Multi-Objective Optimization of Vector Fitting for Accurate and Compact S-Parameter Models

Vector Fitting is widely used in electromagnetic system modeling to approximate large datasets of scattering parameters with a compact rational function. However, its effectiveness heavily depends on the initial selection of poles, which significantly impacts the accuracy and stability of the approximation. Traditionally, the number of poles must be determined a priori, often requiring trial-and-error adjustments. To overcome these limitations, this work solves the problem using a multi-objective optimization with a variable number of dimensions approach. The proposed approach automatically determines both the optimal number and distribution of poles in a single optimization run. Three state-of-the-art multi-objective optimization algorithms are evaluated on two different antenna models, represented by their scattering parameters. Experimental results demonstrate that the proposed method effectively searches for the Pareto front expressing a tradeoff between model complexity and approximation accuracy, reducing the need for manual adjustments.