Abstract
Modern antenna systems are designed to meet stringent performance requirements pertinent to both their electrical and field properties. The objectives typically stay in conflict with each other. As the simultaneous improvement of all performance parameters is rarely possible, compromise solutions have to be sought. The most comprehensive information about available design trade-offs can be obtained through multi-objective optimization (MO), typically in the form of a Pareto set. Notwithstanding, MO is a numerically challenging task, in a large part due to high CPU cost of evaluating the antenna properties, normally carried out through full-wave electromagnetic (EM) analysis. Surrogate-assisted procedures can mitigate the cost issue to a certain extent but construction of reliable metamodels is hindered by the curse of dimensionality, and often highly nonlinear antenna characteristics. This work proposes an alternative approach to MO of antennas. The major contribution of our work consists in establishing a deterministic machine learning procedure, which involves sequential generation of Pareto-optimal designs based on the knowledge gathered so far in the process (specifically, by triangulation of the already obtained Pareto set), and local surrogate-assisted refinement procedures. Our methodology allows for rendering uniformly-distributed Pareto designs at the cost of a few hundreds of antenna EM simulations, as demonstrated by means of three verification case studies. Benchmarking against state-of-the-art MO techniques is provided as well.
Highlights
Contemporary antenna systems have to satisfy multiple and often stringent requirements concerning their electrical and field characteristics, such as broadband [1] or multi-band operation [2], multi-input multi-output (MIMO) functionality [3], circular polarization [4], tunability [5], pattern diversity [6], or enhanced gain [7]. These specifications are rooted in the needs pertinent to specific application areas, including the emerging technologies such as 5G [10]–[12], or the internet of things (IoT) [13], [14]
Perhaps the most common example is the design of compact antennas, where diminishing the antenna size leads to various undesirable effects
It should be emphasized that the considered multi-objective optimization (MO) algorithm is fully deterministic, it does not require any auxiliary stochastic search procedures, and its computational cost can be estimated beforehand based on the target number of Pareto optimal designs to be generated
Summary
Contemporary antenna systems have to satisfy multiple and often stringent requirements concerning their electrical and field characteristics, such as broadband [1] or multi-band operation [2], multi-input multi-output (MIMO) functionality [3], circular polarization [4], tunability [5], pattern diversity [6], or enhanced gain [7]. The introductory part of the paper briefly discussed possible ways of mitigating the issue related to high computational cost of massive EM simulations required by conventional MO algorithms These include both the hybrid approaches, primarily combinations of nature-inspired algorithms and surrogate modeling methods [41]–[45], deterministic algorithms [56], [59], as well as multi-fidelity methodologies combined with the refinement strategies [40]. The design xtmp.alt is obtained in the same way as (4) but using the linear model established using the (parameter space) vertices of the simplex S(jmax) Having both xtmp and xtmp.alt , the better of the two (in terms of the smaller value of the objective F1) is selected as the initial design. The procedure is terminated when the required number of designs along the front have been identified
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