Techniques for high-dimensional global optimization and response surface methodology

Scammell, Megan 2022. Techniques for high-dimensional global optimization and response surface methodology. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

This thesis aims to improve the efficiency and accuracy of optimization algorithms. High-dimensional optimization problems are frequently encountered in many practical situations due to the advancements in technology and availability of big data. Also, the analytical form of a black-box objective function is unknown, adding to the challenging nature of high-dimensional optimization problems. Multistart is a celebrated global optimization algorithm that involves sampling points at random from the feasible domain and applying a local optimization algorithm to find the corresponding local minimizer. The main drawback of multistart is the low efficiency since the same local minimizers may be found repeatedly. A vital research contribution in this thesis improves the efficiency of multistart for high-dimensional optimization problems by reducing the number of local searches to the same local minimizers. Ensuring local optimization methods are reliable and accurate when only objective function values containing errors are available is an important area of research. Specifically, the central focus is on the first phase of the Box-Wilson (BW) algorithm, a response surface methodology (RSM) strategy. The first phase of BW consists of performing a succession of moves toward a subregion of the minimizer. A significant research contribution in this thesis enhances the accuracy of the first phase of BW and RSM, in general, for high-dimensional optimization problems by employing a different choice of search direction. Producing high-quality software is vital to ensure accurate research investigations and to allow other researchers to apply the software, which is an additional research contribution demonstrated in this thesis. Furthermore, increasingly complex high-dimensional optimization problems are encountered in various areas of machine learning. Therefore, the development of advanced optimization methods is essential to the progression of many machine learning algorithms. Consequently, the final research contribution in this thesis outlines the potential enhancements to optimization methods applied within various areas of machine learning.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Date of First Compliant Deposit:	19 August 2022
Last Modified:	11 Mar 2023 02:23
URI:	https://orca.cardiff.ac.uk/id/eprint/152027

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