gra2006-03

Enhancing parallel pattern search optimization with a Gaussian process oracle.

by:
G.A. Gray, M. Martinez-Canales, M.A. Taddy, H.K.H. Lee and R.B. Gramacy

ABSTRACT

We consider a derivative-free method from the pattern search class of algorithms for the solution of simulation- based optimization problems. Because simulations often require significant computational time and resources, we are striving to reduce the number of runs needed by the optimization method. Moreover, since pattern searches are local methods, we are investigating ways of introducing robustness and some global properties. To accomplish these goals, we are using ideas from the design of computer experiments literature and using random functions to model the deterministic computer output function. We treat the output of the simula- tions as realizations of a Gaussian Process (GP). Then, the uncertainty about future computer evaluations can be quantified by finding the predictive distribution for new input locations conditional on the points that have already been evaluated. These ideas have been adapted to complex computer simulations in an R code referred to as tgp. This work combines the search properties of a pattern search with the statistical properties of the GP to create a new hybrid algorithm. In this paper, we will describe the optimization algorithm, the GP algorithm, and the resulting hybrid method, and we will present some numerical results.

BIBTEX

@InProceedings{gray:2006,       author = {G.A. Gray nd M. Martinez-Canales and M.A. Taddy and H.K.H. Lee and R.B. Gramacy},      title = {Enhancing parallel pattern search optimization with a Gaussian process oracle},       booktitle = {Proceedings of the NECDC},       year = 2006,       volume = {SAND2006-794C}      }

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