Optimization strategies for metasurface antenna design

The automated design of metasurface (MTS) antennas has been a subject of extensive research, encompassing both theoretical and practical aspects. The inherent complexity of these antennas, made by sub-wavelength scattering elements organized in a periodic lattice over large areas, has forced researchers to devise more efficient methods for addressing this challenge. Recent strategies have shifted towards fully numerical modelling, with solutions attained through either direct methods or optimization algorithms. Among the latter, recently the current-based approach has emerged as a promising avenue for tackling the design of large antennas. Nonetheless, like all non-linear and non-convex optimization problems, it encounters common issues such as slow convergence and the occurrence of local minima. In this work, a novel adaptive weighting scheme for the current-based optimization of MTS antennas is proposed. The design of MTS antennas is a multi-objective optimization problem, i.e., a set of constraints must be concurrently met, including passivity, losslessness, pattern masks, and more. In order to reduce its numerical complexity, the problem is formulated as a single objective minimization with the weighted sum method. The weights assigned to each objective function reflect the relative significance of specific objectives, nonetheless, it is generally a complex task to definitively determine the hierarchy of importance. It is possible to demonstrate that an a priori choice of a set of weights leads to suboptimal solutions or to the convergence to a local minimum. Therefore, a scheme capable of adaptively modifying the weights of individual objective functions is valuable for exploring the Pareto front. The algorithm proposed in this work is based on the geometrical interpretation of the weights: anchor points can be identified on the Pareto front, then, a hyperplane is constructed from these points. The components of the normal unit vector to the hyperplane, which points in the direction of the knee point, can be used as weights for the objective function. To assess the performance of the proposed algorithm, its results have been compared to those achieved by a conventional minimization algorithm performed over an equal number of iterations for various antenna size and pattern masks. The proposed solution is able to achieve satisfactory results within a limited number of iterations, whereas the conventional solution is still far from convergence. In conclusion, the algorithm proposed in this study allows the design process to be freed from the selection of an accurate initial set of weights. Moreover, the numerical results demonstrate an enhancement in the achieved performance and an increase in the convergence speed compared to standard algorithms.