Hybrid meta-model-based design space exploration method for expensive problems

Multiple meta-models used together in the search process at least can offer an insurance against the poorly fitted meta-models and can improve robustness of the predictions, compared with the single meta-model based methods. In this work, a hybrid meta-model-based design space exploration (HMDSE) method is proposed. In the proposed method, a part of the current expensive points which are evaluated by the expensive problems to be solved are used firstly to construct a so-called important region. And then, three representative meta-models, kriging, radial basis functions (RBF), and quadratic function (QF), are used in the search of the obtained important region. To avoid the local minima, the remaining region will be searched simultaneously. In addition, the whole design space will also be searched to further demonstrate the global optimum. Through test by six benchmark math functions with design variables ranging from 10 to 24, the proposed HMDSE method shows great accuracy, efficiency, and robustness compared with the efficient global optimization (EGO). Then, it is applied in a practical vehicle lightweight design problem with 30 design variables, achieving desired results.

[1]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[2]  Richard H. Byrd,et al.  A Trust Region Algorithm for Nonlinearly Constrained Optimization , 1987 .

[3]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[4]  Zuomin Dong,et al.  Hybrid and adaptive meta-model-based global optimization , 2012 .

[5]  Raphael T. Haftka,et al.  Making the Most Out of Surrogate Models: Tricks of the Trade , 2010, DAC 2010.

[6]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[7]  H. Fang,et al.  Global response approximation with radial basis functions , 2006 .

[8]  Jian Liu,et al.  An efficient ensemble of radial basis functions method based on quadratic programming , 2016 .

[9]  D G Krige,et al.  A statistical approach to some mine valuation and allied problems on the Witwatersrand , 2015 .

[10]  Richard A. Tapia,et al.  A trust region strategy for nonlinear equality constrained op-timization , 1984 .

[11]  Yizhong Wu,et al.  An adaptive metamodel-based global optimization algorithm for black-box type problems , 2015 .

[12]  Jaewook Lee,et al.  A novel three-phase trajectory informed search methodology for global optimization , 2007, J. Glob. Optim..

[13]  M. Rais-Rohani,et al.  Ensemble of metamodels with optimized weight factors , 2008 .

[14]  G. Fadel,et al.  Automatic evaluation of move-limits in structural optimization , 1993 .

[15]  Layne T. Watson,et al.  Efficient global optimization algorithm assisted by multiple surrogate techniques , 2012, Journal of Global Optimization.

[16]  T. Simpson,et al.  Analysis of support vector regression for approximation of complex engineering analyses , 2005, DAC 2003.

[17]  N. Cressie.  Spatial prediction and ordinary kriging , 1988 .

[18]  Douglass J. Wilde,et al.  Globally optimal design , 1978 .

[19]  Ernesto P. Adorio,et al.  MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization , 2005 .

[20]  R. Haftka,et al.  Ensemble of surrogates , 2007 .

[21]  Lei Zhang,et al.  Multiple meta-models based design space differentiation method for expensive problems , 2018 .

[22]  Dong-Hoon Choi,et al.  Pointwise ensemble of meta-models using v nearest points cross-validation , 2014 .

[23]  Wallace G. Ferreira,et al.  Ensemble of metamodels: the augmented least squares approach , 2016 .

[24]  J. Renaud,et al.  New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2 , 1998 .

[25]  R. Grandhi,et al.  A global structural optimization technique using an interval method , 2001 .

[26]  G. G. Wang,et al.  Mode-pursuing sampling method for global optimization on expensive black-box functions , 2004 .

[27]  L. Watson,et al.  Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization , 1998 .

[28]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[29]  Runze Li,et al.  Design and Modeling for Computer Experiments , 2005 .

[30]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[31]  Wallace G. Ferreira,et al.  Ensemble of metamodels: extensions of the least squares approach to efficient global optimization , 2017 .

[32]  Shutian Liu,et al.  Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures , 2016 .

[33]  Panos M. Pardalos,et al.  Filled functions for unconstrained global optimization , 2001, J. Glob. Optim..

[34]  G. Gary Wang,et al.  ADAPTIVE RESPONSE SURFACE METHOD - A GLOBAL OPTIMIZATION SCHEME FOR APPROXIMATION-BASED DESIGN PROBLEMS , 2001 .

[35]  G. G. Wang,et al.  Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points , 2003 .

[36]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007 .

[37]  S. Rippa,et al.  Numerical Procedures for Surface Fitting of Scattered Data by Radial Functions , 1986 .

[38]  J. Friedman.  Multivariate adaptive regression splines , 1990 .

[39]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[40]  Pengcheng Ye,et al.  Global optimization method using ensemble of metamodels based on fuzzy clustering for design space reduction , 2017, Engineering with Computers.

[41]  J. Barthelemy,et al.  Two point exponential approximation method for structural optimization , 1990 .

[42]  Masoud Rais-Rohani,et al.  A comparative study of metamodeling methods for multiobjective crashworthiness optimization , 2005 .

[43]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[44]  K. K. Choi,et al.  Development and validation of a dynamic metamodel based on stochastic radial basis functions and uncertainty quantification , 2014, Structural and Multidisciplinary Optimization.

[45]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[46]  Jianwei Lu,et al.  Reliability-based design optimization for vehicle occupant protection system based on ensemble of metamodels , 2015 .

[47]  G. G. Wang,et al.  Mode Pursuing Sampling Method for Discrete Variable Optimization on Expensive Black-Box Functions , 2008 .

[48]  Kyung K. Choi,et al.  Metamodeling Method Using Dynamic Kriging for Design Optimization , 2011 .

[49]  Hongbing Fang,et al.  On the ensemble of metamodels with multiple regional optimized weight factors , 2018 .