Expedited antenna optimization with numerical derivatives and gradient change tracking

Anna Pietrenko-Dabrowska*, Slawomir Koziel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Purpose: 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. Design/methodology/approach: 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. Findings: 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. Research limitations/implications: 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. Originality/value: 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.

Original languageEnglish
Pages (from-to)1179-1193
Number of pages15
JournalEngineering Computations (Swansea, Wales)
Issue number4
Publication statusPublished - 16 Apr 2020

Bibliographical note

Funding Information:
The authors thank Dassault Systemes, France, for making CST Microwave Studio available. This work is partially supported by the Icelandic Centre for Research (RANNIS) Grant 174114051, and by National Science Centre of Poland Grant 2015/17/B/ST6/01857.

Publisher Copyright:
© 2019, Emerald Publishing Limited.

Other keywords

  • Antenna design
  • Antenna response sensitivity
  • Computer-aided design
  • Finite differentiation
  • Input characteristics
  • Simulation-driven design
  • Trust-region methods
  • Updating formulas


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