摘要
针对具有显式约束的昂贵多目标优化问题,提出了一种基于聚类分区混合代理模型(CPEM)的多目标序列优化方法(MOSOM-CPEM).在MOSOM-CPEM中引入了约束域最优拉丁超立方设计(CDOLHD),使其能够在边界形状复杂的可行域内构造样本点.多区域混合代理模型(EM-MROWF)中的可行域划分方法在分割非矩形域时将导致部分区域样本点数量较少从而影响该区域混合代理模型的预测精度.为了解决这一缺陷,在CPEM中提出了一种基于K-means聚类的可行域分区方法和相应的边界光滑方法.CPEM与多项式响应面(PRS)、径向基函数(RBF)、克里金(KRG)模型和两种混合代理模型(GOEL和ACAR)在10个测试函数上进行了拟合精度比较.结果表明,CPEM的整体拟合精度优于对比的代理模型,证实了所提出的可行域分区方法的有效性.MOSOM-CPEM在CEC2021中的6个工程约束多目标优化问题上与其他基于代理模型的优化方法进行了比较.结果表明,在使用相同的样本点数量的前提下,MOSOM-CPEM获得的Pareto前沿收敛性和分布性更好.MOSOM-CPEM应用于履带式起重机超长桁架臂的腰绳结构优化问题,结果证实了其优势,表明MOSOM-CPEM具有较高的工程应用价值.
For the expensive multi-objective optimization problem with explicit constraints,this paper proposes a multiobjective sequential optimization method based on clustering-partitioned ensemble of metamodels(CPEM)called MOSOM-CPEM.The constrained domain optimal Latin hypercube design(CDOLHD)is introduced in MOSOMCPEM,which enables it to obtain sample points in feasible domains with complex boundary shapes.A key challenge in utilizing ensembles of metamodels with multiple regional optimized weight factors(EM-MROWF)lies in the unequal distribution of sample points across non-rectangular domains,often resulting in a dearth of samples in certain regions and subsequently compromising the predictive accuracy of the metamodel ensemble within those areas.To mitigate this limitation,the CPEM incorporates a feasible domain division method grounded in K-means clustering,complemented by a matching boundary smoothing technique.This dual strategy ensures a more balanced and effective distribution of sample points across the entire domain,thereby enhancing the overall fitting accuracy of the model.To validate the efficacy of CPEM,its fitting accuracy is rigorously compared against several established metamodels,including the polynomial response surface(PRS),radial basis function(RBF),kriging(KRG)model,and two types of ensemble of metamodels,namely GOEL and ACAR.The results show that the fitting accuracy of CPEM is better than the compared metamodels,confirming the effectiveness of the proposed feasible domain division method.Furthermore,the performance of MOSOM-CPEM is benchmarked against other metamodel-based optimization techniques within the context of six constrained multi-objective optimization problems featured in the CEC2021 competition.The findings reveal that,when employing an identical number of sample points,the Pareto fronts yielded by MOSOM-CPEM exhibit superior convergence and distribution characteristics.MOSOM-CPEM is applied to the optimization problem of the waist rope structure of the extra-long truss boom of crawler cranes,and the results confirm its superiority,indicating that MOSOM-CPEM has high value for engineering applications.
作者
丁家斌
尹汉锋
文桂林
刘杰
Ding Jiabin;Yin Hanfeng;Wen Guilin;Liu Jie(College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410000,China;School of Mechanical Engineering,Yanshan University,Qinhuangdao 066000,Hebei,China)
出处
《力学学报》
EI
CAS
CSCD
北大核心
2024年第10期3051-3068,共18页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家重点研发计划(2022YFB4201501)
国家自然科学基金(12472011,123320020)
湖南省自然科学基金(2021JJ10009)资助项目.
关键词
K-MEANS
聚类
混合代理模型
边界光滑方法
序列优化
多目标优化
K-means clustering
ensemble of metamodels
boundary smoothing methods
sequential optimization
multi-objective optimization
作者简介
通讯作者:尹汉锋,教授,主要研究方向为结构冲击动力学、优化设计理论和方法.E-mail:yinhanfeng@hnu.edu.cn。
