Abstract
This article presents a novel model management technique to be implemented in population-based heuristic optimization. This technique adaptively selects different computational models (both physics-based models and surrogate models) to be used during optimization, with the overall objective to result in optimal designs with high fidelity function estimates at a reasonable computational expense. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low fidelity models such as given by the vortex lattice method, or a high fidelity finite volume model, or a surrogate model that substitutes the high-fidelity model. The information from these models with different levels of fidelity is integrated into the heuristic optimization process using the new adaptive model switching (AMS) technique. The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criterion is based on whether the uncertainty associated with the current model output dominates the latest improvement of the relative fitness function, where both the model output uncertainty and the function improvement (across the population) are expressed as probability distributions. For practical implementation, a measure of critical probability is used to regulate the degree of error that will be allowed, i.e., the fraction of instances where the improvement will be allowed to be lower than the model error, without having to change the model. In the absence of this critical probability, model management might become too conservative, leading to premature model-switching and thus higher computing expense. The proposed AMS-based optimization is applied to two design problems through Particle Swarm Optimization, which are: (i) Airfoil design, and (ii) Cantilever composite beam design. The application case studies of AMS illustrated: (i) the computational advantage of this method over purely high fidelity model-based optimization, and (ii) the accuracy advantage of this method over purely low fidelity model-based optimization.
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References
Hutchison MG, Unger ER, Mason WH, Grossman B, Haftka RT (1994) Variable-complexity aerodynamic optimization of a high-speed civil transport wing. J Aircr 31(1):110–116
Jeong S, Murayama M, Yamamoto K (2005) Efficient optimization design method using kriging model. J Aircr 42(2):413–420
Oktem H, Erzurumlu T, Kurtaran H (2005) Application of response surface methodology in the optimization of cutting conditions for surface roughness. J Mater Proces Technol 170(1):11–16
Simpson T, Booker A, Ghosh D, Giunta A, Koch P, Yang RJ (2004) Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct Multidiscip Optim 27(5):302–313
Simpson T, Toropov V, Balabanov V, Viana F (2008) Design and analysis of computer experiments in multidisciplinary design optimization: a review of how far we have come or not. In: 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, Victoria, Canada
Wang G, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–381
Jin R, Chen W, Simpson TW (2000) Comparative studies of metamodeling techniques under multiple modeling criteria. AIAA (4801)
Forrester A, Keane A (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45(1–3):50–79
Simpson T, Korte J, Mauery T, Mistree F (2001) Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J 39(12):2233–2241
Choi K, Young B, Yang R (2001) Moving least square method for reliability-based design optimization. In: 4th world congress of structural and multidisciplinary optimization, Dalian, China, pp 4–8
Toropov VV, Schramm U, Sahai A, Jones RD, Zeguer T (2005) Design optimization and stochastic analysis based on the moving least squares method. In: 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro
Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76:1905–1915
Clarke SM, Griebsch JH, Simpson TW (2005) Analysis of support vector regression for approximation of complex engineering analyses. J Mech Des 127(6): 1077–1087
Yegnanarayana B (2004) Artificial neural networks. PHI Learning Pvt, Ltd, New Delhi
Zhang J, Chowdhury S, Messac A (2012) An adaptive hybrid surrogate model. Struct Multidiscip Optim 46(2):223–238
Mehmani A, Chowdhury S, Messac A (2014) A novel approach to simultaneous selection of surrogate models, constitutive kernels, and hyper-parameter values. In: 55th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference. National Harbor, MD, USA
Zhang J, Chowdhury S, Mehmani A, Messac A (2014) Characterizing uncertainty attributable to surrogate models. J Mech Des 136(3):031004
Barthelemy JF, Haftka R (1993) Approximation concepts for optimum structural design (in a review). Struct Optim 5(3):129–144
Haftka RT (1991) Combining global and local approximations. AIAA J 29(9):1523–1525
Keane A, Nair P (2005) Computational approaches for aerospace design: the pursuit of excellence. Wiley, Chichester
Zadeh PM, Mehmani A (2010) Multidisciplinary design optimization using variable fidelity modeling: application to a wing based on high fidelity models. In: Third international conference on multidisciplinary design optimziation, Paris, France
