Research Papers

Structural optimization

, Volume 17, Issue 1, pp 1-13

First online:

A rigorous framework for optimization of expensive functions by surrogates

  • A. J. BookerAffiliated withBoeing Shared Services Group, Applied Research and Technology, Mathematics & Engineering Analysis
  • , J. E. DennisJr.Affiliated withDepartment of Computational and Applied Mathematics & Center for Research on Parallel Computation, Rice University
  • , P. D. FrankAffiliated withMathematics & Engineering Analysis, Boeing Shared Services Group, Applied Research and Technology
  • , D. B. SerafiniAffiliated withE.O. Lawrence Berkeley National Laboratory, National Energy Research Scientific Computing Center
  • , V. TorczonAffiliated withDepartment of Computer Science, College of William & Mary
  • , M. W. TrossetAffiliated withDepartment of Mathematics, College of William & Mary

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Abstract

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.