A Global Optimization Algorithm Based on Incremental Metamodel Method

Abstract

Abstract:

A new global optimization method based on incremental metamodel was proposed for the complex simulation model problem. Firstly, to overcome the defects of existing incremental Latin hyper-cube design, which was hard to control the number of sampling points and limited to multiples, we proposed an improved incremental Latin hyper-cube sampling method based on subtraction rule idea.Secondly, combined incremental Latin hyper-cube design and the method of incremental update radial basis functions, we proposed a new efficient global optimization algorithm. Finally, the method was applied to a pressure vessel design problem and the results of the example demonstrate the efficiency and engineering practicability of the presented method.

Key words: metamodel, global optimization, radial basis function, incremental Latin hyper-cube sampling

摘要：

针对复杂仿真模型的全局优化问题，提出一种基于增量元模型方法的全局优化算法。首先，分析了现有增量拉丁超立方采样方法新增点数量难以控制以及其数值必须为原采样点数量的整数倍的缺陷，在此基础上利用减法规则思想改进了增量拉丁超立方采样;其次，将改进后的增量拉丁超立方采样与径向基函数的增量更新方法相结合，提出了一种全新的高效全局优化算法;最后，将该算法应用于压力容器的优化设计，计算结果证明了该方法的实用性与工程有效性。

关键词: 元模型, 全局优化, 径向基函数, 增量拉丁超立方采样

CLC Number:

TP391.9

WEI Cuan-1, TUN Xi-Zhong-2, CHEN Li-Beng-2. A Global Optimization Algorithm Based on Incremental Metamodel Method[J]. China Mechanical Engineering, 2013, 24(5): 623-627.

魏昕1, 吴义忠2, 陈立平2. 一种基于增量元模型方法的全局优化算法[J]. 中国机械工程, 2013, 24(5): 623-627.

References

[1]Gu L A. Comparison of Polynomial Based Regression Models in Vehicle Safety Analysis[C]//Design Engineering Technical Conferences. Pittsburgh：ASME，2001：DAC-21063.
[2]Wang G G，Shan S. Review of Metamodeling Techniques in Surpport of Engineering Design Optimization[J]. Journal of Mechanical Design，2007，129：370-380.
[3]Lin Y. An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design[D]. Atlanta：Georgia Institute of Technology，2004.
[4]Wang G G，Simpson T W. Fuzzy Clustering Based Hierarchical Metamodeling for Space Reduction and Design Optimization[J].Engineering Optimization，2004，36（3）：313-335.
[5]Wild S M，Regis R G，Shoemaker C A. ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions[J]. Sci. Comput.，2008，30（6）：3197-3219.
[6]Gutmann H M. A Radial Basis Function Method for Global Optimization[J]. Journal of Global Optimization, 2001，19: 201-227.
[7]Jones D R，Schonlau M，Welch W. Efficient Global Optimization of Expensive Black-Box Functions[J]. Journal of Global Optimization，1998，13：455-492.
[8]邹林君, 吴义忠, 毛虎平. Kriging模型的增量构造及其在全局优化中的应用[J]. 计算机辅助设计与图形学报，2011，23(4)：649-655.
Zou Linjun, Wu Yizhong, Mao Huping. Incremental Kriging Model Rebuilding Method and Its Application in Efficient Global Optimization[J]. Journal of Computer-Aided Design ＆ Computer Graphics，2011，23(4)：649-655.
[9]Wang G G. Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points[J]. J. Mech. Des.，2003，125：210-220.
[10]吴义忠，陈立平. 多领域物理系统的仿真优化方法[M]. 北京: 科学出版社, 2011.
[11]Cao Y J，Wu Q H. Mechanical Design Optimization by Mixed-Variable Evolutionary Programming[C]//Proceedings of IEEE Conference on Evolutionary Computation.Indianapolis： ICEC，1997：13-16.

