Vast majority of practical engineering design problems require simultaneous handling of several criteria. For the sake of simplicity and through a priori preference articulation one can turn many design tasks into single-objective problems that can be handled using conventional numerical optimization routines. However, in some situations, acquiring comprehensive knowledge about the system at hand, in particular, about possible trade-offs between conflicting objectives may be necessary. This calls for multi-objective optimization that aims at identifying a set of alternative, Pareto-optimal designs. The most popular solution approaches include population-based metaheuristics. Unfortunately, such methods are not practical for problems involving expensive computational models. This is particularly the case for microwave and antenna engineering where design reliability requires utilization of CPU-intensive electromagnetic (EM) analysis. In this work, we discuss methodologies for expedited multi-objective design optimization of expensive EM simulation models. The solution approaches that we present here rely on surrogate-based optimization (SBO) paradigm, where the design speedup is obtained by shifting the optimization burden into a cheap replacement model (the surrogate). The latter is utilized for generating the initial approximation of the Pareto front representation as well as further front refinement (to elevate it to the high-fidelity EM simulation model level). We demonstrate several application case studies, including a wideband matching transformer, a dielectric resonator antenna and an ultra-wideband monopole antenna. Dimensionality of the design spaces in the considered examples vary from six to fifteen, and the design optimization cost is about one hundred of high-fidelity EM simulations of the respective structure, which is extremely low given the problem complexity.
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