2012-09-18
Application of the Particle Swarm Optimization to the Computation of the GO/UTD Reflection Points Over NURBS Surfaces
By
Progress In Electromagnetics Research Letters, Vol. 35, 19-28, 2012
Abstract
A new method to find the Geometrical Optics/Uniform Theory of Diffraction reflection points over Non Uniform Rational B-Splines surfaces is presented. The approach is based on the Particle Swarm Optimization (PSO) technique, and the cost function used to find the reflection points is based on Snell's law. The technique can be used as an alternative to classic minimization techniques in cases where convergence problems arise.
Citation
Oscar Gutierrez Blanco, Francisco Manuel Adana Herrero, and Antonio Del Corte Valiente, "Application of the Particle Swarm Optimization to the Computation of the GO/UTD Reflection Points Over NURBS Surfaces," Progress In Electromagnetics Research Letters, Vol. 35, 19-28, 2012.
doi:10.2528/PIERL12062507
References

1. Namara, D. A., C. W. I. Pistorious, and J. A. G. Maherbe, C. W. I. Pistorious, and J. A. G. Maherbe, Artech House, 1990.

2. Gomez, R., L. E. Garcia Castillo, F. Saez de Adana, and M. Salazar-Palma, "A novel hybrid FEM high frequency technique for the analysis of scattering and radiation problems," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 7, 939-956, 2004.
doi:10.1163/156939304323105763        Google Scholar

3. Polka, L. A., C. A. Balanis, and A. C. Polycarpou, "High-frequency methods for multiple diffraction modeling: Application and comparison," Journal of Electromagnetic Waves and Applications, Vol. 8, No. 9-10, 1223-1246, 1994.
doi:10.1163/156939394X01019        Google Scholar

4. Catedra, M. F., J. Perez, F. Saez de Adana, and O. Gutierrez, "Efficient ray-tracing techniques for three-dimensional analysis of propagation in mobile communications: Application to picocell and microcell scenarios," IEEE Antennas and Propagation Magazine, Vol. 40, No. 2, 15-28, 1998.
doi:10.1109/74.683539        Google Scholar

5. Rustako, A. J., N. Amitay, G. J. Owens, and R. S. Roman, "Radio propagation at microwave frequencies for line-of-sight microcellular mobile and personal communications," IEEE Transactions on Vehicular Technology, Vol. 40, No. 2, 203-210, 1991.
doi:10.1109/25.69989        Google Scholar

6. Perez, J., J. A. Saiz, O. M. Conde, R. P. Torres, M. F. Catedra, "Analysis of antennas on board arbitrary structures modeled by NURBS surfaces," IEEE Transactions on Antennas and Propagation, Vol. 45, No. 6, 1045-1053, 1997.
doi:10.1109/8.585754        Google Scholar

7. Lozano, L., F. Saez de Adana, and M. F. Catedra, "Ray-tracing acceleration techniques to compute diffraction and double and triple e®ects in RCS prediction methods based on physical optics," PIERS Proceedings, 573-577, Tokyo, Japan, Aug. 2-5, 2006.        Google Scholar

8. Wang, N., Y. Zhang, and C. H. Liang, "Creeping ray-tracing algorithm of UTD method based on NURBS models with the source on surface," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 1981-1990, 2006.
doi:10.1163/156939306779322602        Google Scholar

9. Nocedal, J., "Theory of algorithms for unconstrained optimization," Acta Numerica, Vol. 1, 199-242, Department of Electrical Engineering and Computer Science, Northwestern University,1992.        Google Scholar

10. Byrne, L., "A first course in optimization,", 1, 494, Department of Mathematical Sciences, University of Massachusetts Lowell, 2012.        Google Scholar

11. Ming, C., Z. Yu, and C. H. Liang, "Calculation of the field distribution near electrically large NURBS surfaces with physical optics method," Journal of Electromagnetic Waves and Applications, Vol. 19, No. 11, 1511-1524, 2005.
doi:10.1163/156939305775701886        Google Scholar

12. Gonzalez, I., O. Gutierrez, F. Saez de Adana, and M. Felipe Catedra, "Computation of the scattering of arbitrary shape bodies modeled by parametric surfaces using the multilevel fast multipole method," PIERS Proceedings, 672-676, Tokyo, Japan, Aug. 2-5, 2006.        Google Scholar

13. Adana, F. S., O. Gutierrez, I. Gonzalez, J. Perez, and M. F. Catedra, "General method for the ray tracing on convex bodies," Applied Computational Electromagnetics Society Journal, Vol. 16, No. 1, 20-26, 2001.        Google Scholar

14. Shewchuk, R., "An introduction to the conjugate gradient method without the agonizing pain,", 1, 64, School of Computer Science, Carnegie Mellon University, 1994.        Google Scholar

15. Pytlak, R., "Conjugate gradient methods for non-convex problems," Non-convex Optimization and Its Applications, 63,108, Springer-Verlag, Berlin, Heidelberg, 2009 .        Google Scholar

16. Trgo, A., "On numerical approximation of non-convex variational problems using stochastic optimization algorithm,", 1, 23, Department of Mathematical Sciences, Carnegie Mellon University, 1995.        Google Scholar

17. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 2004.
doi:10.1109/TAP.2004.823969        Google Scholar

18. Chamaani, S., S. A. Mirta, M. Teshnehlab, M. A. Shooredeli, V. Seydi, and , "Modified multi-objective particle swarm optimization for electromagnetic absorber design," Progress In Electromagnetics Research, Vol. 79, 353-366, 2008.
doi:10.2528/PIER07101702        Google Scholar

19. Poyatos, D., D. Escot, I. Montiel, I. Gonzalez, F. Saez de Adana, and M. F. Catedra, "Evaluation of particle swam optimization applied to single snapshot direction of arrival estimation," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 16, 2251-2258, 2008.
doi:10.1163/156939308787522528        Google Scholar

20. Rubio, A., O. Gutierrez Blanco, F. Saez de Adana, and M. F. Catedra, "Calculation of GTD/UTD reflection points over parametric surfaces using particle swarm optimization," Progress In Electromagnetics Research Symposium, 276, Prague, Czech Republic, Aug. 27-30, 2007.        Google Scholar

21. Salakhutdinov, R., "E±cient optimization algorithms for learning,", 1, 84, Department of Computer Science, University of Toronto, 2003.        Google Scholar

22. Salakhutdinov, R., "On the convergence of bound optimization algorithms," Proc. 19th Conference in Uncertainty in Artificial Intelligence , 509-516, University of Toronto, 2003.        Google Scholar

23. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley and Sons, 1989.