[1]	QU Xiaozhang, ZHANG Jiabei, ZHAI Fangzhi. Sensitivity Analysis and Optimization of High Speed Train Cooling Centrifugal Fan Performance [J]. China Mechanical Engineering, 2023, 34(20): 2504-2512.
[2]	WANG Dongjie, WANG Pengjiang, LI Yue, GUO Mingze, ZHENG Weixiong, SHEN Yang, WU Miao. Research on Adaptive Cutting Control Strategy of Roadheader Cutting Arms [J]. China Mechanical Engineering, 2022, 33(20): 2492-2501.
[3]	ZHANG Yang, GAO Shu, HE Wei, CAI Jing. Navigation Trajectory Prediction Method of Inland Ships Based on Multi-model Fusion [J]. China Mechanical Engineering, 2022, 33(10): 1142-1152.
[4]	ZHAO Fuqiang1,2;DENG Hailong1;XIE Canming1;DONG Jing1;LI Yugui1;WANG Tie2. Residence Time Prediction of Waste Particles in Dust Suction Ports for Sweepers in RBFNN Based on Entropy Method [J]. China Mechanical Engineering, 2018, 29(23): 2792-2798.
[5]	LIU Niansi;CAI Yongzhou;GU Jichao;ZHENG Hao. Design Space Differentiation Optimization Method and Its Applications to Vehicle Lightweight Design [J]. China Mechanical Engineering, 2018, 29(05): 597-601,622.
[6]	ZENG Guang, , JIANG Chao, NI Bingyu. Hybrid Reliability Analysis for Flexible Manipulator Vibrations in Engineering Machinery [J]. China Mechanical Engineering, 2017, 28(12): 1400-1405,1412.
[7]	HU Junfeng, ZHENG Changhu, CAI Jianyang. Adaptive Motion Tracking Control of a Micro-manipulation Stage [J]. China Mechanical Engineering, 2017, 28(08): 905-911,916.
[8]	Yu Limin, Xiong Huiyuan, , Zong Zhijian, Wu Yizhong. Multi-objective Robust Design of Electric Vehicle Powertrain Parameters [J]. China Mechanical Engineering, 2016, 27(20): 2828-2834.
[9]	Gu Jichao, Xu Dongyang, Li Guangyao, Gan Nianfei, Fan Tao. Lightweight Design of Vehicle Based on Multiple Hybrid Meta-model Method [J]. China Mechanical Engineering, 2016, 27(14): 1982-1987.
[10]	Ye Ming, Ren Hong, Li Xin. Global Optimization for Electric Vehicle Equipped with EMCVT Based on Shifting Energy [J]. China Mechanical Engineering, 2016, 27(09): 1257-1262.
[11]	Yin Weiyang, Wang Hu, Feng Hui, Tang Long. Inverse Determination of Material Parameters Based on Decoupled GMDH Algorithm [J]. China Mechanical Engineering, 2015, 26(9): 1215-1221.
[12]	Li Kai, Yang Xujing, Zheng Juan. Robust Design Optimization for Stamping Based on Parametric and Metamodel Uncertainty [J]. China Mechanical Engineering, 2015, 26(23): 3234-3239.
[13]	Cheng Junsheng, Yuan Yi, Yu Zhentao, Yuan Hui. Predicative Methods of Tovo-Benasciutti Fatigue Life under Considering Mean Stress Effects [J]. China Mechanical Engineering, 2015, 26(2): 196-199.
[14]	Yang Dan, Zhou Yu, Ye Qingwei, Wang Xiaodong. Extraction of Unit Pulse Response Function Based on Sparse RBF Network Applyed in Rail Anchor Screw [J]. China Mechanical Engineering, 2015, 26(19): 2606-2612.
[15]	Li Aiping, Bao Jin, Li Cong, Liu Xuemei , Xie Nan. Global Optimization with Multi-targets for Rough and Finish End-milling Parameters Based on Minimum Energy Performance [J]. China Mechanical Engineering, 2015, 26(14): 1888-1894.