A modified particle swarm optimization (PSO) algorithm applied to planar array synthesis considering complex weights and directive element patterns is presented in this paper. The modern heuristic classical PSO scheme with asynchronous updates of the swarm and a global topology has been modified by introducing tournament selection, one of the most effective selection strategies performing in genetic algorithms the equivalent role to natural selection, and elitism. The modified PSO proposed combines the abilities of the classical PSO to explore the search space and the pressure exerted by the selection operator to speed up convergence. Regarding the optimization problem, the synthesis of the feeds for rectangular planar arrays consisting of microstrip patches or subarrays of microstrip patches is considered. Results comparing the performance and limitations of classical and modified PSO-based schemes are included considering both test functions and planar array complex synthesis to best meet certain far-field radiation pattern restrictions given in terms of 3D-masks. Finally, representative synthesis results for sector antennas for worldwide interoperability for microwave access (WiMAX) applications are also included and discussed.
2. Rahmat-Samii, Y. and E. Michielssen, Electromagnetic Optimization by Genetic Algorithms, John Wiley & Sons, New York, 1999.
3. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Trans. Antennas Propagat., Vol. 52, No. 2, 397-407, 2004.
4. Coleman, C. M., E. J. Rothwell, and J. E. Ross, "Investigation of simulated annealing, ant-colony optimization, and genetic algorithms for self-structuring antennas," IEEE Trans. Antennas Propagat., Vol. 52, No. 4, 1007-1014, 2004.
5. Lim, T. S., V. C. Koo, H. T. Ewe, and H. T. Chuah, "A SAR autofocus algorithm based on particle swarm optimization," Progress In Electromagnetics Research B, Vol. 1, 159-176, 2008.
6. Lee, K. C., C. W. Huang, and Y. H. Chen, "Analysis of nonlinear microwave circuits by particle swarm algorithm," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 10, 1353-1365, 2007.
7. Li, J. F., B. H. Sun, Q. Z. Liu, and L. Gong, "PSO-based fast optimization algorithm for broadband array antenna by using the cubic spline interpolation," Progress In Electromagnetics Research Letters, Vol. 4, 173-181, 2008.
8. Mahmoud, K. R., M. El-Adawy, S. M. M. Ibrahem, R. Bansa, and S. H. Zainud-Deen, "Performance of circular Yagi-Uda arrays for beamforming applications using particle swarm optimization algorithm," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2-3, 353-364, 2008.
9. Zainud-Deen, S. H., W. M. Hassen, E. El deen Ali, and K. H. Awadalla, "Breast cancer detection using a hybrid finite di®erence frequency domain and particle swarm optimization techniques," Progress In Electromagnetics Research B, Vol. 3, 35-46, 2008.
10. Chen, T. B., Y. L. Dong, Y. C. Jiao, and F. S. Zhang, "Synthesis of circular antenna array using crossed particle swarm optimization algorithm," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1785-1795, 2006.
11. Li, W. T., X. W. Shi, and Y. Q. Hei, "An improved particle swarm optimization algorithm for pattern synthesis of phased arrays," Progress In Electromagnetics Research, Vol. 82, 319-332, 2008.
12. Liu, X. F., Y. B. Chen, Y. C. Jiao, and F. S. Zhang, "Modified particle swarm optimization for patch antenna design based on IE3D," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1819-1828, 2007.
13. Chamaani, S., S. A. Mirtaheri, M. Teshnehlab, M. A. Shoorehdeli, and V. Seydi, "Modified multi-objective particle swarm optimization for electromagnetic absorber design," Progress In Electromagnetics Research, Vol. 79, 353-366, 2008.
14. Li, W.-T., X.-W. Shi, L. Xu, and Y.-Q. Hei, "Improved ga and pso culled hybrid algorithm for antenna array pattern synthesis," Progress In Electromagnetics Research, Vol. 80, 461-476, 2008.
15. Grimaccia, F., M. Mussetta, and R. E. Zich, "Genetical swarm optimization: Self-adaptive hybrid evolutionary algorithm for electromagnetics," IEEE Trans. Antennas Propagat., Vol. 55, No. 3, 781-785, 2007.
16. Boeringer, D. W. and D. H.Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propagat., Vol. 52, No. 3, 771-779, 2004.
17. Jin, N. and Y. Rahmat-Samii, "Advances in particle swarm optimization for antenna designs: Real-number, binary, singleobjective and multiobjective implementation," IEEE Trans. Antennas Propagat., Vol. 55, No. 3, 556-567, 2007.
18. Perez, J. R. and J. Basterrechea, "Particle swarms applied to array synthesis and planar near-field antenna measurement," Microwave Opt. Technol. Lett., Vol. 50, No. 2, 544-548, 2008.
19. Perez, J. R. and J. Basterrechea, "Particle swarm optimization with tournament selection for linear array synthesis," Microwave Opt. Technol. Lett., Vol. 50, No. 3, 627-632, 2008.
20. Balanis, C. A., Antenna Theory, John Wiley & Sons, New Jersey, 2005.
21. Ludwig, A. C., "The definition of cross polarization," IEEE Trans. Antennas Propagat., Vol. 21, No. 1, 116-119, 1973.
22. Perez, J. R. and J. Basterrechea, "Particle-swarm optimization and its application to antenna far-field-pattern prediction from planar scanning," Microwave Opt. Technol. Lett., Vol. 44, No. 5, 398-403, 2005.
23. Pérez, J. R. and J. Basterrechea, "Hybrid particle swarm-based algorithms and their application to linear array synthesis," Progress In Electromagnetics Research, Vol. 90, 63-74, 2009.
24. Clerc, M. and J. Kennedy, "The particle swarm-explosion, stability, and convergence in a multidimensional complex space," IEEE Trans. Evolutionary Comp., Vol. 6, No. 1, 58-73, 2002.
25. Isernia, T., P. D. Iorio, and F. Soldovieri, "An effective approach for the optimal focusing of array fields subject to upper bounds," IEEE Trans. Antennas Propagat., Vol. 48, No. 12, 1837-1847, 2000.
26. ETSI EN 302 085 v1.2.3, "Fixed radio systems; point-to-multipoint antennas; antennas for point-to-multipoint fixed radio systems in the 3 GHz to 11 GHz band," European Standard (Telecommunications Series), 2005.
27. Isernia, T., O. M. Bucci, and N. Fiorentino, "Shaped beam antenna synthesis problems: Feasibility criteria and new strategies," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 1, 103-138, 1998.