Cross-entropy method for electromagnetic optimization with constraints and mixed variables

Maria Kovaleva, David Bulger, Basit Ali Zeb, Karu P. Esselle

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


An elegant and simple approach is presented for electromagnetic optimizations, especially when mixed variables and/or constraints are involved. In mixed-variable optimization, some variables are continuous (can take any value within a range) and others are discrete (can take only values in a database). An example constraint is when the total length of a device under optimization is specified. Our approach can handle such optimization problems and is based on an abstract probabilistic evolutionary optimization algorithm, called the Cross-Entropy Method (CE). We believe that this is the first application of CE with fullwave EM simulations. A quick performance benchmarking on two test functions was performed to compare convergence of CE and two other established optimization algorithms. Then, the advantages of the CE method when simultaneously optimizing a mix of discrete and continuous variables and imposing geometric constraints are illustrated. Lastly, six resonant cavity antennas (RCAs) were optimized, and one was prototyped and tested to verify predicted results. This one-layer-superstrate RCA prototype has a measured peak directivity of 17.6 dBi with a 3-dB directivity bandwidth of 51%and lower sidelobes, outperforming all such prototypes in the literature.

Original languageEnglish
Pages (from-to)5532-5540
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Issue number10
Publication statusPublished - Oct 2017


  • antennas
  • bandwidth
  • CE
  • CMA-ES
  • covariance matrix adaptation
  • Cross-entropy
  • directivity
  • electromagnetic
  • electromagnetics
  • evolutionary
  • Fabry-Perot cavity antenna
  • high-frequency
  • high-gain
  • microwave
  • optimization
  • particle swarm optimization
  • probability distribution
  • PSO
  • radio-frequency
  • resonant cavity antenna
  • shape
  • sociology
  • statistics
  • wideband


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