Journal of Global Optimization

, Volume 13, Issue 4, pp 455–492

Efficient Global Optimization of Expensive Black-Box Functions

  • Donald R. Jones
  • Matthias Schonlau
  • William J. Welch

DOI: 10.1023/A:1008306431147

Cite this article as:
Jones, D.R., Schonlau, M. & Welch, W.J. Journal of Global Optimization (1998) 13: 455. doi:10.1023/A:1008306431147


In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.

Bayesian global optimization Kriging Random function Response surface Stochastic process Visualization 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Donald R. Jones
    • 1
  • Matthias Schonlau
    • 2
  • William J. Welch
    • 3
  1. 1.Operations Research DepartmentGeneral Motors R&D OperationsWarrenUSA
  2. 2.National Institute of Statistical Sciences, Research Triangle ParkUSA
  3. 3.Department of Statistics and Actuarial Science and The Institute for Improvement in Quality and ProductivityUniversity of WaterlooWaterlooCanada

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