Top

Structural and Multidisciplinary Optimization

Published in:

30-09-2017 | RESEARCH PAPER

Employing partial metamodels for optimization with scarce samples

Authors: Di Wu, Kambiz H. Hajikolaei, G. Gary Wang

Published in: Structural and Multidisciplinary Optimization | Issue 3/2018

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

To deal with high-dimensional, computationally expensive and black-box optimization (HEB) problems, a Partial Metamodel-based Optimization (PMO) method using Radial Basis Function-High Dimensional Model Representation (RBF-HDMR) along with a moving cut-center strategy is developed. To reduce the exponentially increasing cost of building an accurate metamodel for high dimensional problems, partial RBF-HDMR models of selected design variables are constructed at every iteration in the proposed strategy based on sensitivity analysis. After every iteration, the cut center of RBF-HDMR is moved to the most recent optimum point in order to pursue the optimum. Numerical tests show that the PMO method in general performs better than optimization with a complete RBF-HDMR for high-dimensional problems in terms of both effectiveness and efficiency. To improve the performance of the PMO method, a trust region based PMO (TR-PMO) is developed. When the allowed number of function calls is scarce, TR-PMO has advantages over compared metamodel-based optimization methods. The proposed method was then successfully applied to an airfoil design problem. The use of a partial metamodel for the purpose of optimization shows promises and may lead to development of other novel algorithms.

previous article Topology optimization of thermal actuator and its support using the level set based multiple–type boundary method and sensitivity analysis based on constrained variational principle

next article Automatic blade blend modeling and hexahedral mesh regeneration for aircraft engine optimization

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Adorio E, Diliman U (2005)MVF–multivariate test functions library in c for unconstrained global optimization, Available at: http://geocities.com/eadorio/mvf.pdf

Alexandrov NM, Dennis JE, Lewis RM, Torczon V (1998) A trust-region framework for managing the use of approximation models in optimization. Struct Optim 15(1):16–23CrossRef

Allison JT, Kokkolaras M, Papalambros PY (2009) Optimal Partitioning and Coordination Decisions in Decomposition-Based Design Optimization. J Mech Des 131(8):81008CrossRef

Bates RA, Buck RJ, Riccomagno E, Wynn HP (1996) Experimental Design and Observation for Large Systems. J R Stat Soc Ser B 58(1):77–94MathSciNetMATH

Bloebaum C, Hajela P, Sobieszczanski-Sobieski J (1992) Non-Hierarchic System Decomposition in Structural Optimization. Eng Optim 19(3):171–186CrossRef

Cai X, Qiu H, Gao L, Yang P, Shao X (2016) An enhanced RBF-HDMR integrated with an adaptive sampling method for approximating high dimensional problems in engineering design. Struct Multidiscip Optim 53(6):1209–1229CrossRef

Cheng GH, Younis A, Haji Hajikolaei K, Gary Wang G (2015) Trust Region Based Mode Pursuing Sampling Method for Global Optimization of High Dimensional Design Problems. J Mech Des 137(2):21407CrossRef

Cressie N (1988) Spatial prediction and ordinary kriging. Math Geol 20(4):405–421MathSciNetCrossRefMATH

Duan X, Wang GG, Kang X, Niu Q, Naterer G, Peng Q (2009) Performance study of mode-pursuing sampling method. Eng Optim 41(1):1–21CrossRef

Fang H, Horstemeyer MF (2006) Global response approximation with radial basis functions. Eng Optim 38(4):407–424MathSciNetCrossRef

Friedman JH (1991) Multivariate Adaptive Regression Splines. Ann Stat 19(1):1–67MathSciNetCrossRefMATH

Goldberg DE (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman Publishing Co., Inc., BostonMATH

Haji Hajikolaei K, Cheng GH, Wang GG (2015) Optimization on Metamodeling-Supported Iterative Decomposition. J Mech Des 138(2):21401CrossRef

Hajikolaei KH, Wang GG (2013) High Dimensional Model Representation with Principal Component Analysis. J Mech Des 36(1):11003CrossRef

Hajikolaei KH, Pirmoradi Z, Cheng GH, Wang GG (2014) Decomposition for Large Scale Global Optimization Based on Quantified Variable Correlations Uncovered by Metamodeling. Eng Optim 47(4):429–452CrossRef

Hajikolaei KH, Cheng GH, Wang GG (2016) Optimization on Metamodeling- Supported Iterative Decomposition. ASME J Mech Des 138:21401CrossRef

Huang Z, Qiu H, Zhao M, Cai X, Gao L (2015) An adaptive SVR-HDMR model for approximating high dimensional problems. Eng Comput Int J Comput Eng Softw 32(3):643–667

Jones DR, Law C (1993) Lipschitzian Optimization Without the Lipschitz Constant. J Optim Theory Appl 79(1):157–181MathSciNetCrossRefMATH

Jones DR, Schonlau M, Welch WJ (1998) Efficient Global Optimization of Expensive Black-Box Functions. J Glob Optim 13(4):455–492MathSciNetCrossRefMATH

