Skip to main content
SpringerLink
Log in

Overview and Comparison of Gaussian Process-Based Surrogate Models for Mixed Continuous and Discrete Variables: Application on Aerospace Design Problems

  • Chapter
  • First Online:
High-Performance Simulation-Based Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 833))

Abstract

Surrogate modeling is an increasingly popular tool for engineering design as it enables to model the performance of very complex systems with a limited computational cost. A large number of techniques exists for the surrogate modeling of continuous functions, however, only a very few methods for the surrogate modeling of mixed continuous/discrete functions have been developed. In this chapter, existing adaptations and variants of Gaussian process-based surrogate modeling techniques for mixed continuous/discrete variables are described, discussed and compared on several analytical test-cases and aerospace design problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Agresti A (1996) An Introduction to Categorical Data Analysis. Wiley, New York

    Google Scholar 

  2. Balesdent, M., Brevault, L., Price, N.B., Defoort, S., Le Riche, R., Kim, N.H., Haftka, R.T., Bérend, N.: Advanced Space Vehicle Design Taking into Account Multidisciplinary Couplings and Mixed Epistemic/Aleatory Uncertainties, pp. 1–48. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41508-6_1

    MATH  Google Scholar 

  3. Bartz-Beielstein, T., Zaefferer, M.: Model-based methods for continuous and discrete global optimization. Appl. Soft. Comput. 55, 154–167 (2017). https://doi.org/10.1016/j.asoc.2017.01.039

    Article  Google Scholar 

  4. Betts, J.T.: Survey of numerical methods for trajectory optimization. J. Guid, Control, Dyn. 21(2), 193–207 (1998). https://doi.org/10.2514/2.4231

    Article  MATH  Google Scholar 

  5. Bischl, B., Lang, M., Kotthoff, L., Schiffner, J., Richter, J., Studerus, E., Casalicchio, G., Jones, Z.M.: Mlr: machine learning in R. J Mach Learn Res 17(170), 1–5 (2016)

    MathSciNet  MATH  Google Scholar 

  6. Bonnans, J.F., Gilbert, J.C., Lemarechal, C.: Numerical Optimization: Theoretical and Practical Aspects. Springer, Berlin Heidelberg (2006)

    MATH  Google Scholar 

  7. Castellini, F.: Multidisciplinary Design Optimization for Expendable Launch Vehicles p. 179 (2012)

    Google Scholar 

  8. Champigny, P., Denis, P.: The ONERA aeroprediction code missile. In: 21st AIAA Advanced Measurement Technology and Ground Testing Conference (2004)

    Google Scholar 

  9. Davis, M.J.: Contrast coding in multiple regression analysis: strengths, weaknesses, and utility of popular coding structures. J. Data. Sci. 8, 61–73 (2010)

    Google Scholar 

  10. Deng, X., Lin, C.D., Liu, K.W., Rowe, R.K.: Additive gaussian process for computer models with qualitative and quantitative factors. Technometrics 59(3), 283–292 (2017). https://doi.org/10.1080/00401706.2016.1211554

    Article  MathSciNet  Google Scholar 

  11. Filomeno Coelho, R.: Metamodels for mixed variables based on moving least squares. Optim. Eng.15(2), 311–329 (2014). https://doi.org/10.1007/s11081-013-9216-8

    Article  MathSciNet  Google Scholar 

  12. Ford, H., Alexander, J.M.: Advanced mechanics of materials. In: Horwood, E (1977)

    Google Scholar 

  13. Gower, J.C.: A general coefficient of similarity and some of its properties. Biometrics 27(4), 857 (1971). https://doi.org/10.2307/2528823

    Article  Google Scholar 

  14. Gramacy, R.B., Lee, H.K.H.: Bayesian treed gaussian process models with an application to computer modeling. J. Am. Stat. Assoc. 103(483), 1119–1130 (2008). https://doi.org/10.1198/016214508000000689

