Surrogate optimization with algebraic notes and applications within the electromagnetics context
This thesis deals with surrogate optimization for applications within the electromagnetics context. Regarding the electromagnetics context, in particular, the magnetoquasistatic model of Maxwell’s theory is discussed. Moreover, relevant points regarding the magnetoquasistatic model’s numerical simulation and numerical optimization are examined. The key notion surrogate optimization is thoroughly elaborated which is partitioned into three sub-notions: (1) surrogate modeling & simulation, (2) surrogate-based optimizaton, and (3) surrogate-guided optimization. The various notions of surrogate optimization are tagged with algebraic notes in order to anticipate the toolset of the formal language of category theory. Moreover, the capability of the category theory toolset as an algebraic modeling framework for applications in surrogate optimization is investigated. Finally, representatives of the class of inductive components are invoked and the surrogate optimization tools of the present work are applied to four high-fidelity optimization problems that are embedded within the setting of a two-dimensional linear boundary value problem and a three-dimensional linear boundary value problem, respectively. Concerning these optimization problems, some promising spots for a useful application of the category theory toolset are illuminated. From the bird’s-eye view, this thesis achieves some progress in the scientific thicket of full automation of the virtual prototyping of power electronic systems. From the frog’s-eye view, i.e., at a more technical level, some of the present work’s achievements deal with hybrid model management strategies of surrogate-guided optimization methods, the repercussions of the choice of a sampling plan on these methods, and formalization issues regarding surrogate optimization with multiple low-fidelity models.
Networked Digital Library of Theses and Dissertations