A Taxonomy of Global Optimization Methods Based on Response Surfaces

This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach.

[1]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

[2]  P. C. Gehlen,et al.  Computer Experiments , 1996 .

[3]  Bruce E. Stuckman,et al.  A global search method for optimizing nonlinear systems , 1988, IEEE Trans. Syst. Man Cybern..

[4]  John E. Dennis,et al.  Direct Search Methods on Parallel Machines , 1991, SIAM J. Optim..

[5]  C. D. Perttunen,et al.  A computational geometric approach to feasible region division in constrained global optimization , 1991, Conference Proceedings 1991 IEEE International Conference on Systems, Man, and Cybernetics.

[6]  J. Elder Global R/sup d/ optimization when probes are expensive: the GROPE algorithm , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[7]  Antanas Zilinskas,et al.  A review of statistical models for global optimization , 1992, J. Glob. Optim..

[8]  D. Dennis,et al.  A statistical method for global optimization , 1992, [Proceedings] 1992 IEEE International Conference on Systems, Man, and Cybernetics.

[9]  Jonas Mockus,et al.  Application of Bayesian approach to numerical methods of global and stochastic optimization , 1994, J. Glob. Optim..

[10]  D. Dennis,et al.  SDO : A Statistical Method for Global Optimization , 1997 .

[11]  Marco Locatelli,et al.  Bayesian Algorithms for One-Dimensional Global Optimization , 1997, J. Glob. Optim..

[12]  Donald R. Jones,et al.  Global versus local search in constrained optimization of computer models , 1998 .

[13]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[14]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[15]  P. A. Newman,et al.  Optimization with variable-fidelity models applied to wing design , 1999 .

[16]  Panos Y. Papalambros,et al.  Metamodeling sampling criteria in a global optimization framework , 2000 .

[17]  Hans-Martin Gutmann,et al.  A Radial Basis Function Method for Global Optimization , 2001, J. Glob. Optim..

[18]  J. Elder Global Rd Optimization when Probes are Expensive : the GROPE Algorithm , 2003 .