## 1 Introduction
On the other hand, aggregation techniques provide only one solution to the problem per algorithm run, whereas the quality of the result depends on the weights assigned to individual figures of interest [35]. Alternatively, MO optimization can be performed using the genuine MO algorithms [39; 43]. The latter ones are especially useful when the designer's priorities are not clearly defined, as they provide a set of solutions representing trade-offs between the requirements. Such cognitive studies are useful from the perspective of gaining a detailed insight into the capabilities of the antenna, with respect to the desired application scenarios or environments [45]. Although multi-objective problems could be solved using population-based metaheuristic methods, their practical applications are limited to rather simple structures due to the prohibitive computational cost [35; 37]. Less numerically demanding routines involve the execution of evolutionary algorithms on the approximation models. Due to the curse of dimensionality [46], the usefulness of approximation models and metaheuristics for reliable MO optimization is limited either to low-dimensional structures or narrow search spaces [43; 47]. Notwithstanding, the mentioned methods proved to be useful for solving problems characterized by over a dozen design parameters [43]. Alternatively, MO design can be handled using dedicated heuristic approaches oriented toward the sequential generation of Pareto-optimal solutions [43; 47]. Nonetheless, neither of the mentioned methods are suitable for handling antenna models characterized by a flexible number of adjustable parameters. The above considerations indicate that contemporary UWB antennas can be categorized into a few classes [16; 17; 18; 19; 20; 21; 22; 23; 24]. The topologies from each group are similar except for features such as slots or stubs that are normally introduced as a result of manual, greedy search-based studies to alter the functionality of the structure. In this regard, representation of the antenna using a generic model might be useful for the automated development of its topology regarding the imposed performance and geometry requirements. Although \"universal\" antenna models have been reported in the literature, they lack flexibility in terms of the number of degrees of freedom used for their representation. Consequently, they are either too simple or too complex (parameter-wise) to obtain compromise designs. The application of generic topology (or its derivatives) for a range of application scenarios should reduce the cost of system development, as well as its time to market. Unfortunately, the available MO routines are inadequate for handling models with flexible parameterization due to the lack of mechanisms for the adjustment of problem dimensionality in the course of the optimization process. The motivation of this work is to address the mentioned challenges. In this paper, a generic EM model of a planar antenna with flexible parameterization is presented. The structure is optimized in a bi-objective setup concerning minimization of in-band reflection within a 3.1 GHz to 10.6 GHz band and size. A set of designs, representing the trade-off between the requirements, is obtained using a novel framework that sequentially generates candidate solutions. The latter are refined in a nested trust region-based optimization loop that enables one to gradually increase the number of parameters. The proposed model and optimization framework are demonstrated through the generation of nine Pareto-optimal designs. Their geometries are represented using 30 to 46 input parameters. The variability of the antenna's in-band performance and size along the Pareto set is from \(-10.3\) dB to \(-20.5\) dB (over 10 dB) and from 230 mm\({}^{2}\) to 757 mm\({}^{2}\) (almost 70 percent), respectively. The presented algorithm has been compared against other population-based metaheuristic routines in terms of optimization cost and the quality of obtained solutions.