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The purpose of this study is to propose a framework for expedited antenna optimization with numerical derivatives involving gradient variation monitoring throughout the optimization run and demonstrate it using a benchmark set of real-world wideband antennas. A comprehensive analysis of the algorithm performance involving multiple starting points is provided. The optimization results are compared with a conventional trust-region (TR) procedure, as well as the state-of-the-art accelerated TR algorithms.

The proposed algorithm is a modification of the TR gradient-based algorithm with numerical derivatives in which a monitoring of changes of the system response gradients is performed throughout the algorithm run. The gradient variations between consecutive iterations are quantified by an appropriately developed metric. Upon detecting stable patterns for particular parameter sensitivities, the costly finite differentiation (FD)-based gradient updates are suppressed; hence, the overall number of full-wave electromagnetic (EM) simulations is significantly reduced. This leads to considerable computational savings without compromising the design quality.

Monitoring of the antenna response sensitivity variations during the optimization process enables to detect the parameters for which updating the gradient information is not necessary at every iteration. When incorporated into the TR gradient-search procedures, the approach permits reduction of the computational cost of the optimization process. The proposed technique is dedicated to expedite direct optimization of antenna structures, but it can also be applied to speed up surrogate-assisted tasks, especially solving sub-problems that involve performing numerous evaluations of coarse-discretization models.

The introduced methodology opens up new possibilities for future developments of accelerated antenna optimization procedures. In particular, the presented routine can be combined with the previously reported techniques that involve replacing FD with the Broyden formula for directions that are satisfactorily well aligned with the most recent design relocation and/or performing FD in a sparse manner based on relative design relocation (with respect to the current search region) in consecutive algorithm iterations.

Benchmarking against a conventional TR procedure, as well as previously reported methods, confirms improved efficiency and reliability of the proposed approach. The applications of the framework include direct EM-driven design closure, along with surrogate-based optimization within variable-fidelity surrogate-assisted procedures. To the best of the authors’ knowledge, no comparable approach to antenna optimization has been reported elsewhere. Particularly, it surmounts established methodology by carrying out constant supervision of the antenna response gradient throughout successive algorithm iterations and using gathered observations to properly guide the optimization routine.

A framework for reliable modeling of high-frequency structures by nested kriging with an improved sampling procedure is developed and extensively validated. A comprehensive benchmarking including conventional kriging and previously reported design of experiments technique is provided. The proposed technique is also demonstrated in solving parameter optimization task.

The keystone of the proposed approach is to focus the modeling process on a small region of the parameter space (constrained domain containing high-quality designs with respect to the selected performance figures) instead of adopting traditional, hyper-cube-like domain defined by the lower and upper parameter bounds. A specific geometry of the domain is explored to improve a uniformity of the training data set. In consequence, the predictive power of the model is improved.

Building the model in a constrained domain allows for a considerable reduction of a training data set size without a necessity to either narrow down the parameter ranges or to reduce the parameter space dimensionality. Improving uniformity of training data set allocation permits further reduction of the computational cost of setting up the model. The proposed technique can be used to expedite the parameter optimization and enables locating good initial designs in a straightforward manner.

The developed framework opens new possibilities inaccurate surrogate modeling of high-frequency structures described by a large number of geometry and/or material parameters. Further extensions can be investigated such as the inclusion of the sensitivity data into the model or exploration of the particular geometry of the model domain to further reduce the computational overhead of training data acquisition.

The efficiency of the proposed method has been demonstrated for modeling and parameter optimization of high-frequency structures. It has also been shown to outperform conventional kriging and previous constrained modeling approaches. To the authors’ knowledge, this approach to formulate and handle the modeling process is novel and permits the establishment of accurate surrogates in highly dimensional spaces and covering wide ranges of parameters.

This study aims to propose a computationally efficient framework for multi-objective optimization (MO) of antennas involving nested kriging modeling technology. The technique is demonstrated through a two-objective optimization of a planar Yagi antenna and three-objective design of a compact wideband antenna.

