In this paper, we propose a hybrid optimization approach that combines the Efficient Global Optimization (EGO) algorithm with Taguchi's method. This hybrid optimized algorithm is suited for problems with expensive cost functions. As a Bayesian analysis optimization algorithm, EGO algorithm begins with fitting the Kriging model with n sample points, and finds the (n+1)th point where the expected improvement is maximized to update the model. We employ Taguchi's method in EGO to obtain the (n+1)th point in this paper. A numerical simulation demonstrates that our algorithm has advantage over the original EGO. Finally, we apply this hybrid optimized algorithm to optimize an ultra-wide band (UWB) transverse electromagnetic (TEM) horn antenna and a linear antenna array. Compared to Taguchi's method and the Integer Coded Differential Evolution Strategy, our algorithm converges to the global optimal value more efficiently.
1. Kerkhoff, A. J. and H. Ling, "Design of a band-notched planar monopole antenna using genetic algorithm optimization," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 3, 604-610, March 2007. doi:10.1109/TAP.2007.891563
2. Altshuler, E. E. and D. S. Linden, "Wire-antenna designs using genetic algorithms," IEEE Antennas and Propagation Magazine, Vol. 39, No. 2, 33-42, April 1997. doi:10.1109/74.584498
3. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, 397-407, 2004. doi:10.1109/TAP.2004.823969
4. Mahmoud, K. R., "Design optimization of a Bow-Tie antenna for 2.45 GHz RFID readers using a hybrid BSO-NM algorithm," Progress In Electromagnetics Research, Vol. 100, 105-107, 2010. doi:10.2528/PIER09102903
5. Inman, M. J., J. M. Earwood, A. Z. Elsherbeni, and C. E. Smith, "Bayesian optimization techniques for antenna design," Progress In Electromagnetics Research, Vol. 49, 71-86, 2004. doi:10.2528/PIER04021302
6. Jone, D. R., M. Schonlau, and W. J. Welch, "Efficient global optimization of expensive black-box function," Journal of Global Optimization, Vol. 13, 455-492.
7. Knowles, J., "ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems," IEEE Transactions on Evolutionary Computation, Vol. 10, No. 1, 50-66, February 2005. doi:10.1109/TEVC.2005.851274
8. Taguchi, G., S. Chowdhury, and Y. Wu, Taguchi's Quality Engineering Handbook, John Wiley & Sons Inc., New Jersey, 2005.
9. Weng, W. C., F. Yang, and A. Z. Elsherbeni, "Linear antenna array synthesis using Taguchi's method: A novel optimization technique in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 3, 723-730, March 2007. doi:10.1109/TAP.2007.891548
10. McKay, M. D., R. J. Beckman, and W. J. Conover, "A comparison of three methods for selecting values of input variables in the analysis of out put from a computer code," Technometrics, Vol. 21, No. 2, 239-245, 1979. doi:10.2307/1268522
11. Krige, D. G., A statistical approach to some mine valuations and allied problems at the Witwatersrand, Master's thesis, University of Witwatersrand, 1951.
12. O'Donnell, T. H., H. L. Southall, and L. B. Kaanta, "Efficient global optimization of a limited parameter antenna design," Proceedings of SPIE, Vol. 6964, 69640J.1-69640J.14, 2008.
13. Nelder, J. A. and R. A. Mead, "Simplex method for function minimiza tion," Computer Journal, Vol. 7, No. 4, 308-313, 1965.
14. Dib, N., S. K. Goudos, and H. Muhsen, "Application of Taguchi's optimization method and self-adaptive differential evolution to the synthesis of linear antenna arrays," Progress In Electromagnetics Research, Vol. 102, 159-180, 2010. doi:10.2528/PIER09122306
15. Schonlau, M., W.Welch, and D. Jones, "A data-analytic approach to bayesian global optimization," American Statistical Association Proceedings, Section of Physical Engineering Sciences, 186-191, 1997.
16. Chang, L., C. Liao, X. Zheng, L. L. Chen, and G. Su, "Application of parallel integer coded differential evolution strategy on ultrawide band TEM horn antenna," International Conference on Microwave and Millimeter Wave Technology, 2010.