## 1 Introduction
Some of the widely used modeling techniques include neural networks [58; 59; 60], kriging [61], radial basis functions [62], polynomial chaos expansion [63], support vector regression [64], etc. Data-driven surrogates are used for global [65] and multi-objective design [66] and statistical analysis [67], and they are often combined with machine learning methods [68]. Their fundamental drawback is related to the curse of dimensionality [69], which hinders their applicability in higher-dimensional parameter spaces. Physics-based surrogates are built using a core low-fidelity model (e.g., equivalent circuit [70], coarse-mesh EM simulations [71]). They are less susceptible to dimensionality issues yet lack universal approximation capability [72]; therefore, they are more suitable for local search purposes [57]. Representative methods comprise space mapping [73], cognition-driven design [74], and adaptive response scaling [75]. Other techniques for accelerating simulation-based design procedures include response feature technology [76; 77] and also variable-resolution techniques and models (co-kriging [78], multi-fidelity algorithms [44; 79]). Antenna size reduction, when considered in the context of optimization, is a numerically intricate task. On the one hand, all challenges of EM-driven design mentioned before still apply. On the other hand, it is a problem with expensive constraints. For practical reasons, i.e., to avoid excessive computational costs, it is typically solved using local (e.g., gradient-based) algorithms [80], with the constraints tackled in an implicit fashion using a penalty function approach [81]. Notwithstanding, compact antennas exhibit parameter redundancy, being a result of all kinds of additional components (stubs, slots, DSGs, etc. )that have to be properly dimensioned. As a result, miniaturization tasks are multimodal problems: an optimization procedure normally finds a local optimum, which is highly dependent on the starting point [82]. Although this implies the necessity for global search, available methods are incapable of handling miniaturization tasks. In particular, the computational complexity of nature-inspired algorithms is excessively high for direct EM-based optimization, whereas constructing reliable surrogate models over the entire parameter space of a compact antenna is hindered by both dimensionality issues and typically wide ranges of structure parameters. In this work, we present a novel algorithm for knowledge-based globalized size reduction of antenna structures, which addresses most of the challenges elaborated on in the previous paragraph. Our framework consists of several steps. These include an approximation of the boundary of the feasible region using random observables selected in an automated decision-making process, which takes into account their distance from the feasible region boundary, and auxiliary optimization runs, the establishment of a dimensionality-reduced domain, as well as construction of fast data-driven surrogate therein. Further steps include global optimization of the metamodel followed by ultimate miniaturization-oriented refinement of antenna parameters. The dimensionality of the surrogate model domain is explicitly reduced using spectral analysis of the selected observables, which undergo initial pre-optimization. For the sake of computational efficiency, the first few stages of the optimization procedure are performed with the use of the low-fidelity EM model. The proposed approach is extensively validated with the use of four broadband microstrip antennas and benchmarked against local search algorithms in several variations initiated from random starting points, along with particle swarm optimization (as a commonly used, nature-inspired global search method). The results show that our approach yields superior miniaturization rates with good repeatability of solutions while ensuring satisfactory constraint violation control. At the same time, its computational efficacy is practically acceptable.