Constrained multi-objective optimization of compact microwave circuits by design triangulation and pareto front interpolation

Development of microwave components is an inherently multi-objective task. This is especially pertinent to the design closure stage, i.e., final adjustment of geometry and/or material parameters carried out to improve the electrical performance of the system. The design goals are often conflicting so that the improvement of one normally leads to a degradation of others. Compact microwave passives constitute a representative case: reduction of the circuit footprint area is detrimental to electrical figures of merit (e.g., the operating bandwidth). Identification of the best available trade-off designs requires multi-objective optimization (MO). This is a computationally expensive task, especially when executed at the level of full-wave electromagnetic (EM) simulation. The computational complexity issue can be mitigated through the employment of surrogate modeling methods, yet their application is limited by a typically high nonlinearity of system responses, and the curse of dimensionality. In this paper, a novel technique for fast MO of compact microwave components is proposed, which allows for sequential rendition of the trade-off designs using triangulation of the already available Pareto front as well as rapid refinement algorithms. Our methodology is purely deterministic; in particular, it does not rely on population-based nature-inspired procedures. The three major benefits are low computational cost, possibility of handling explicit design constraints, and a capability of producing a visually uniform representation of the Pareto front. The algorithm is demonstrated using a compact branch-line coupler and a three-section impedance matching transformer. In both cases, considerable savings are obtained over the benchmark, here, the state-of-the-art surrogate-assisted MO technique.