Advertisement

A developed surrogate-based optimization framework combining HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems

  • Xiaojing Wu
  • Xuhao Peng
  • Weisheng Chen
  • Weiwei ZhangEmail author
Research Paper
  • 57 Downloads

Abstract

The traditional surrogate-based optimization techniques are facing severe challenges for high-dimensional engineering optimization problems. The main challenges are how to overcome metamodeling and optimization difficulties in high-dimensional design space. To solve the above difficulties, a developed surrogate-based optimization framework combining high-dimensional model representation (HDMR)-based modeling technique and teaching-learning-based optimization (TLBO) algorithm is developed. A high-dimensional model can be decomposed into a series of low-dimensional models by HDMR-based modeling technique, which can greatly reduce the difficulty of building high-dimensional model. The TLBO algorithm which has strong optimization ability and non-parameter setting characteristic is introduced to optimize the HDMR-based model to overcome the difficulty of optimization. Several representative functions are selected as examples to verify the developed optimization method for high-dimensional problems. In addition, The developed surrogate-based optimization is applied to solve a typical engineering optimization problem: high-dimensional aerodynamic shape optimization. It can be concluded that the optimization ability of the traditional surrogate-based optimization framework can be improved with assistance of HDMR-based modeling technique and TLBO algorithm for high-dimensional engineering problems.

Keywords

High-dimensional engineering problems Surrogate model High-dimensional model representation (HDMR) Teaching-learning-based optimization (TLBO) Aerodynamic shape optimization 

Notes

Funding information

“111” project of China (No. B17037), the National Science Fund for Excellent Young Scholars (No. 11622220) supported this work, China Postdoctoral Science Foundation (2018 M643588).

