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

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.