Abstract
Surrogate-based global optimization (SBO) has gained rapid dominance in engineering design. However, traditional SBO method over entire design space with large size interval would be considerably time-consuming. In order to improve the optimization efficiency in SBO, an adaptive design space reconstruction (ADS) method based on fuzzy clustering method and effective sample points is proposed in this paper. Fuzzy c mean clustering method is applied to divide the initial design space into several sub-regions from which we choose the sub-region which is most likely to contain the global optima. During the optimization process, effective sample points are collected to be the center of new space constructed by trust region method, instead of a single sample point, to keep optimization from getting trapped in local minimums. Then the optimization search will be managed in the reconstructed promising sub-region. We test and verify the proposed method with the airfoil drag minimization problems proposed by Aerodynamic Design Optimization Discussion Group (ADODG), which could demonstrate that better results can be obtained within the reconstructed design space with high efficiency.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Queipo, N.V., Haftka, R.T., Wei, S., Goel, T., Vaidyanathan, R., Tucker, P.K.: Surrogate-based analysis and optimization. Prog. Aerosp. Sci. 41(1), 1–28 (2005)
Fernández-Godino, M.G., Haftka, R.T., Balachandar, S., Gogu, C., Bartoli, N., Dubreuil, S.: Noise filtering and uncertainty quantification in surrogate based optimization. In: 2018 AIAA Non-Deterministic Approaches Conference (2018)
Soilahoudine, M., Gogu, C., Bes, C.: Accelerated adaptive surrogate-based optimization through reduced-order modeling. AIAA J. 55(5), 1681–1694 (2017). https://doi.org/10.2514/1.j055252
Ghoman, S., Wang, Z., Ping, C., Kapania, R.: A POD-based reduced order design scheme for shape optimization of air vehicles. In: AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference AIAA/ASME/AHS Adaptive Structures Conference AIAA (2013)
Berguin, S.H., Mavris, D.N.: Dimensionality reduction using principal component analysis applied to the gradient. AIAA J. 53(4), 1078–1090 (2014)
Capristan, F.M., Alonso, J.J.: Active subspaces applied to range safety analysis and optimization. In: 17th AIAA Non-Deterministic Approaches Conference (2015)
Viswanath, A., Forrester, A.I.J., Keane, A.J.: Constrained design optimization using generative topographic mapping. AIAA J. 52(5), 1010–1023 (2014)
Chen, W., Chiu, K., Fuge, M.: Aerodynamic design optimization and shape exploration using generative adversarial networks. In: AIAA Scitech 2019 Forum (2019)
Wang, G.G., Simpson, T.: Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization. Eng. Optim. 36(3), 313–335 (2004)
Tseng, H.H., Wang, S.W., Chen, J.Y., Liu, C.N.J.: A novel design space reduction method for efficient simulation-based optimization. In: IEEE International Symposium on Circuits & Systems (2014)
Wang, Y., Cai, Z., Zhou, Y.: Accelerating adaptive trade-off model using shrinking space technique for constrained evolutionary optimization. Int. J. Numer. Methods Eng. 77(11), 1501–1534 (2010)
Long, T., Li, X., Shi, R., Liu, J., Guo, X., Liu, L.: Gradient-free trust-region-based adaptive response surface method for expensive aircraft optimization. AIAA J. 56(2), 862–873 (2018). https://doi.org/10.2514/1.j054779
Bezdek, J.C.: Pattern recognition with fuzzy objective function algorithms. Adv. Appl. Pattern Recognit. 22(1171), 203–239 (1981)
Powell, M.J.D.: On the global convergence of trust region algorithms for unconstrained minimization. Math. Program. 29(3), 297–303 (1984)
Sun, Z.B., Sun, Y.Y., Li, Y., Liu, K.P.: A new trust region–sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control. Eng. Optim. 51(6), 1071–1096 (2019)
McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1), 55–61 (2000)
Chen, P.H., Lin, C.J., Scholkopf, B.: A tutorial on v-support vector machines. Appl. Stoch. Models Bus. Ind. 21(2), 111–136 (2005)
Masters, D.A., Taylor, N.J., Rendall, T., Allen, C.B.: Progressive subdivision curves for aerodynamic shape optimisation. In: 54th AIAA Aerospace Sciences Meeting (2016)
Nadarajah, S.: Adjoint-based aerodynamic optimization of benchmark problems. In: 53rd AIAA Aerospace Sciences Meeting (2015)
Poole, D.J., Allen, C.B., Rendall, T.: Control point-based aerodynamic shape optimization applied to AIAA ADODG test cases. AIAA J. (2015)
Carrier, G., et al.: Gradient-based aerodynamic optimization with the elsA software. In: 52nd Aerospace Sciences Meeting - AIAA Scitech (2014)
Acknowledgement
The authors would like to acknowledge the financial support received from the key laboratory funding with the reference number 6142201200106 and natural science funding with the reference number 11772266.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Zuo, Y., Wang, C., Zhang, W., Xia, L., Gao, Z. (2022). Adaptive Design Space Reconstruction Method in Surrogate Based Global Optimization. In: Neri, F., Du, KL., Varadarajan, V.K., Angel-Antonio, SB., Jiang, Z. (eds) Computer and Communication Engineering. CCCE 2022. Communications in Computer and Information Science, vol 1630. Springer, Cham. https://doi.org/10.1007/978-3-031-17422-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-17422-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-17421-6
Online ISBN: 978-3-031-17422-3
eBook Packages: Computer ScienceComputer Science (R0)