References

  1. Cai X, Qiu H, Gao L, al e (2016) An enhanced RBF-HDMR integrated with an adaptive sampling method for approximating high dimensional problems in engineering design. Struct Multidiscip Optim 53(6):1209–1229Google Scholar
  2. Cai X, Qiu H, Gao L et al (2017) Metamodeling for high dimensional design problems by multi-fidelity simulations. Struct Multidiscip Optim 56(1):151–166MathSciNetGoogle Scholar
  3. Chen S, Xiong Y, Chen W (2012) Multiresponse and multistage metamodeling approach for design optimization. AIAA J 47(1):206–218Google Scholar
  4. Chung IB, Park D, Choi DH (2018) Surrogate-based global optimization using an adaptive switching infill sampling criterion for expensive black-box functions. Struct Multidiscip Optim 57:1443–1459MathSciNetGoogle Scholar
  5. Cruz NC, Redondo JL, Álvarez JD, et.al. (2016) A parallel teaching–learning-based optimization procedure for automatic heliostat aiming. J Supercomput 1–16Google Scholar
  6. Duan Y, Cai J, Li Y (2012) Gappy proper orthogonal decomposition-based two-step optimization for airfoil design. AIAA J 50(4):968–971Google Scholar
  7. Dulikravich GS (1992) Aerodynamic shape design and optimization-status and trends. J Aircr 29(29):1020–1026Google Scholar
  8. Forrester AIJ, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aeosp Sci 45(1):50–79Google Scholar
  9. Gao CQ, Zhang WQ, Li XT et al (2017) Mechanism of frequency lock-in in transonic buffeting flow. J Fluid Mech 818:528–561MathSciNetzbMATHGoogle Scholar
  10. Genyuan L, Carey Rosenthal A, Rabitz H (2001) High dimensional model representations. J Phys Chem A 105(33):7765–7777zbMATHGoogle Scholar
  11. Giannakoglou KC, Papadimitriou DI, Kampolis IC (2006) Aerodynamic shape design using evolutionary algorithms and new gradient-assisted metamodels. Comput Methods Appl Mech Eng 195(44–47):6312–6329zbMATHGoogle Scholar
  12. Glaz B, Goel T, Liu L et al (2012) Multiple-surrogate approach to helicopter rotor blade vibration reduction. AIAA J 47(1):271–282Google Scholar
  13. Gomes WJDS, Beck AT (2013) Global structural optimization considering expected consequences of failure and using ANN surrogates. Comput Struct 126(1):56–68Google Scholar
  14. Han ZH, Zimmermann, Goertz S (2012) Alternative cokriging model for variable-fidelity surrogate modeling. AIAA J 50(5):1318–1330Google Scholar
  15. Huang Z, Qiu H, Zhao M et al (2015) An adaptive SVR-HDMR model for approximating high dimensional problems. Eng Comput 32(3):643–667Google Scholar
  16. Iuliano E, Quagliarella D (2013) Proper orthogonal decomposition, surrogate modelling and evolutionary optimization in aerodynamic design. Comput Fluids 84(19):327–350MathSciNetzbMATHGoogle Scholar
  17. Jahangirian A, Shahrokhi A (2011) Aerodynamic shape optimization using efficient evolutionary algorithms and unstructured CFD solver. Comput Fluids 46(1):270–276MathSciNetzbMATHGoogle Scholar
  18. Jeong S, Murayama M, Yamamoto K (2005) Efficient optimization design method using kriging model. J Aircr 42(2):413–420Google Scholar
  19. Jouhaud JC, Sagaut P, Montagnac M et al (2007) A surrogate-model based multi-disciplinary shape optimization method with application to a 2D subsonic airfoil. Comput Fluids 36(3):520–529zbMATHGoogle Scholar
  20. Kieslich CA, Boukouvala F, Floudas CA (2018) Optimization of black-box problems using Smolyak grids and polynomial approximations. J Glob Optim 71:845–869MathSciNetzbMATHGoogle Scholar
  21. Li E, Wang H, Li G (2012) High dimensional model representation (HDMR) coupled intelligent sampling strategy for nonlinear problems. Comput Phys Commun 183(9):1947–1955MathSciNetGoogle Scholar
  22. Liu J, Song WP, Han ZH et al (2017) Efficient aerodynamic shape optimization of transonic wings using a parallel infilling strategy and surrogate models. Struct Multidiscip Optim 55(3):925–943Google Scholar
  23. Liu H, Hervas JR, Ong YS et al (2018) An adaptive RBF-HDMR modeling approach under limited computational budget. Struct Multidiscip Optim 57(3):1–18MathSciNetGoogle Scholar
  24. Mackman TJ, Allen CB, Ghoreyshi M et al (2013) Comparison of adaptive sampling methods for generation of surrogate aerodynamic models. AIAA J 51(4):797–808Google Scholar
  25. Monge F, Monge F (2012) Efficient aerodynamic design through evolutionary programming and support vector regression algorithms. Expert Syst Appl 39(12):10700–10708Google Scholar
  26. Qu X, Zhang R, Liu B et al (2017) An improved TLBO based memetic algorithm for aerodynamic shape optimization. Eng Appl Artif Intell 57:1–15Google Scholar
  27. Queipo NV, Haftka RT, Wei S et al (2005) Surrogate-based analysis and optimization. Prog Aeosp Sci 41(1):1–28Google Scholar
  28. Rao RV, Savsani VJ, Balic J (2012a) Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems. Eng Optim 44(12):1447–1462Google Scholar
  29. Rao RV, Savsani VJ, Vakharia DP (2012b) Teaching–learning-based optimization: an optimization method for continuous non-linear large-scale problems. Inf Sci 183(1):1–15MathSciNetGoogle Scholar
  30. Satapathy SC, Naik A (2014) Modified teaching–learning-based optimization algorithm for global numerical optimization—a comparative study. Swarm Evol Comput 16:28–37Google Scholar
  31. Segura C, Coello CAC, Hernández-Díaz AG (2015) Improving the vector generation strategy of differential evolution for large-scale optimization. Inf Sci 323(C):106–129MathSciNetGoogle Scholar
  32. Shan S, Wang GG (2010) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41(2):219–241MathSciNetzbMATHGoogle Scholar
  33. Song W, Keane AJ (2007) Surrogate-based aerodynamic shape optimization of a civil aircraft engine nacelle. AIAA J 45(10):2565–2574Google Scholar
  34. Tang L, Wang H, Li G (2013) Advanced high strength steel springback optimization by projection-based heuristic global search algorithm. Mater Des 43:426–437Google Scholar
  35. Wang H, Zhu X, Du Z (2010) Aerodynamic optimization for low pressure turbine exhaust hood using Kriging surrogate model. Int Commun Heat Mass Transf 37(8):998–1003Google Scholar
  36. Wang H, Tang L, Li GY (2011) Adaptive MLS-HDMR metamodeling techniques for high dimensional problems. Expert Syst Appl 38(11):14117–14126Google Scholar
  37. Wu X, Zhang W, Song S (2017) Uncertainty quantification and sensitivity analysis of transonic aerodynamics with geometric uncertainty. Int J Aerosp Eng 2017:1):1–1)16Google Scholar
  38. Wu X, Zhang W, Song S (2018a) Robust aerodynamic shape design based on an adaptive stochastic optimization framework. Struct Multidiscip Optim 57(2):639–651MathSciNetGoogle Scholar
  39. Wu X, Zhang W, Song S et al (2018b) Sparse grid-based polynomial chaos expansion for aerodynamics of an airfoil with uncertainties. Chin J Aeronaut 31(5):997–1011Google Scholar
  40. Zhang WW, Gao CQ, Liu YL, et.al. (2015a) The interaction between flutter and buffet in transonic flow. Nonlinear Dyn 82(4):1851–1865Google Scholar
  41. Zhang WW, Li XT, Ye ZY, et.al. (2015b) Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers. J Fluid Mech 783: 72–102Google Scholar
  42. Zhao L, Choi KK, Lee I (2012) Metamodeling method using dynamic kriging for design optimization. AIAA J 49(9):2034–2046Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xiaojing Wu
    • 1
    • 2
  • Xuhao Peng
    • 2
  • Weisheng Chen
    • 1
  • Weiwei Zhang
    • 2
    Email author
  1. 1.School of Aerospace Science and TechnologyXidian UniversityXi’anChina
  2. 2.School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

Personalised recommendations