乘变换
KRIGING模型
高斯核函数
期望改进准则
差分进化算法
有效全局优化
partial least squares method
Kriging model
Gaussian kernel function
expectation improvement criterion
differential evolution algorithm
efficient global optimization
