## 1 Introduction  
Modern antenna systems are designed to fulfill numerous and often stringent performance requirements concerning impedance matching (e.g., multi-band [1] or broadband [2] operation), polarization (polarization diversity [3], circular polarization [4]), radiation characteristics (high gain [5], low sidelobe levels [6], beam scanning [7]), reconfigurable [8], efficiency [9], etc. These are driven by the demands of new fields of application including the Internet of Things (IoT) [10, 11], microwave imaging [12], mobile and space communications [13, 14], automotive radars [15], and implantable devices [16], to mention just a few. For most of the aforementioned applications, maintaining a small size of the radiator is an important consideration. At the same time, reducing an antenna's physical dimensions often results in a degradation of its performance figures (efficiency [17], pattern stability [18], bandwidth [19]). Therefore, the design of compact antennas is a search for trade-offs between conflicting objectives. Antenna miniaturization is basically a two-stage process. The initial stage is a selection of the basic architecture, supposedly ensuring compact dimensions [20; 21]. This is normally achieved by trial and error, i.e., introducing and testing various geometry alterations of the radiator [22], feeding network [23], or the ground plane [24]. The most popular of these include stubs [25], radiator slots [26], meandered radiating components [27], ground plane slits [28], cross slots [29], tapered or stepped-impedance feeding lines [30], shorting pins [31], custom-shaped radiating elements [32], and defected ground structures (DSG) [33]. These and other methods often enable considerable miniaturization rates but also result in an increased number of geometry parameters that need to be carefully adjusted to control both the antenna size and electrical performance. While the initial dimensions of the modified structures may be obtained with parameter sweeping, numerical optimization using rigorous means is requisite to boost the performance of the structure and also to verify the pertinence of specific topology modifications introduced into the antenna. It has been demonstrated that certain geometrical changes turn counterproductive upon proper parameter tuning [34]. Nowadays, the awareness and use of numerical optimization techniques have become widespread in antenna design [35; 36; 37], both to enhance specific performance figures (gain [38], bandwidth [39], sidelobe level reduction [40], mutual coupling reduction [41]) and to solve more involved tasks (uncertainty quantification [42], multi-criterial optimization [43]). Still, antenna optimization is a challenging undertaking. First, it typically involves full-wave electromagnetic (EM) simulations, thereby entailing sizeable computational expenditures, especially when a global search is of interest [44] or statistical design [45]. Furthermore, the geometrical complexity of contemporary antenna systems indicates a large number of parameters that have to be tuned, whereas the optimization tasks may be quite intricate (several design goals and constraints). The literature is replete with techniques developed to facilitate optimization processes. Available methods include acceleration of gradient-based algorithms that exploit adjoint sensitivities [46] or sparse sensitivity updating schemes [47; 48; 49], utilization of fast solvers [50], and mesh deformation techniques [51], along with the incorporation of surrogate modeling techniques [52; 53]. With no exaggeration, surrogate-based optimization (SBO) can be considered a paradigm shift in EM-driven design, becoming a standard for an increasing number of tasks (e.g., yield optimization [54], multi-objective design [55]). SBO methods may involve approximation-based (data-driven) [56] or physics-based surrogates [57]. The first group is more generic and directly applicable to a variety of problems, thereby, it is also more popular.