Fast Multi-Objective Optimization of Antenna Structures by Means of Data-Driven Surrogates and Dimensionality Reduction

Abstract

Design of contemporary antenna structures needs to account for several and often conflicting objectives. These are pertinent to both electrical and field properties of the antenna but also its geometry (e.g., footprint minimization). For practical reasons, especially to facilitate efficient optimization, single-objective formulations are most often employed, through either a priori preference articulation, objective aggregation, or casting all but one (primary) objective into constraints. Notwithstanding, the knowledge of the best possible design trade-offs provides a more comprehensive insight into the properties of the antenna structure at hand. Genuine multi-objective optimization is a proper way of acquiring such data, typically rendered in the form of a Pareto set that represents the mentioned trade-off solutions. In antenna design, the fundamental challenge is high computational cost of multi-objective optimization, normally carried out using populationbased metaheuristic algorithms. In most practical cases, the use of reliable, yet costly, full-wave electromagnetic models is imperative to ensure evaluation reliability, which makes conventional multiobjective optimization procedures prohibitively expensive. The employment of fast surrogates (or metamodels) can alleviate these difficulties, yet, construction of metamodels faces considerable challenges by itself, mostly related to the curse of dimensionality. This work proposes a novel surrogate-assisted approach to multi-objective optimization, where the data-driven model is only rendered in a small region spanned by the selected principal components of the extreme Pareto-optimal design set obtained using local search routines. The region is limited in terms of parameter ranges but also dimensionality, yet contains the majority of Pareto front, therefore surrogate construction therein does not incur considerable costs. The typical cost of identifying the Pareto set is just a few hundred of full-wave analyses of the antenna under design. Our technique is validated using two antenna examples (a planar Yagi and an ultra-wideband monopole antenna) and favorably compared to state-of-the-art surrogate-assisted multi-objective optimization methods. INDEX TERMS Antenna design; multi-objective optimization; surrogate modeling; domain confinement; principal components; dimensionality reduction.

A Method to Co-Design Antenna Element and Array Patterns

“…We create a model for determining the realized gain at different angles as a function of element-level port impedances and signals, and array-level weights. As an example, the proposed model is then used to find Pareto optimal solutions [19] by means of multi-objective genetic algorithm optimization.…”

“…Generally, Pareto optimality means that no objective can be improved without degrading another [19]. Thus in this work, Pareto optimality means that gain at one angle cannot be increased without decreasing the gain at another angle.…”

“…Note that generally there does not exist feasible solution x that would maximize all the objective functions simultaneously. Hence, multi-objective optimization algorithms seek to identify Pareto optimal solutions: a feasible solution is Pareto optimal if no other feasible solution yields a better or equal value in all objective functions and strictly better at least in one objective function [19].…”

On geometry parameterization for simulation-driven design closure of antenna structures

“…Some of available options include methods for expediting the EM-driven optimization procedures, e.g., adjoint sensitivities 25 , sparse Jacobian updates 26 , surrogate-assisted methods, involving both data-driven (kriging 27 , radial-basis functions 28 , neural networks 29 , Gaussian process regression 30 , ensemble learning methods 31 ), and physics-based models (space mapping 32 , manifold mapping 33 , response correction methods 34 , 35 , cognition-driven design 36 ), or machine learning techniques 37 , 38 . Handling of multiple objectives is often realized using surrogate-enhanced population-based methods 39 – 41 or penalty function approaches (e.g., for size reduction under multiple constraints imposed on antenna electrical performance 42 ), whereas dimensionality issues are often addressed using high-dimensional model representation (HDMR) 43 , principal component analysis (PCA) 44 , model order reduction methods 45 , or—in the context of response surface approximation—techniques such as orthogonal matching pursuit (OMP) 46 , or least angle regression (LAR) 47 . Surrogate-based methods are also popular for aiding global optimization 48 , 49 .…”

On geometry parameterization for simulation-driven design closure of antenna structures

“…Some of available options include methods for expediting the EM-driven optimization procedures, e.g., adjoint sensitivities 25 , sparse Jacobian updates 26 , surrogateassisted methods, involving both data-driven (kriging 27 , radial-basis functions 28 , neural networks 29 , Gaussian process regression 30 , ensemble learning methods 31 ), and physics-based models (space mapping 32 , manifold mapping 33 , response correction methods 34,35 , cognitiondriven design 36 ), or machine learning techniques 37,38 . Handling of multiple objectives is often realized using surrogate-enhanced population-based methods [39][40][41] or penalty function approaches (e.g., for size reduction under multiple constraints imposed on antenna electrical performance 42 ), whereas dimensionality issues are often addressed using high-dimensional model representation (HDMR) 43 , principal component analysis (PCA) 44 , model order reduction methods 45 , or-in the context of response surface approximation-techniques such as orthogonal matching pursuit (OMP) 46 , or least angle regression (LAR) 47 . Surrogate-based methods are also popular for aiding global optimization 48,49 .…”