Global R/sup d/ optimization when probes are expensive: the GROPE algorithm

A global optimization algorithm is introduced which generalizes H.J. Kushner's (1964) univariate search. It aims to minimize the number of probes required for a given confidence in the results. All known probes contribute to a stochastic model of the underlying score surface, and this model is interrogated for the location most likely to exceed the current result goal. The surface is assumed to be fractal, leading to a piecewise Gaussian model, where the local regions are defined by the Delaunay triangulation of the probes. The algorithm balances the competing aims of (1) sampling in the vicinity of known peaks, and (2) exploring new regions. Preliminary tests on a standard 2-D search problem were very encouraging.<<ETX>>

[1]  H. Kushner.  A versatile stochastic model of a function of unknown and time varying form , 1962 .

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

[3]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[4]  R. E. Miles.  On the homogeneous planar Poisson point process , 1970 .

[5]  George A. Bekey,et al.  A Comparative Evaluation of Two Global Search Algorithms , 1974, IEEE Trans. Syst. Man Cybern..

[6]  John Aitchison,et al.  Statistical Prediction Analysis , 1975 .

[7]  Robin Sibson,et al.  Locally Equiangular Triangulations , 1978, Comput. J..

[8]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[9]  Eric Walter,et al.  A general-purpose global optimizer: implementation and applications , 1984 .

[10]  A. Groch,et al.  A new global optimization method for electronic circuit design , 1985 .

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

[12]  Roger L. Barron,et al.  Automated Design of Continuously-Adaptive Control: The "Super-Controller" Strategy for Reconfigurable Systems , 1988, 1988 American Control Conference.

[13]  B. Joe.  Three-dimensional triangulations from local transformations , 1989 .

[14]  Bruce E. Stuckman,et al.  The rank transformation applied to a multi-univariate method of global optimization , 1990, IEEE 1989 International Conference on Systems Engineering.

[15]  ElderJohn F.Iv,et al.  Creating ‘Optimally Complex’ Models for Forecasting , 1991 .

[16]  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.

[17]  V. T. Rajan,et al.  Optimality of the Delaunay triangulation in Rd , 1991, SCG '91.

[18]  B. Stuckman,et al.  A multidimensional Bayesian global search method which incorporates knowledge of an upper bound , 1991, Conference Proceedings 1991 IEEE International Conference on Systems, Man, and Cybernetics.

[19]  J. C. Tipper.  FORTRAN programs to construct the planar Voronoi diagram , 1991 .

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

[21]  Leo Breiman,et al.  Hinging hyperplanes for regression, classification, and function approximation , 1993, IEEE Trans. Inf. Theory.