Cost-efficient variable-fidelity machine learning for globalized optimization of microwave structures

This paper proposes a novel methodology for cost-efficient optimization of microwave circuits. The design task at hand is the identification of the solution that minimizes the assumed scalar cost function (encoding the design specifications) in a global sense over the prescribed domain, which is defined using lower and upper bounds on decision variables (here, geometry parameters of the circuit of interest). Our technique involves a kriging-based machine learning procedure carried out in a decreased-dimensionality domain established by means of rapid global sensitivity analysis, as well as final local tuning in the initial (full-dimensionality) parameter space. Domain confinement facilitates the construction of accurate surrogate models, thereby improving the reliability and efficiency of the search process. Additional acceleration is obtained by conducting the global optimization stage using lower-fidelity EM simulations and by incorporating a restricted sensitivity updating strategy at the stage of local refinement. The presented methodology has been validated using four microwave components, including rat-race and branch-line couplers, and a dual-band power divider. Comprehensive numerical experiments demonstrate its superior performance over the benchmark algorithms available in literature, both with regard to reliability, repeatability of solutions, and computational efficiency. In absolute terms, the average optimization cost corresponds to less than 80 EM analyses of the circuit at hand, which is remarkably low, especially considering the global search capability of the method. The fundamental factors providing the competitive edge of our methodology compared to the benchmark are explicit dimensionality reduction, variable-resolution EM simulations, and a two-stage process where fast local tuning compensates for possible inaccuracy of the global search stage and its relaxed termination criteria (contributing to cost efficiency).