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Mid-range metamodel assembly building based on linear regression for large scale optimization problems

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Abstract

In this work an approach to building a high accuracy approximation valid in a larger range of design variables is investigated. The approach is based on an assembly of multiple surrogates into a single surrogate using linear regression. The coefficients of the model assembly are not weights of the individual models but tuning parameters determined by the least squares method. The approach was utilized in the Multipoint Approximation Method (MAM) method within the mid-range approximation framework. The developed technique has been tested on several benchmark problems with up to 1000 design variables and constraints. The obtained results show a high degree of accuracy of the built approximations and the efficiency of the technique when applied to large-scale optimization problems.

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References

  • Acar E, Rais-Rohani M (2009) Ensemble of metamodels with optimized weight factors. Struct Multidisc Optim 37:279–294

    Article  Google Scholar 

  • Belsley DA (1991) Conditioning diagnostics: collinearity and weak data in regression. Wiley, New York

    MATH  Google Scholar 

  • Box GEP, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New York

    MATH  Google Scholar 

  • Burgee SL, Watson LT, Giunta AA, Grossman B, Haftka RT, Mason WH (1994) Parallel multipoint variable-complexity approximations for multidisciplinary optimization. In: Proceedings of the IEEE scalable high-performance computing conference, June 1994, pp 734–740

  • Canfield RA (2004) Multipoint cubic surrogate function for sequential approximate optimization. Struct Multidisc Optim 27:326–336

    Article  Google Scholar 

  • Fadel GM, Riley MF, Barthelemy JM (1990) Two point exponential approximation method for structural optimization. Struct Optim 2:117–124

    Article  Google Scholar 

  • Fleury C (1989) CONLIN: an efficient dual optimizer based on convex approximation concepts. Struct Optim 1:81–89

    Article  Google Scholar 

  • Haftka RT, Nachlas JA, Watson LT, Rizzo T, Desai R (1987) Two-point constraint approximation in structural optimization. Comp Meth Appl Mech Eng 60:289–301

    Article  MATH  Google Scholar 

  • Polynkin A, Toropov V, Shaphar S (2008) Adaptive and parallel capabilities in the Multipoint Approximation Method. In: AIAA 2008-5803, Proceeding of 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Proceedings. AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Victoria, British Columbia, Canada

  • Salazar C, Cuyt A, Verdonk B (2007) Rational approximation of vertical segments. Numer Algorithms 45:375–388

    Article  MathSciNet  MATH  Google Scholar 

  • Shahpar S, Polynkin A, Toropov VV (2008) Large scale optimization of transonic axial compressor rotor blades. In: AIAA 2008-2056, Proceedings of the 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials conference. Schaumburg, IL

  • Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:259–373

    Article  MathSciNet  Google Scholar 

  • Toropov VV (1989) Simulation approach to structural optimization. Struct Optim 1:37–46

    Article  Google Scholar 

  • Toropov VV, Filatov AA, Polynkin AA (1993) Multiparameter structural optimization using FEM and multipoint explicit approximations. Struct Optim 6:7–14

    Article  Google Scholar 

  • Vanderplaats GN (1999) Numerical optimization techniques for engineering design. 3rd edn. VR&D, Colorado Springs

    Google Scholar 

  • van Keulen F, Toropov VV (1997) New developments in structural optimization using adaptive mesh refinement and multi-point approximations. Eng Optim 29:217–234

    Article  Google Scholar 

  • Viana FAC, Haftka RT (2008) Using multiple surrogates for metamodeling. In: Proceedings of 7th ASMO-UK/ISSMO international conference on engineering design optimization, Bath, UK, 7–8 July 2008, pp 132–137

  • Viana FAC, Haftka RT, Steffen Jr V (2009) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidisc Optim 39:439–457

    Article  Google Scholar 

  • Wang LP, Grandhi RV (1995) Improved two-point function approximations for design optimization. AIAA J 33:1720–1727

    Article  MATH  Google Scholar 

  • Wang LP, Grandhi RV (1996) Multi-point approximations: comparisons using structural size, configuration and shape design. Struct Optim 12:177–185

    Article  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the UK Department of Trade and Industry, Rolls-Royce plc and Airbus UK Ltd for the support of this work within the CFMS R&D programme.

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Authors and Affiliations

  1. University of Leeds, Leeds, LS2 9JT, UK

    Andrey Polynkin & Vassili V. Toropov

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  1. Andrey Polynkin
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  2. Vassili V. Toropov
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Correspondence to Andrey Polynkin.

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Polynkin, A., Toropov, V.V. Mid-range metamodel assembly building based on linear regression for large scale optimization problems. Struct Multidisc Optim 45, 515–527 (2012). https://doi.org/10.1007/s00158-011-0692-1

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  • DOI: https://doi.org/10.1007/s00158-011-0692-1

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