Zadeh PM, Toropov VV, Wood AS (2009) Metamodel-based collaborative optimization framework. Struct Multidiscip Optim 38(2):103–115
Alexandrov NM, Lewis RM, Gumbert C, Green L, Newman P (1999) Optimization with variable-fidelity models applied to wing design. Technical report, ICASE, Institute for Computer Applications in Science and Engineering. NASA Langley Research Center, Hampton, Virginia
Booker AJ, Dennis JE, Frank PD, Serafini DB, Torczon V, Trosset MW (1999) A rigorous framework for optimization of expensive functions by surrogates. Struct Optim 17(1):1–13
Marduel X, Tribes C, Trepanier JY (2006) Variable-fidelity optimization: efficiency and robustness. Optim Eng 7(4):479–500
Robinson TD, Eldred MS, Willcox KE, Haimes R (2008) Surrogate-based optimization using multifidelity models with variable parameterization and corrected space mapping. AIAA J 46(11):2814–2822
Rodriguez JF, Perez VM, Padmanabhan D, Renaud JE (2001) Sequential approximate optimization using variable fidelity response surface approximations. Struct Multidiscip Optim 22(1):24–34
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):16–23
Toropov VV, Alvarez LF (1998) Development of mars-multipoint approximation method based on the response surface fitting. AIAA J 98: 4769
Forrester A, Sobester A, Keane A (2008) Engineering design via surrogate modelling: a practical guide. Wiley, Chichester
Sugiyama M (2006) Active learning in approximately linear regression based on conditional expectation of generalization error. J Mach Learn Res 7:141–166
Trosset MW, Torczon V (1997) Numerical optimization using computer experiments. Technicl report, DTIC Document
Bichon BJ, Eldred MS, Mahadevan S, McFarland JM (2013) Efficient global surrogate modeling for reliability-based design optimization. J Mech Des 135(1):011, 009
Duan Q, Sorooshian S, Gupta V (1992) Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res 28(4):1015–1031
Jones D, Schonlau M, Welch W (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492
Kleijnen JP, Beers WV, Nieuwenhuyse IV (2012) Expected improvement in efficient global optimization through bootstrapped kriging. J Glob Optim 54(1):59–73
Jin Y, Olhofer M, Sendhoff B (2002) A framework for evolutionary optimization with approximate fitness functions. IEEE Trans Evolut Comput 6(5):481–494
Graning L, Jin Y, Sendhoff B (2007) Individual-based management of meta-models for evolutionary optimization with application to three-dimensional blade optimization. In: Evolutionary computation in dynamic and uncertain environments, pp 225–250
Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):3–12
Ulmer H, Streichert F, Zell A (2004) Evolution strategies with controlled model assistance. In: Evolutionary computation, 2004, IEEE congress on CEC2004, vol 2, pp 1569–1576
Jin Y, Sendhoff B (2004) Reducing fitness evaluations using clustering techniques and neural network ensembles. In: Genetic and evolutionary computation, GECCO 2004, pp 688–699
Chowdhury S, Tong W, Messac A, Zhang J (2013) A mixed-discrete particle swarm optimization algorithm with explicit diversity-preservation. Struct Multidiscip Optim 47(3):367–388
Epanechnikov V (1969) Non-parametric estimation of a multivariate probability density. Theory Probab Appl 14:153–158
Duong T, Hazelton M (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Nonparametric Stat 15(1):17–30
Mehmani A, Chowdhury S, Messac A (2015) Predictive quantification of surrogate model fidelity based on modal variations with sample density. Struct Multidiscip Optim (Accepted)
Mehmani A, Chowdhury S, Zhang J, Tong W, Messac A (2013) Quantifying regional error in surrogates by modeling its relationship with sample density. In: 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Boston, MA, USA
Chowdhury S, Mehmani A, Messac A (2014) Concurrent surrogate model selection (cosmos) based on predictive estimation of model fidelity. In: ASME 2014 international design engineering technical conferences (IDETC), Buffalo, NY
Kennedy J, Eberhart RC (1995) Particle swarmoptimization. In: IEEE international conference on neural networks, vol 6, pp 1942–1948
Coelho F, Breitkopf P, Knopf-Lenoir C (2008) Model reduction for multidisciplinary optimization: application to a 2d wing. Struct Multidiscip Optim 37(1):29–48
Acknowledgments
Support from the National Science Foundation Awards CMMI-1100948 and CMMI-1437746 is gratefully acknowledged. Any opinions, findings, conclusions, or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the NSF.
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Mehmani, A., Chowdhury, S., Tong, W., Messac, A. (2015). Adaptive Switching of Variable-Fidelity Models in Population-Based Optimization. In: Lagaros, N., Papadrakakis, M. (eds) Engineering and Applied Sciences Optimization. Computational Methods in Applied Sciences, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-18320-6_10
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