Structural and Multidisciplinary Optimization

, Volume 32, Issue 5, pp 369–382 | Cite as

Sequential kriging optimization using multiple-fidelity evaluations

  • D. Huang
  • T. T. Allen
  • W. I. Notz
  • R. A. Miller
Research Paper

Abstract

When cost per evaluation on a system of interest is high, surrogate systems can provide cheaper but lower-fidelity information. In the proposed extension of the sequential kriging optimization method, surrogate systems are exploited to reduce the total evaluation cost. The method utilizes data on all systems to build a kriging metamodel that provides a global prediction of the objective function and a measure of prediction uncertainty. The location and fidelity level of the next evaluation are selected by maximizing an augmented expected improvement function, which is connected with the evaluation costs. The proposed method was applied to test functions from the literature and a metal-forming process design problem via finite element simulations. The method manifests sensible search patterns, robust performance, and appreciable reduction in total evaluation cost as compared to the original method.

Keywords

Multiple fidelity Surrogate systems Kriging Efficient global optimization Computer experiments 

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References

  1. Ackley DH (1987) A connectionist machine for genetic hill-climbing. Kluwer, BostonGoogle Scholar
  2. Alexandrov NM, Dennis JE Jr, Lewis RM, Torczon V (1998) A trust region framework for managing the use of approximation models in optimization. Struct Optim 15(1):16–23CrossRefGoogle Scholar
  3. Audet C, Dennis JE Jr, Moore DW, Booker A, Frank PD (2000) A surrogate-model-based method for constrained optimization. In: Proceedings of the 8th AIAA/NASA/USAF/ISSMO symposium on multidisciplinary analysis and optimization, AIAA-2000-4891, Long Beach, 6–8 September 2000Google Scholar
  4. Bandler JW, Ismail MA, Rayas-Sanchez JE, Zhang Q (1999) Neuromodelling of microwave circuits exploiting space-mapping technology. IEEE Trans Microwave Theor Tech 47:2417–2427CrossRefGoogle Scholar
  5. Björkman M, Holström K (2000) Global optimization of costly nonconvex functions using radial basis functions. Opt Eng 1:373–397MATHCrossRefGoogle Scholar
  6. Cressie NAC (1993) Statistics for spatial data, revised edn. Wiley, New YorkGoogle Scholar
  7. Currin C, Mitchell M, Morris M, Ylvisaker D (1991) Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. J Am Stat Assoc 86:953–963MathSciNetCrossRefGoogle Scholar
  8. Edy D, Averill RC, Punch WF III, Goodman ED (1998) Evaluation of injection island GA performance on flywheel design optimization. In: Parmee IC (ed) Adaptive computing in design and manufacture. Springer, Berlin Heidelberg New YorkGoogle Scholar
  9. Hartman JK (1973) Some experiments in global optimization. Nav Res Logist Q 20:569–576MATHGoogle Scholar
  10. Huang D, Allen TT, Notz WI, Zheng N (2006) Global optimization of stochastic black-box systems via sequential kriging meta-models. J Global Optim 34(3):441–466MATHMathSciNetCrossRefGoogle Scholar
  11. Hutchinson MG, Unger ER, Mason WH, Grossman B, Haftka RT (1994) Variable-complexity aerodynamic optimization of a high speed civil transport wing. J Aircr 31:110–116Google Scholar
  12. Jones D, Schonlau M, Welch W (1998) Efficient global optimization of expensive black-box functions. J Global Optim 13:455–492MATHMathSciNetCrossRefGoogle Scholar
  13. Kaufman M, Balabanov V, Burgee SL, Giunta AA, Grossman B, Mason WH, Watson LT (1996) Variable-complexity response surface approximations for wing structural weight in HSCT design. Proceedings of the 34th aerospace sciences meeting and exhibit, AIAA-96-0089, Reno, 15–18 January 1996Google Scholar
  14. Keane AJ (2003) Wing optimization using design of experiment, response surface, and data fusion methods. J Aircr 40(4):741–750MathSciNetCrossRefGoogle Scholar
  15. Kennedy MC, O'Hagan A (2000) Predicting the output of a complex computer code when fast approximation are available. Biometrika 87(1):1–13MATHMathSciNetCrossRefGoogle Scholar
  16. Kennedy MC, O'Hagan A (2001)Bayesian calibration of computer models (with discussion). J R Stat Soc, Ser B 63(3):425–464MathSciNetCrossRefGoogle Scholar
  17. Koehler JR, Owen AB (1996) Computer experiments. In: Ghosh S, Rao CR (eds) Handbook of statistics, vol 13. Elsevier, AmsterdamGoogle Scholar
  18. Kushner HJ (1964) A new method of locating the maximum point of an arbitrary multipeak curve in the presence of noise. J Basic Eng 86:97–106Google Scholar
  19. Leary SJ, Bhaskar A, Keane AJ (2003) A knowledge-based approach to response surface modelling in multifidelity optimization. J Global Optim 26(3):297–319MATHMathSciNetCrossRefGoogle Scholar
  20. McDaniel WR, Ankenman BE (2000) A response surface test bed. Qual Reliab Eng Int 16:363–372CrossRefGoogle Scholar
  21. O'Hagan A (1989) Comment: design and analysis of computer experiments. Stat Sci 4:430–432Google Scholar
  22. Rodriguez JF, Perez VM, Padmanabhan D, Renaud JE (2001) Sequential approximate optimization using multiple fidelity response surface approximation. Struct Multidisc Optim 22(1):23–34CrossRefGoogle Scholar
  23. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989a) Design and analysis of computer experiments (with discussion). Stat Sci 4:409–430MATHMathSciNetGoogle Scholar
  24. Sacks J, Schiller SB, Welch W (1989b) Design for computer experiments. Technometrics 31:41–47MathSciNetCrossRefGoogle Scholar
  25. Santner TJ, Williams BJ, Notz WI (2003) The design and analysis of computer experiments. Springer, Berlin Heidelberg New YorkMATHGoogle Scholar
  26. Sasena MJ (2002) Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. Ph.D. dissertation, University of Michigan, Ann ArborGoogle Scholar
  27. Sasena MJ, Papalambros PY, Goovaerts P (2002) Exploration of metamodeling sampling criteria for constrained global optimization. Eng Optim 34:263–278CrossRefGoogle Scholar
  28. Schonlau M (1997) Computer experiments and global optimization. Ph.D. dissertation, University of Waterloo, WaterlooGoogle Scholar
  29. Stein M (1987) Large sample properties of simulation using Latin hypercube sampling. Technometrics 29:143–151MATHMathSciNetCrossRefGoogle Scholar
  30. Watson PM, Gupta KC (1996) EM-ANN models for microstrip vias and interconnects in dataset circuits. IEEE Trans Microwave Theor Tech 44:2495–2503CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • D. Huang
    • 1
  • T. T. Allen
    • 2
  • W. I. Notz
    • 3
  • R. A. Miller
    • 2
  1. 1.Computational Sciences and Mathematics DivisionPacific Northwest National LaboratoryRichlandUSA
  2. 2.Department of Industrial, Welding, and Systems EngineeringOhio State UniversityColumbusUSA
  3. 3.Department of StatisticsOhio State UniversityColumbusUSA

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