The keystone of the proposed approach is the usage of recently introduced nested kriging modeling for identifying the design space region containing the Pareto front and constructing fast surrogate model for the MO algorithm. Surrogate-assisted design refinement is applied to improve the accuracy of Pareto set determination. Consequently, the Pareto set is obtained cost-efficiently, even though the optimization process uses solely high-fidelity electromagnetic (EM) analysis.

The optimization cost is dramatically reduced for the proposed framework as compared to other state-of-the-art frameworks. The initial Pareto set is identified more precisely (its span is wider and of better quality), which is a result of a considerably smaller domain of the nested kriging model and better predictive power of the surrogate.

The proposed technique can be generalized to accommodate low- and high-fidelity EM simulations in a straightforward manner. The future work will incorporate variable-fidelity simulations to further reduce the cost of the training data acquisition.

The fast MO optimization procedure with the use of the nested kriging modeling technology for approximation of the Pareto set has been proposed and its superiority over state-of-the-art surrogate-assisted procedures has been proved. To the best of the authors’ knowledge, this approach to multi-objective antenna optimization is novel and enables obtaining optimal designs cost-effectively even in relatively high-dimensional spaces (considering typical antenna design setups) within wide parameter ranges.

A technique for accelerated design optimization of antenna input characteristics is developed and comprehensively validated using real-world wideband antenna structures. Comparative study using a conventional trust-region algorithm is provided. Investigations of the effects of the algorithm control parameters are also carried out.

An optimization methodology is introduced that replaces finite differentiation (FD) by a combination of FD and selectively used Broyden updating formula for antenna response Jacobian estimations. The updating formula is used for directions that are sufficiently well aligned with the design relocation that occurred in the most recent algorithm iteration. This allows for a significant reduction of the number of full-wave electromagnetic simulations necessary for the algorithm to converge; hence, it leads to the reduction of the overall design cost.

Incorporation of the updating formulas into the Jacobian estimation process in a selective manner considerably reduces the computational cost of the optimization process without compromising the design quality. The algorithm proposed in the study can be used to speed up direct optimization of the antenna structures as well as surrogate-assisted procedures involving variable-fidelity models.

This study sets a direction for further studies on accelerating procedures for the local optimization of antenna structures. Further investigations on the effects of the control parameters on the algorithm performance are necessary along with the development of means to automate the algorithm setup for a particular antenna structure, especially from the point of view of the search space dimensionality.

The proposed algorithm proved useful for a reduced-cost optimization of antennas and has been demonstrated to outperform conventional algorithms. To the authors’ knowledge, this is one of the first attempts to address the problem in this manner. In particular, it goes beyond traditional approaches, especially by combining various sensitivity estimation update measures in an adaptive fashion.

A novel framework for expedited antenna optimization with an iterative prediction-correction scheme is proposed. The methodology is comprehensively validated using three real-world antenna structures: narrow-band, dual-band and wideband, optimized under various design scenarios.

The keystone of the proposed approach is to reuse designs pre-optimized for various sets of performance specifications and to encode them into metamodels that render good initial designs, as well as an initial estimate of the antenna response sensitivities. Subsequent design refinement is realized using an iterative prediction-correction loop accommodating the discrepancies between the actual and target design specifications.

The presented framework is capable of yielding optimized antenna designs at the cost of just a few full-wave electromagnetic simulations. The practical importance of the iterative correction procedure has been corroborated by benchmarking against gradient-only refinement. It has been found that the incorporation of problem-specific knowledge into the optimization framework greatly facilitates parameter adjustment and improves its reliability.

The proposed approach can be a viable tool for antenna optimization whenever a certain number of previously obtained designs are available or the designer finds the initial effort of their gathering justifiable by intended re-use of the procedure. The future work will incorporate response features technology for improving the accuracy of the initial approximation of antenna response sensitivities.

The proposed optimization framework has been proved to be a viable tool for cost-efficient and reliable antenna optimization. To the knowledge, this approach to antenna optimization goes beyond the capabilities of available methods, especially in terms of efficient utilization of the existing knowledge, thus enabling reliable parameter tuning over broad ranges of both operating conditions and material parameters of the structure of interest.