摘要
代理模型是数值优化的关键技术,为探究克里金和径向基函数同名组合代理模型的性能,本文以6种具有不同协方差函数的克里金代理模型、5种具有不同核函数的径向基函数代理模型分别作为同名组合代理模型的子模型;通过简单平均法、反比例平均化法、启发式算法等3种加权方法构建出了2组共6种同名组合代理模型,并对6种典型的函数问题进行了测试;分析了不同训练样本容量、加权方法以及待测函数复杂程度对克里金和径向基函数2类同名代理模型性能的影响,得出了构建其优性同名组合代理模型的相关规律。结果表明:克里金和径向基函数同名组合代理模型的性能在小训练样本容量时易表现优性,但精度不高;在训练样本充足时,同名组合代理模型精度趋于最优子代理模型;且同名组合代理模型性能受测试问题阶数影响不大,更适用于非线性度较高的问题;而采用反比例平均化加权方法构建的同名组合代理模型性能优于另外2种加权方法;此外,同名组合代理模型具有更好的鲁棒性和普适性。
The surrogate model is a key technology in numerical optimization.To explore the performance of the homogeneous ensemble of surrogate models(HO-ES)based on kriging(KRG)or radial basis function(RBF),two sets of six types of HO-ES were constructed.These sets utilized six KRG surrogate models with different covari-ance functions and five RBF surrogate models with varying kernel functions as the base surrogates.Three types of weighted average methods were employed:simple average weighing,weight factor selection based on prediction va-riance in inverse proportion,and weight factor selection based on the generalized mean square cross-validation er-ror.Six representative test function problems were assessed.The effects of different training sample sizes,weighting average methods,and the complexity of the test function on the performance of the HO-ES based on KRG or RBF were explored.The rules of constructing the superior HO-ES were summarized.The results demonstrate that the HO-ES based on KRG or RBF performs significantly better when the training sample size is small,but the accuracy remains inadequate.The accuracy of HO-ES approaches that of the best individual surrogate model with an ade-quate training sample size.Furthermore,the performance of HO-ES is not affected by the order of the test function,but it is particularly well suited for highly nonlinear problems.Notably,the HO-ES constructed by weight factor se-lection based on prediction variance in inverse proportion outperforms the two other weighting methods.Finally,the HO-ES has better robustness and universality.
作者
刘鹏
欧阳宇文
范立云
张如琴
LIU Peng;OUYANG Yuwen;FAN Liyun;ZHANG Ruqin(College of Mechanical and Vehicle Engineering,Changsha University of Science&Technology,Changsha 410114,China;College of Power and Energy Engineering,Harbin Engineering University,Harbin 150001,China)
出处
《哈尔滨工程大学学报》
北大核心
2025年第6期1197-1208,共12页
Journal of Harbin Engineering University
基金
国家自然科学基金项目(52001032,52071106)
湖南省自然科学基金项目(2021JJ40588)
湖南省教育厅科学研究优秀青年项目(23B0305)。
关键词
代理模型
同名组合
克里金
径向基函数
加权方法
试验设计
碗型函数
谷型函数
多峰函数
surrogate model
homogeneous ensemble
kriging
radial basis functions
weighted average method
design of experiment
bowl-shaped function
valley-shaped function
multimodal function
作者简介
通信作者:刘鹏,男,副教授,硕士生导师,E-mail:hrbdllp@163.com.
