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Structural and Multidisciplinary Optimization

, Volume 45, Issue 1, pp 53–64 | Cite as

An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions

  • Mark A. Abramson
  • Thomas J. Asaki
  • John E. DennisJr.
  • Raymond MagallanezJr.
  • Matthew J. Sottile
Research Paper

Abstract

In this paper, we characterize a new class of computationally expensive optimization problems and introduce an approach for solving them. In this class of problems, objective function values may be directly related to the computational time required to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate the objective is significantly less than at points farther away from the solution. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected positive correlation between function values and their CPU times, a time cutoff parameter is added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLAB® software packages, and results are presented.

Keywords

Surrogate optimization Derivative-free optimization Black box optimization Mesh Adaptive Direct Search (MADS) Pattern search Image registration Kriging 

Notes

Acknowledgments

The authors wish to thank David Bethea and two anonymous referees for some useful comments and discussions. Support for the first author was provided by Los Alamos National Laboratory (LANL). Support for the third author was provided by LANL, Air Force Office of Scientific Research F49620-01-1-0013, The Boeing Company, and ExxonMobil Upstream Research Company.

The views expressed in this document are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, United States Government, or corporate affiliations of the authors.

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Copyright information

© Springer-Verlag (outside the USA) 2011

Authors and Affiliations

  • Mark A. Abramson
    • 1
  • Thomas J. Asaki
    • 2
  • John E. DennisJr.
    • 3
  • Raymond MagallanezJr.
    • 4
  • Matthew J. Sottile
    • 5
  1. 1.The Boeing CompanySeattleUSA
  2. 2.Department of MathematicsWashington State UniversityPullmanUSA
  3. 3.Department of Computational and Applied MathematicsRice UniversitySeattleUSA
  4. 4.Department of Mathematical SciencesUnited States Air Force AcademyColorado SpringsUSA
  5. 5.Galois, Inc.PortlandUSA

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