    Article  MathSciNet  Google Scholar 

  15. Gray, J., Moore, K., Naylor, B.: OpenMDAO: an open source framework for multidisciplinary analysis and optimization. In: 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference pp. 1–12 (2010). https://doi.org/10.2514/6.2010-9101

  16. Halstrup, M.: Black-box optimization of mixed discrete-continuous optimization problems (2016). https://doi.org/10.17877/DE290R-17800

  17. Hansen, N.: Towards a new evolutionary computation: advances in the estimation of distribution algorithms. In: Towards a New Evolutionary Computation, pp. 75–102. Springer Berlin Heidelberg, Berlin, Heidelberg (2006). https://doi.org/10.1007/3-540-32494-1_4

  18. Herrera, M., Guglielmetti, A., Xiao, M., Filomeno Coelho, R.: Metamodel-assisted optimization based on multiple kernel regression for mixed variables. Struct. Multidiscip. Optim. 49(6), 979–991 (2014). https://doi.org/10.1007/s00158-013-1029-z

    Article  Google Scholar 

  19. Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13, 455–492 (1998)

    Article  MathSciNet  Google Scholar 

  20. Lee, N., Kim, J.M.: Conversion of categorical variables into numerical variables via Bayesian network classifiers for binary classifications. Omputational Stat. Data Anal. 54(5), 1247–1265 (2010). https://doi.org/10.1016/j.csda.2009.11.003

    Article  MathSciNet  Google Scholar 

  21. Levine, I.N.: Physical Chemistry. McGraw-Hill (2009)

    Google Scholar 

  22. Li, R., Emmerich, M.T.M., Eggermont, J., Bovenkamp, E.G., Bäck, T., Dijkstra, J., Reiber, J.H.: Metamodel-assisted mixed integer evolution strategies and their application to intravascular ultrasound image analysis. In: 2008 IEEE Congress on Evolutionary Computation, CEC 2008, pp. 2764–2771. IEEE, Hong Kong (2008). https://doi.org/10.1109/CEC.2008.4631169

  23. Loh, W.Y.: Classification and regression trees. Wiley Interdiscip. Rev.: Data Min. Knowl. Discov. 1(1), 14–23 (2011). https://doi.org/10.1002/widm.8

    Google Scholar 

  24. MacNeal, R.H., McCormick, C.W.: The NASTRAN computer program for structural analysis. In: SAE Technical Paper. SAE International (1969). https://doi.org/10.4271/690612

  25. McBride, B.J., Gordon, S.: Computer program for calculation of complex chemical equilibrium compositions and applications. User Manual and Program Description. Technical report, NASA (1996)

    Google Scholar 

  26. Meckesheimer, M., Barton, R.R., Simpson, T., Limayem, F., Yannou, B.: Metamodeling of combined discrete/continuous responses. AIAA J. 39(10) (2001). https://doi.org/10.2514/2.1185

    Article  Google Scholar 

  27. Minasny, B., McBratney, A.B.: The Matérn function as a general model for soil variograms. In: Geoderma, vol. 128, pp. 192–207. Elsevier (2005). https://doi.org/10.1016/j.geoderma.2005.04.003

    Article  Google Scholar 

  28. Nie, Z., Racine, J.S.: The crs package: nonparametric regression splines for continuous and categorical predictors. R J. 4(2), 1–10 (2012)

    Article  Google Scholar 

  29. Oliver, M.A., Webster, R.: Kriging: a method of interpolation for geographical information systems. Int. J. Geogr. Inf. Syst. 4(3), 313–332 (1990). https://doi.org/10.1080/02693799008941549

    Article  Google Scholar 

  30. Qian, P.Z.G., Wu, H., Wu, C.F.J.: Gaussian process models for computer experiments with qualitative and quantitative factors. Technometrics 50(3), 383–396 (2008). https://doi.org/10.1198/004017008000000262

    Article  MathSciNet  Google Scholar 

  31. Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., Kevin Tucker, P.: Surrogate-based analysis and optimization. Prog. Aerosp. Sci. 41(1), 1–28 (2005). https://doi.org/10.1016/j.paerosci.2005.02.001

