Year: 2003
Type: dissertation
Abstract: In some optimization problems the evaluation of the objective function is very expensive.It is theiefore desirable to find the global optimum of the function with only comparatively few function evaluations.Because of the expense of evaluations it is justified to put significant effort into finding good sample points and using all the available information about the objective function.One way of achieving this is by assuming that the function can be modelled as a stochastic process and fitting a response surface or surrogate function to it, based on function evaluations at a set of points determined by an initial design.Parameters in the model are estimated when fitting the response surface to the available data.In determining the next point at which to evaluate the objective function, a balance must be struck between local search and global search.Local search in a neighbourhood of the minimum of the approximating function has the aim of finding a point with improved objective value.The aim of global search is to improve the approximation by maximizing an error function which reflects the uncertainty in the approximating function.Such a balance is achieved by using the expected improvement criterion.In this approach the next sample point is chosen where the expected improvement is maximized.The expected improvement at any point in the range reflects the expected amount of improvement of the approximating function beyond a target value (usually the best function value found up to this point) at that point, taking into account the uncertainty in the approximating function.In this thesis, we present and examine the expected improvement approach and the maximization of the expected improvement function.Sometimes the data are deceptive and parameters estimated from the data can give misleading approximating and error functions.We discuss a variation of the expected improvement criterion which takes into account the potential error in the estimated parameters, and we consider a different stopping rule.We also investigate how the availability of derivatives may be exploited and the use of a non-constant regression function in the approximating function.As test functions we mainly use our own functions.These are sample paths of stochastic processes generated for this purpose.The generating process of these functions is also described. Table of
Source: ERA
Author: Theresia Mayer
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2340243034