# Performance-Driven Yield Optimization of High-Frequency Structures by Kriging Surrogates
## 5 Conclusions  
This work discussed the recent techniques for surrogate-based yield maximization of high-frequency components. The main ingredients of the optimization framework are domain-confined metamodels constructed by keeping in mind the parameter-space directions that are the most influential in terms of affecting the system's performance. By maintaining the low overall volume of the domain, it is possible to construct reliable surrogates using a limited number of training data samples, and it is possible to carry out the yield optimization process without the need to rebuild the model. As demonstrated using two microstrip structures (an antenna and a rat-race coupler), the robust design process can be accomplished at remarkably low costs of a few dozens of EM simulations. Thorough benchmarking indicates significant savings, with >80 percent over reference surrogate-based approach and >60 percent over the SAO algorithm. At the same time, reliability has been corroborated using EM-driven Monte Carlo simulations. The optimization techniques considered in the paper offer improved computational efficiency over the state-of-the-art methods without compromising reliability. They are applicable to a variety of antenna and microwave components, and they may be viewed as potential replacements of conventional (also surrogate-assisted) procedures, especially for more complex, e.g., higher-dimensional design scenarios. Since in the considered approach, the surrogate domain is spanned by the directions that influence yield values in the most significant manner, the generalization of the technique would require properly defining these directions so that they reflect the respective design requirements.  
Figure 12: Monte Carlo analysis of the coupler of Figure 10 using EM simulations (gray plots): (**a**) nominal design; (**b**) yield-optimized design obtained using the algorithm of Section 3.2. Black plots show the antenna response at the nominal and the optimized designs, respectively.  
In general, the two specific approaches for constructing the domain of the surrogate model (extension along the one-dimensional curve for the antenna example, and along two vectors corresponding to the maximum changes of the considered performance figures for the coupler example) could be applied to either of the case studies. However, maintaining the domain extension's dimensionality as equal to the number of considered performance figures is recommended, which is to provide sufficient room for yield improvement within the domain.  
Conceptualization, A.P.-D. and S.K.; methodology, A.P.-D. and S.K.; software, A.P.-D.; validation, A.P.-D. and S.K.; formal analysis, A.P.-D. and S.K.; investigation, A.P.-D.; resources, S.K.; data curation, A.P.-D.; writing--original draft preparation, A.P.-D. and S.K.; writing--review and editing, A.P.-D. and S.K.; visualization, A.P.-D.; supervision, S.K.; project administration, S.K.; funding acquisition, S.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Icelandic Centre for Research (RANNIS), Grant 206606, and by National Science Centre of Poland, Grant 2018/31/B/ST7/02369.  
Not applicable.  
The authors thank Dassault Systemes, France, for making CST Microwave Studio available.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.