    Article  Google Scholar 

  32. Rasmussen, C.E., Williams, C.K.I.: Gaussian processes for machine learning. MIT Press (2006)

    Google Scholar 

  33. Rebonato, R., Jaeckel, P.: The most general methodology to create a valid correlation matrix for risk management and option pricing purposes. SSRN Electron. J. (2011). https://doi.org/10.2139/ssrn.1969689

  34. Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4(4), 409–423 (1989). https://doi.org/10.1214/ss/1177012413

    Article  MathSciNet  Google Scholar 

  35. Seeger, M.: Gaussian processes for machine learning. Int. J. Neural Syst. 14(02), 69–106 (2004). https://doi.org/10.1142/S0129065704001899

    Article  Google Scholar 

  36. Simpson, T., Poplinski, J., Koch, P.N., Allen, J.: Metamodels for computer-based engineering design: survey and recommendations. Eng. Comput. 17(2), 129–150 (2001). https://doi.org/10.1007/PL00007198

    Article  Google Scholar 

  37. Suits, D.B.: Use of dummy variables in regression equations. J. Am. Stat. Assoc. 52(280), 548–551 (1957). https://doi.org/10.1080/01621459.1957.10501412

    Article  Google Scholar 

  38. Suli, E., Mayers, D.F.: An introduction to numerical analysis. Cambridge University Press (2003)

    Google Scholar 

  39. Swiler, L.P., Hough, P.D., Qian, P., Xu, X., Storlie, C., Lee, H.: Surrogate models for mixed discrete-continuous variables (2012)

    Google Scholar 

  40. Wendorf, C.A.: Primer on multiple regression coding: common forms and the additional case of repeated contrasts. Underst. Stat. 3(1), 47–57 (2004). https://doi.org/10.1207/s15328031us0301_3

    Article  Google Scholar 

  41. Zhou, Q., Qian, P.Z.G., Zhou, S.: A simple approach to emulation for computer models with qualitative and quantitative factors. Technometrics 53(3), 266–273 (2011). https://doi.org/10.1198/TECH.2011.10025

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ONERA/DTIS, Université Paris Saclaym, CNES, Direction des lanceurs, University of Lille, Lille, France

    Julien Pelamatti

  2. ONERA/DTIS, Université Paris Saclay, 91123, Palaiseau Cedex, France

    Loïc Brevault & Mathieu Balesdent

  3. Polytech Lille – University of Lille CNRS/CRIStAL, Inria Lille – Nord Europe, 59650, Villeneuve d’Ascq, Lille, France

    El-Ghazali Talbi

  4. CNES, Diréction des lanceurs, 75612, Paris Cedex, Paris, France

    Yannick Guerin

Authors
  1. Julien Pelamatti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Loïc Brevault
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mathieu Balesdent
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. El-Ghazali Talbi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yannick Guerin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to El-Ghazali Talbi .

Editor information

Editors and Affiliations

  1. TH Köln, Cologne, Germany

    Thomas Bartz-Beielstein

  2. Jožef Stefan Institute, Ljubljana, Slovenia

    Bogdan Filipič

  3. Jožef Stefan Institute, Ljubljana, Slovenia

    Peter Korošec

  4. University Lille, Lille, France

    El-Ghazali Talbi

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Pelamatti, J., Brevault, L., Balesdent, M., Talbi, EG., Guerin, Y. (2020). Overview and Comparison of Gaussian Process-Based Surrogate Models for Mixed Continuous and Discrete Variables: Application on Aerospace Design Problems. In: Bartz-Beielstein, T., Filipič, B., Korošec, P., Talbi, EG. (eds) High-Performance Simulation-Based Optimization. Studies in Computational Intelligence, vol 833. Springer, Cham. https://doi.org/10.1007/978-3-030-18764-4_9

Download citation

Publish with us

Policies and ethics

Search

Navigation