EFFICIENT AND ROBUST MULTI-OBJECTIVE OPTIMIZATION APPLIED TO PROBLEMS IN ELECTROSTATICS, ELECTROMAGNETICS AND OPTICS
Open Access
- Author:
- Nagar, Jogender
- Graduate Program:
- Electrical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- November 03, 2018
- Committee Members:
- Douglas H. Werner, Dissertation Advisor/Co-Advisor
Douglas H. Werner, Committee Chair/Co-Chair
Pingjuan L. Werner, Committee Member
Viktor Pasko, Committee Member
Ram Rajagopalan, Outside Member - Keywords:
- Multi-objective optimization
optimization
electromagnetics
optics
gradient-index lens
antennas
electrostatics
topology optimization - Abstract:
- Most design problems in electromagnetics and optics have multiple, often conflicting design objectives. A classic example is performance vs. price, where the designer is forced to trade-off one desired objective for another. Multi-objective optimization (MOO) provides the designer with a set of solutions which show the intrinsic trade-offs between multiple conflicting objectives. This gives insight into the underlying physics of the problem and enables the designer to choose the best solution for a particular application. Despite its utility, MOO isn’t as popular in electromagnetics as it is in other fields such as economics, finance, mechanical and chemical engineering. The most popular commercial design tools do not support the MOO paradigm. This thesis will give an introduction and brief overview of different aspects of MOO, including methods for faster convergence and speed increases along with a variety of metrics for comparing the performance of different algorithms. Then a set of MOO algorithms will be described, with a focus on three state of the art optimizers, each of which has a unique design philosophy. BORG is an auto-adaptive genetic algorithm, the Multi-Objective Covariance Matrix Adaptation (MO-CMA) is an evolutionary strategy based on the popular single-objective CMA, and the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is a scalarization algorithm which uses a Tchebysheff decomposition. The convergence, robustness and efficiency of these state-of-the-art optimizers has been studied exhaustively on simple test functions. In contrast, the algorithms here are tested on practical electromagnetic applications where the function evaluations are computationally expensive, making the convergence rate and sensitivity of these algorithms crucial factors in determining their feasibility. Another popular topic in the literature is in applying and comparing classical multi-objective optimizers (typically NSGA-II or one of its derivatives) on more complex practical problems. In contrast, the algorithms chosen for this study are state of the art and better suited for the extremely multi-modal and noisy objective landscapes encountered in electromagnetics. In order to study the algorithms, a comprehensive strategy will be described for comparing the quality of the three algorithms in the fairest manner possible. In addition, this thesis will provide guidelines on the appropriate optimizer to choose for a given problem and the recommended optimizer settings. The applications considered cover a diverse range of electromagnetics applications, including the optimization of an Electromagnetic Band Gap (EBG), a Vivaldi antenna and a PIFA antenna near a human head. Particular attention will be shown to the performance of a series of increasingly complicated stacked patch antenna operating in the RF. For this problem, a thorough statistical study will be performed on this model to determine the sensitivity of the optimizers to the intrinsic optimizer parameters, number of variables and objectives, and complexity of the model. In addition, optimization problems in which the number of feasible solutions is an extremely small fraction of the overall design space will be explored. This is common in optical lens design, where a large number of designs converge to the wrong spot or even diverge completely. Strategies for dealing with this difficulty will be presented. In particular, a novel surrogate model based on quasi-conformal transformation optics (qTO) will be presented for the optimization of gradient-index (GRIN) lenses. In addition, a novel alternative to qTO called “wavefront matching” will be proposed and a variety of examples will highlight its usefulness. Then, a new optical device which combines the advantages of both a metasurface and a GRIN lens will be described. For these new devices and design paradigms, multi-objective trade-offs will be discussed. Finally, the problem of insulator optimization in high-voltage electrostatics problems will be discussed by a novel technique which extends the concept of topology optimization to include multiple objectives. In addition to providing a set of solutions for trade-off analysis, MOO provides insight into the underlying physics and limitations of a given design problem. By correlating the design variables with the objectives, the designer can gain insight into the dynamics of a problem. Physical insight into various problems in electromagnetics, optics and electrostatics will be gleaned by examining the intrinsic trade-offs.