Global optimization method using adaptive and parallel ensemble of surrogates for engineering design optimization

Abstract As a robust and efficient technique for global optimization, surrogate-based optimization method has been widely used in dealing with the complicated and computation-intensive engineering design optimization problems. It’s hard to select an appropriate surrogate model without knowing the behaviour of the real system a priori in most cases. To overcome this difficulty, a global optimization method using an adaptive and parallel ensemble of surrogates combining three representative surrogate models with optimized weight factors has been proposed. The selection of weight factors is treated as an optimization problem with the desired solution being one that minimizes the generalized mean square cross-validation error. The proposed optimization method is tested by considering several well-known numerical examples and one industrial problem compared with other optimization methods. The results show that the proposed optimization method can be a robust and efficient approach in surrogate-based optimization for locating the global optimum.

[1]  Byeongdo Kim,et al.  Comparison study on the accuracy of metamodeling technique for non-convex functions , 2009 .

[2]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[3]  Achille Messac,et al.  An adaptive hybrid surrogate model , 2012, Structural and Multidisciplinary Optimization.

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

[5]  A. Messac,et al.  Adaptive Hybrid Surrogate Modeling for Complex Systems , 2013 .

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

[7]  Néstor V. Queipo,et al.  Toward an optimal ensemble of kernel-based approximations with engineering applications , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

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

[9]  Carolyn Conner Seepersad,et al.  A Comparative Study of Metamodeling Techniques for Predictive Process Control of Welding Applications , 2009 .

[10]  K. Yamazaki,et al.  Sequential Approximate Optimization using Radial Basis Function network for engineering optimization , 2011 .

[11]  T. Simpson,et al.  Use of Kriging Models to Approximate Deterministic Computer Models , 2005 .

[12]  Farrokh Mistree,et al.  Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size , 1999 .

[13]  R. Haftka,et al.  Multiple surrogates: how cross-validation errors can help us to obtain the best predictor , 2009 .

[14]  Christine A. Shoemaker,et al.  Parallel Stochastic Global Optimization Using Radial Basis Functions , 2009, INFORMS J. Comput..

[15]  Masoud Rais-Rohani,et al.  Ensemble of Metamodels with Optimized Weight Factors , 2008 .

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

[17]  R. Haftka,et al.  Surrogate-based Optimization with Parallel Simulations using the Probability of Improvement , 2010 .

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

[19]  Sanjay B. Joshi,et al.  Metamodeling: Radial basis functions, versus polynomials , 2002, Eur. J. Oper. Res..

[20]  Andy J. Keane,et al.  On the Design of Optimization Strategies Based on Global Response Surface Approximation Models , 2005, J. Glob. Optim..

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

[22]  Tapabrata Ray,et al.  ENGINEERING DESIGN OPTIMIZATION USING A SWARM WITH AN INTELLIGENT INFORMATION SHARING AMONG INDIVIDUALS , 2001 .

[23]  J. F. Rodríguez,et al.  Sequential approximate optimization using variable fidelity response surface approximations , 2000 .

[24]  Xiao Jian Zhou,et al.  Ensemble of surrogates with recursive arithmetic average , 2011 .

[25]  Christine A. Shoemaker,et al.  Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems , 2014, J. Glob. Optim..

[26]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[27]  Bithin Datta,et al.  Coupled simulation‐optimization model for coastal aquifer management using genetic programming‐based ensemble surrogate models and multiple‐realization optimization , 2011 .

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

[29]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

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

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

[32]  Sidney Addelman,et al.  trans-Dimethanolbis(1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionato)zinc(II) , 2008, Acta crystallographica. Section E, Structure reports online.

[33]  Peng Wang,et al.  A Novel Latin Hypercube Algorithm via Translational Propagation , 2014, TheScientificWorldJournal.

[34]  Salvador Pintos,et al.  An Optimization Methodology of Alkaline-Surfactant-Polymer Flooding Processes Using Field Scale Numerical Simulation and Multiple Surrogates , 2004 .

[35]  Jooyoung Park,et al.  Approximation and Radial-Basis-Function Networks , 1993, Neural Computation.

[36]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007, DAC 2006.

[37]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

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