A Suboptimal Approach to Antenna Design Problems With Kernel Regression

This paper proposes a novel iterative algorithm based on a Kernel regression as a suboptimal approach to reliable and efficient antenna optimization. In our approach, the complex and non-linear cost surface calculated from antenna characteristics is fitted into a simple linear model using Kernels, and an argument that minimizes this Kernel regression model is used as a new input to calculate its cost using numerical simulations. This process is repeated by updating coefficients of the Kernel regression model with new entries until meeting the stopping criteria. At every iteration, existing inputs are partitioned into a limited number of clusters to reduce the computational time and resources and to prevent unexpected over-weighted situations. The proposed approach is validated for the Rastrigins function as well as a real engineering problem using an antipodal Vivaldi antenna in comparison with a genetic algorithm. Furthermore, we explore the most appropriate Kernel that minimizes the least-square error when fitting the antenna cost surface. The results demonstrate that the proposed process is suitable to be used in antenna design problems as a reliable approach with a fast convergence time.