Date of Award

Spring 2021

Project Type

Dissertation

Program or Major

Electrical and Computer Engineering

Degree Name

Doctor of Philosophy

First Advisor

Michael J Carter

Second Advisor

John Gibson

Third Advisor

Kyle Hughes

Abstract

The need to find the global minimum of a highly non-convex, non-smooth objective function over a high-dimensional and possibly disconnected, feasible domain, within a practical amount of computing time, arises in many fields. Such objective functions and/or feasible domains are so poorly-behaved that gradient-based optimization methods are useful only locally – if at all. Random search methods offer a viable alternative, but their convergence properties are not well-studied. The present work adapts a proof by Baba et al. (1977) to establish asymptotic convergence for Monotonic Basin Hopping, a random search method used in molecular modeling and interplanetary spacecraft trajectory optimization. In addition, the present work uses the framework of First Passage Times (the time required for the first arrival to within a very small distance of the global minimum) and Gamma distribution approximations to First Passage Time Densities, to study MBH convergence speed. The present work then provides analytically supported methods for speeding up Monotonic Basin Hopping. The speed-up methods are novel, complementary, and can be used separately or in combination. Their effectiveness is shown to be dramatic in the case of MBH operating on different highly non-convex, non-smooth objective functions and complicated feasible domains. In addition, explanations are provided as to why some speed-up methods are very effective on some highly non-convex, non-smooth objective functions having complicated feasible domains, but other methods are relatively ineffective. The present work is the first systematic study of the MBH convergence process and methods for speeding it up, as opposed to applications of MBH.

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