Structural optimization

, Volume 17, Issue 1, pp 1–13

A rigorous framework for optimization of expensive functions by surrogates


  • A. J. Booker
    • Boeing Shared Services Group, Applied Research and TechnologyMathematics & Engineering Analysis
  • J. E. DennisJr.
    • Department of Computational and Applied Mathematics & Center for Research on Parallel ComputationRice University
  • P. D. Frank
    • Mathematics & Engineering Analysis, Boeing Shared Services Group, Applied Research and Technology
  • D. B. Serafini
    • E.O. Lawrence Berkeley National LaboratoryNational Energy Research Scientific Computing Center
  • V. Torczon
    • Department of Computer ScienceCollege of William & Mary
  • M. W. Trosset
    • Department of MathematicsCollege of William & Mary
Research Papers

DOI: 10.1007/BF01197708

Cite this article as:
Booker, A.J., Dennis, J.E., Frank, P.D. et al. Structural Optimization (1999) 17: 1. doi:10.1007/BF01197708


The goal of the research reported here is to develop rigorous optimization algorithms to apply to some engineering design problems for which direct application of traditional optimization approaches is not practical. This paper presents and analyzes a framework for generating a sequence of approximations to the objective function and managing the use of these approximations as surrogates for optimization. The result is to obtain convergence to a minimizer of an expensive objective function subject to simple constraints. The approach is widely applicable because it does not require, or even explicitly approximate, derivatives of the objective. Numerical results are presented for a 31-variable helicopter rotor blade design example and for a standard optimization test example.

Copyright information

© Springer-Verlag 1999