A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise

Abstract

A versatile and practical method of searching a parameter space is presented. Theoretical and experimental results illustrate the usefulness of the method for such problems as the experimental optimization of the performance of a system with a very general multipeak performance function when the only available information is noise-distributed samples of the function. At present, its usefulness is restricted to optimization with respect to one system parameter. The observations are taken sequentially; but, as opposed to the gradient method, the observation may be located anywhere on the parameter interval. A sequence of estimates of the location of the curve maximum is generated. The location of the next observation may be interpreted as the location of the most likely competitor (with the current best estimate) for the location of the curve maximum. A Brownian motion stochastic process is selected as a model for the unknown function, and the observations are interpreted with respect to the model. The model gives the results a simple intuitive interpretation and allows the use of simple but efficient sampling procedures. The resulting process possesses some powerful convergence properties in the presence of noise; it is nonparametric and, despite its generality, is efficient in the use of observations. The approach seems quite promising as a solution to many of the problems of experimental system optimization.