## 2 Generic UWB Monopole Antenna  
Consider a planar monopole antenna, shown in Figure 1. The structure consists of a driven element in the form of a spline-parameterized radiator fed through a microstrip line. The ground plane edge oriented toward the radiating component is also implemented in the form of a spline curve. The presented topology generates closely located resonant modes, which contribute to the broadband behavior [48; 49]. Furthermore, the bandwidth-related performance is enhanced using an \(L\)-shaped ground plane stub, which improves the impedance matching of miniaturization-oriented designs [24]. The structure is implemented on a Rogers RO4003 dielectric substrate with a permittivity of 3.58, thickness of 0.813 mm, and loss tangent of 0.0027. The vector of the antenna input parameters is \(\mathbf{y}=[\mathbf{y}_{a}\;\mathbf{y}_{g}\;\mathbf{y}_{r}]^{T}\), where \(\mathbf{y}_{a}=[X\;l_{f}\;l_{1}\;l_{2r}\;w_{1}\;o_{r}]^{T}\), \(\mathbf{y}_{g}=[\mathbf{y}_{g,1}\;\ldots\;y_{g,L}]^{T}\) and \(\mathbf{y}_{r}=[\mathbf{y}_{r,1}\;\ldots\;\mathbf{y}_{r,L}]^{T}\) (\(L=50\) represents the number of points used to represent the ground plane and radiator in the antenna model). The relative variables are \(l_{2}=(X-w_{1})l_{2r}\), \(Y=l_{1}+w_{1}\), \(l_{r}=\min\{0.5X,\)\(0.5(Y-l_{f})\}\), \(o=0.5X+o_{r}\). Dimension \(w_{f}=1.8\) remains fixed to ensure 50 Ohm input impedance. The unit for all variables except dimensionless \(l_{2r}\) is mm. It should be noted that vectors \(\mathbf{y}_{g}=Y\cdot\mathbf{z}_{g}\), and \(\mathbf{y}_{r}=S\cdot\mathbf{z}_{r}\), where \(S=\min\{0.5(X-o_{r}),\)\(0.5(Y-l_{f})\}\) represent the characteristic points (so-called knots) of the spline curves used to define the ground plane and radiator, respectively (see Figure 1). To ensure the structure consistency, the gap between each knot \(\mathbf{y}_{g}\) and \(\mathbf{y}_{r}\) is even. Hence, the vectors denote the relative distance of the curve from the reference point (edge of the substrate for \(\mathbf{y}_{g}\) and center of the radiator for \(\mathbf{y}_{r}\), respectively; Figure 1). It is worth emphasizing that \(\mathbf{y}_{r}\) represents axial dimensions, as the parameters of the radiator are defined in a cylindrical coordinate system. The EM model of the antenna structure \(\mathbf{R}\) is implemented in CST Microwave Studio and evaluated using its time domain solver. The presented antenna supports flexible parameterization. In other words, the number of adjustable variables used for representation of the structure geometry can be changed in the course of the design process. The rationale behind this feature is that--when the generation of compromise design solutions is considered--the initial search space ranges are set to be large to ensure that the optimal designs are captured within them. The application of conventional (population-based) methods for exploration of the search space with wide parameter ranges is numerically impractical due to the tremendous number of iterations required for convergence [38; 43]. Having a model with adjustable dimensionality, one can narrow down the search space to the region of interest using a relatively small number of parameters. The promising region can be further exploited through optimizations of the model characterized by gradually increasing dimensionality. Flexible parameterization has been implemented through implicit handling of the input variables. Let \(\mathbf{x}_{d}=[\mathbf{y}_{a}\,\mathbf{x}_{g,d}\,\mathbf{x}_{r,d}]^{T}\), where \(\mathbf{x}_{g,d}=[x_{g,1}\,\ldots\,\,x_{g,d}]^{T}\), \(\mathbf{x}_{r,d}=[x_{r,1}\,\ldots\,\,x_{r,d}]^{T}\), \(d=1,\,\ldots\,\,L\) represent the \(d\)-knot spline curve used to represent the antenna ground plane and radiator, respectively. Note that when \(d<4\), \(\mathbf{x}_{g,d}=x_{g,1}\) and \(\mathbf{x}_{r,d}=x_{r,1}\), because the implementation of the spline used in this work requires at least four knots.