Kaya H, Kaplan M, Saygın H (2004) A recursive algorithm for finding HDMR terms for sensitivity analysis. Comput Phys Commun 158(2):106–112CrossRefMATH

Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks, Perth, Western Australia, pp 1942–1948

Kim HM, Michelena NF, Papalambros PY, Jiang T (2003) Target Cascading in Optimal System Design. J Mech Des 125(3):474CrossRef

Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by Simulated Annealing. Science 220(4598):671–680MathSciNetCrossRefMATH

Kulfan B, Bussoletti J (2006) ‘Fundamental’ parameteric geometry representations for aircraft component shapes. 11th aiaa/issmo multidiscip. Anal. Optim. Conf., 1, pp 547–591

Liu Y, Yao X, Zhao Q, Higuchi T (2001) Scaling Up Fast Evolutionary Programming with Cooperative Coevolution. In: Proceedings of the 2001 Congress on Evolutionary Computation, Seoul, pp 1101–1108

Michelena N, Papalambros P, Park H, Kulkarni D (1999) Hierarchical Overlapping Coordination for Large-Scale Optimization by Decomposition. AIAA J 37(7):890–896CrossRef

Papadrakakis M, Lagaros ND, Tsompanakis Y (1998) Structural optimization using evolution strategies and neural networks. Comput Methods Appl Mech Eng 156(1–4):309–333CrossRefMATH

Potter M, De Jong K (1994) A Cooperative Coevolutionary Approach to Function Optimization. In: Proceedings of the Third Conference on Parallel Problem Solving from Nature, Springer-Verlag, pp 249–257

Rabitz H, Alis Ö, Alış ÖF (1999) General foundations of high-dimensional model representations. J Math Chem 25(2–3):197–233MathSciNetCrossRefMATH

Rassokhin DN, Lobanov VS, Drive S (2000) Nonlinear Mapping of Massive Data Sets by Fuzzy Clustering and Neural Networks. J Comput Chem 22(4):373–386CrossRef

Schittkowski K (1987) More Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin

Shan S, Wang GG (2009) Development of Adaptive RBF-HDMR Model for Approximating High Dimensional Problems. Volume 5: 35th Design Automation Conference, Parts A and B, ASME, pp 727–740

Shan S, Wang GG (2010a) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41(2):219–241MathSciNetCrossRefMATH

Shan S, Wang GG (2010b) Metamodeling for High Dimensional Simulation-Based Design Problems. J Mech Des 132:51009CrossRef

Shi Y, Teng H, Li Z (2005) Cooperative Co-evolutionary Differential Evolution for Function Optimization. In: Proceedings of the First International Conference on Natural Computation, Springer-Verlag, pp 1080–1088

Sobol′ I (1993) Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp 1(4):407–414MathSciNetMATH

Somorjai RL, Dolenko B, Demko A, Mandelzweig M, Nikulin AE, Baumgartner R, Pizzi NJ (2004) Mapping high-dimensional data onto a relative distance plane--an exact method for visualizing and characterizing high-dimensional patterns. J Biomed Inform 37(5):366–379CrossRef

Srivastava A, Hacker K, Lewis K, Simpson TW (2004) A method for using legacy data for metamodel-based design of large-scale systems. Struct Multidiscip Optim 28(2):146–155

Wang GG, Shan S, (2004) Design Space Reduction for Multi-objective Optimization and Robust Design Optimization Problems. SAE Trans J Mater Manuf, pp 101–110. https://doi.org/10.4271/2004-01-0240

Wang L, Shan S, Wang GG (2004) Mode-pursuing sampling method for global optimization on expensive black-box functions. Eng Optim 36(4):419–438CrossRef

Wang H, Tang L, Li GY (2011) Adaptive MLS-HDMR metamodeling techniques for high dimensional problems. Expert Syst Appl 38(11):14117–14126

Winer EH, Bloebaum CL (2002) Development of visual design steering as an aid in large-scale multidisciplinary design optimization. Part I : method development. Struct Multidiscip Optim 23(6):412–424CrossRef

XFOIL (2013) [Online]. Available at: http://web.mit.edu/drela/Public/web/xfoil/

Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci (Ny) 178(15):2985–2999MathSciNetCrossRefMATH

Title: Employing partial metamodels for optimization with scarce samples
Authors: Di Wu
Kambiz H. Hajikolaei
G. Gary Wang
Publication date: 30-09-2017
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 3/2018
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-017-1815-0

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2018

Topology optimization of thermal actuator and its support using the level set based multiple–type boundary method and sensitivity analysis based on constrained variational principle

An intelligent sampling approach for metamodel-based multi-objective optimization with guidance of the adaptive weighted-sum method

Active expansion sampling for learning feasible domains in an unbounded input space

Thanks to our Reviewers

Topological metallic structure design for microwave applications using a modified interpolation scheme

Optimum energy-based design of BRB frames using nonlinear response history analysis

Premium Partners