Variable-fidelity EM analysis and simplex-anchored regression surrogates for efficient global optimization of microwave passive circuits

Formal optimization is nowadays ubiquitous in microwave design. It is frequently conducted using electromagnetic (EM) simulations, which guarantee dependability. Yet, it is computationally expensive. Local tuning may involve hundreds of system analyses, whereas global EM-driven optimization typically generates unmanageable expenses. However, global search is often imperative, for example, in design of miniaturized components, large-scale operating frequency re-design, problems with multiple local optima (design of metasurfaces or frequency selective surfaces). This study suggests a procedure for low-cost globalized optimization of microwave circuits. Its keystones are simplex-based regression surrogates constructed to represent the circuit's operating parameters. Geometrical simplicity of the surrogate and only a slightly nonlinear relation between the circuit dimensions and operating parameters, as well as conducting global search using low-resolution EM simulations, lead to a remarkable cost efficiency of the algorithm. Meanwhile, the assumed simplex updating rules guarantee convergence. The reliability is secured by a supplementary fine tuning executed using high-resolution EM models. As demonstrated, the presented framework exhibits perfect success rate with satisfactory designs found in each algorithm run out of multiple instances executed. The cost is just sixty high-resolution EM analyses, whereas design quality is competitive over the benchmark methods.