Skip to main content
SpringerLink
Log in

An interior-point sequential approximate optimization methodology

  • Research paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The use of optimization in a simulation-based design environment has become a common trend in industry today. Computer simulation tools are commonplace in many engineering disciplines, providing the designers with tools to evaluate a design’s performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulations. One of these approaches is known as sequential approximate optimization. In sequential approximate minimization a sequence of optimizations are performed over local response surface approximations of the system. This paper details the development of an interior-point approach for trust-region-managed sequential approximate optimization. The interior-point approach will ensure that approximate feasibility is maintained throughout the optimization process. This facilitates the delivery of a usable design at each iteration when subject to reduced design cycle time constraints. In order to deal with infeasible starting points, homotopy methods are used to relax constraints and push designs toward feasibility. Results of application studies are presented, illustrating the applicability of the proposed algorithm.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alexandrov, N.M.; Dennis, J.E.; Lewis, R.M.; Torczon, V. 1998: A trust region framework for managing use of approximation models in optimization. Struct Optim15, 16–23

    Google Scholar 

  2. Byrd, R.H.; Hribar, M.E.; Nocedal, J. 2000: An interior point algorithm for large scale nonlinear programming. SIAM J Optim9, 877–900

    Google Scholar 

  3. Chung, H.; Alonso, J.J. 2000: Comparison of approximation models with merit functions for design optimization. In: Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA 2000-4754, Long Beach, CA

  4. Giunta, A.; Watson, L.T. 1998: A comparison of approximation modeling techniques: Polynomial versus interpolating models. In: Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA 98-4758, 392–404, Saint Louis, MO

  5. Liu, W.; Batill, S.M. 2000: Gradient-enhanced neural network response surface approximations. In: Proceedings of the 8th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA-2000-4923, Long Beach, CA

  6. Pérez, V.M.; Renaud, J.E.; Gano, S.E. 2000: Constructing variable fidelity response surface approximations in the usable feasible region. In: Proceedings of the 8th AIAA/NASA/USAF Multidisciplinary Analysis & Optimization Symposium, AIAA 2000-4888, Long Beach, CA

  7. Pérez, V.M.; Renaud, J.E.; Watson, L.T. 2002a: Adaptive experimental design for construction of response surface approximations. AIAA J40, 2495–2503

  8. Pérez, V.M.; Renaud, J.E.; Watson, L.T. 2002b: Reduced sampling for construction of quadratic response surface approximations using adaptive experimental design. In: Proceedings of the 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA 2002-1587, Denver, Colorado

  9. Potra, F.A.; Wright, S. 2000: Interior-point methods. J Comput Appl Math124, 281–302

    Google Scholar 

  10. Rasmussen, J. 1998: Nonlinear programming by cumulative approximation refinement. Struct Optim15, 1–7

    Google Scholar 

  11. Renaud, J.E.; Gabriele, G.A. 1993: Improved coordination in nonhierarchic system optimization. AIAA J31, 2367–2373

    Google Scholar 

  12. Rodríguez, J.F.; Renaud, J.E.; Watson, L.T. 1998a: Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data. Struct Optim15, 141–156

  13. Rodríguez, J.F.; Renaud, J.E.; Watson, L.T. 1998b: Trust region augmented Lagrangian methods for sequential response surface approximation and optimization. J Mech Des120, 58–66

  14. Rodríguez, J.F.; Pérez, V.M.; Padmanabhan, D.; Renaud, J.E. 2001: Sequential approximate optimization using variable fidelity response surface approximations. Struct Multidisc Optim22, 24–34

    Google Scholar 

  15. Smith, C.F.; Crossley, W.A. 2000: Investigating response surface approaches for drag optimization of subsonic turbofan nacelle. In: Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA 2000-4797, Long Beach, CA

  16. Sobieski, I.P.; Kroo, I.M. 2000: Collaborative optimization using response surface estimation. AIAA J38, 1931–1938

    Google Scholar 

  17. Sobieszczanski-Sobieski, J. 1982: A linear decomposition method for large optimization problems – blueprint for development. Tech. Rep. TM-83248-1982, NASA

  18. Sobieszczanski-Sobieski, J.; Bloebaum, C.L.; Hajela, P. 1991: Sensitivity of control-augmented structure obtained by a system decomposition method. AIAA J29, 264–270

    Google Scholar 

  19. Stelmack, M.; Batill, S.M. 1998: Neural network approximations of mixed continuous/discrete systems in multidisciplinary design. In: Proceeding of the AIAA Aerospace Sciences Meeting and Exhibit, AIAA 98-0916, Reno, Nevada

  20. Vanderbei, R.J.; Shanno, D.F. 1999: An interior point algorithm for nonconvex nonlinear programming. Comput Optim Appl13, 231–252

    Google Scholar 

  21. Watson, L.T. 2000: Theory of globally convergent probability-one homotopies for nonlinear programming. SIAM J Optim11, 761–780

    Google Scholar 

  22. Watson, L.T.; Sosonkina, M.; Melville, R.C.; Morgan, A.P.; Walker, H.F. 1997: Algorithm 777: HOMPACK90: A suite of FORTRAN 90 codes for globally convergent homotopy algorithms. ACM Trans Math Softw23, 514–549

    Google Scholar 

  23. Wright, S.J. 1997: Primal-Dual Interior-Point Methods. SIAM

  24. Wujek, B.A.; Renaud, J.E. 1998a: A new adaptive move-limit management strategy for approximate optimization, part i. AIAA J36, 1911–1921

  25. Wujek, B.A.; Renaud, J.E. 1998b: A new adaptive move-limit management strategy for approximate optimization, part ii. AIAA J36, 1922–1937

  26. Wujek, B.A.; Renaud, J.E.; Batill, S.M.; Brockman, J.B. 1995: Concurrent subspace optimization using design variable sharing in a distributed design environment. In: Azarm, S. (ed.), Proceedings of the Design Engineering Technical Conference, Advances in Design Automation, ASME DE, Vol. 82, 181–188

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana, USA

    V.M. Pérez & J.E. Renaud

  2. Dept. of Computer Science and Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

    L.T. Watson

Authors
  1. V.M. Pérez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J.E. Renaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L.T. Watson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J.E. Renaud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pérez, V., Renaud, J. & Watson, L. An interior-point sequential approximate optimization methodology. Struct Multidisc Optim 27, 360–370 (2004). https://doi.org/10.1007/s00158-004-0395-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0395-y

Keywords

Search

Navigation