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 population-based 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 multi-objective 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.
Highlights
Design of modern antenna structures faces several serious challenges
This paper proposes a novel framework for multi-objective design optimization of antenna structures that capitalizes on performance-driven surrogate modeling concept [57], as well as explicit reduction of the parameter space dimensionality based on the principal component analysis (PCA) [58] of the extreme Pareto-optimal designs
Our methodology involves a surrogate model constructed in a confined domain that is established using a set of Pareto-optimal designs obtained through single-objective optimization runs, and, their principal components
Summary
Design of modern antenna structures faces several serious challenges. These arise from the necessity of satisfying stringent requirements pertinent to electrical and field characteristics (e.g., broadband operation [1], pattern stability [2], circular polarization [3]), implementation of various functionalities (e.g., multi-band operation [4], band notches [5], pattern diversity [6]), demands pertinent to emerging application areas (5G [7], internet of things [8]), and small physical size [9], [10], critical for wearable [11] or implantable devices [12]. This paper proposes a novel framework for multi-objective design optimization of antenna structures that capitalizes on performance-driven surrogate modeling concept [57], as well as explicit reduction of the parameter space dimensionality based on the principal component analysis (PCA) [58] of the extreme Pareto-optimal designs. The originality and major novel contributions of this work include: (i) development of computationally-efficient procedure for multi-objective antenna optimization, (ii) incorporation of the performancedriven modeling concept and PCA-based dimensionality reduction mechanisms into surrogate-assisted multi-objective design framework that allows for initial approximation of the Pareto set (this includes introduction of a rigorous formalism), as well as (iii) demonstration of the efficacy of the resulting MO procedure when handling real-world antenna design tasks as well as its superiority over state-of-the-art surrogate-assisted procedures. The overall operation of the proposed MO procedure is explained in Section II.D and illustrated using a flow diagram
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