In this article a novel numerical technique, called Fitness Adaptive Differential Evolution (FiADE) for optimizing certain pre-defined antenna configuration to attain best possible radiation characteristics is presented. Differential Evolution (DE), inspired by the natural phenomenon of theory of evolution of life on earth, employs the similar computational steps as by any other Evolutionary Algorithm (EA). Scale Factor and Crossover Probability are two very important control parameter of DE .This article describes a very competitive yet very simple form of adaptation technique for tuning the scale factor, on the run, without any user intervention. The adaptation strategy is based on the fitness function value of individuals in DE population. The feasibility, efficiency and effectiveness of the proposed algorithm in the field of electromagnetism are examined over a set of well-known antenna configurations optimization problems. Comparison with the some very popular and powerful metaheuristics reflects the superiority of this simple parameter automation strategy in terms of accuracy, convergence speed, and robustness.
"Optimization of Antenna Configuration with a Fitness-Adaptive Differential Evolution Algorithm," Progress In Electromagnetics Research B,
Vol. 26, 291-319, 2010. doi:10.2528/PIERB10080703
1. Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.
2. Kirkpatrick, S., C. D. Gellat, Jr, and M. P. Vecchi, "Optimization by simulated annealing," Science, Vol. 220, 671-679, 1983. doi:10.1126/science.220.4598.671
3. Kennedy, J. and R. C. Eberhart, Swarm Intelligence, Morgan Kauffman, San Francisco, CA, 2001.
4. Rahmat-Samii, Y. and E. Michielssen, Electromagnetic Optimization by Genetic Algorithms, Wiley, New York, 1999.
5. Coleman, C., E. Rothwell, and J. Ross, "Investigation of simulated annealing, ant-colony optimization, and genetic algorithms for self-structuring antennas," IEEE Trans. Antennas Propag., Vol. 52, 1007-1014, Apr. 2004. doi:10.1109/TAP.2004.825658
6. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Trans. Antennas Propag., Vol. 52, 397-407, 2004. doi:10.1109/TAP.2004.823969
7. Boeringer, D. and D.Werner, "Particle swarm optimization versus genetic algorithms for phased array synthesis," IEEE Trans. Antennas Propag., Vol. 52, 771-779, 2004. doi:10.1109/TAP.2004.825102
8. Price, K., R. Storn, and J. Lampinen, Differential Evolution --- A Practical Approach to Global Optimization, Springer, Berlin, 2005.
9. Storn, R. and K. Price, "Differential evolution --- A simple and efficient heuristic for global optimization over continuous spaces," Journal of Global Optimization, Vol. 11, No. 4, 341-359, 1997. doi:10.1023/A:1008202821328
10. Storn, R. and K. V. Price, Differential evolution --- A simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012, ICSI, http://http.icsi.berkeley.edu/~storn/litera.html, 1995.
11. Storn, R. and K. V. Price, "Minimizing the real functions of the ICEC 1996 contest by differential evolution," Proceedings of the 1996 IEEE International Conference on Evolutionary Computation, 842-844, Nagoya, Japan, 1996.
12. Nelder, J. A. and R. Mead, "A simplex method for function minimization," Computer Journal, Vol. 7, 308-313, 1965.
13. Price, W. L., "Global optimization by controlled random search," Computer Journal, Vol. 20, No. 4, 367-370, 1977. doi:10.1093/comjnl/20.4.367
14. Rechenberg, I., Evolutionsstrategie --- Optimerung technischer systeme nach prinzipien der biologischen evolution, Ph.D. Thesis, 1971, Reprinted by Fromman-Holzboog, 1973.
15. Price, K., R. Storn, and J. Lampinen, Differential Evolution --- A Practical Approach to Global optimization, Springer, Berlin, 2005.
16. Liu, J. and J. Lampinen, "On setting the control parameters of the differential evolution method," Proc. of Mendel 2002, 8th International Conference on Soft Computing, R. Matoušek and P. Ošmera (eds.), 11--18, 2002.
17. Qin, A. K., V. L. Huang, and P. N. Suganthan, "Differential evolution algorithm with strategy adaptation for global numerical optization," IEEE Transaction on Evolutionary Computation, Vol. 13, No. 2, 398-417, April 2009. doi:10.1109/TEVC.2008.927706
18. Brest, J., S. Greiner, B. Boskovic, M. Mernik, and V. Zumer, "Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems," IEEE Transactions on Evolutionary Computation, Vol. 10, No. 6, 646-657, 2006. doi:10.1109/TEVC.2006.872133
19. Liu, J. and J. Lampinen, "A fuzzy adaptive differential evolution algorithm," Soft Computing --- A Fusion of Foundations, Methodologies and Applications, Vol. 9, No. 6, 448-462, 2005.
20. Liu, J. and J. Lampinen, "Adaptive parameter control of differential evolution," Proc. of Mendel 2002, 8th International Conference on Soft Computing, R. Matousek and P. Osmera (eds.), 19--26, 2002.
21. Ronkkonen, J. and J. Lampinen, "On using normally distributed mutation step length for the differential evolution algorithm," Proc. of Mendel 2003, 9th International Conference on Soft Computing, 11-18, Brno, Czeck Republic, Jun. 5--7, 2003.
22. Ali, M. M. and A. Torn, "Population set based global optimization algorithms: Some modifications and numerical studies," Computers and Operations Research, No. 31, 1703-1725, Elsevier, 2004.
23. Chowdhury, A., R. Giri, A. Ghosh, S. Das, A. Abraham, and V. Snasel, "Linear antenna array synthesis using fitness adaptive differential evolution algorithm," Proceedings of the 2010 International Conference on Evolutionary Computation, 3137-3144, IEEE Press Barcelona, Spain, 2010.
24. Pantoja, M. F., A. R. Bretones, and R. G. Martin, "Benchmark antenna problems for evolutionary optimization algorithms," IEEE Trans. Antennas Propag., Vol. 55, No. 4, 1111-1121, 2007. doi:10.1109/TAP.2007.893396
25. Das, S., A. Konar, and U. K. Chakraborty, "Two improved differential evolution schemes for faster global search," ACM-SIGEVO Proceedings of GECCO, 991-998, Washington D.C., Jun. 2005.
26. Balanis, C. A., Antenna Theory. Analysis and Design, 2nd Ed., Wiley, New York, 1997.
27. Kennedy, J. and R. Eberhart, "Particle swarm optimization," Proceedings of IEEE International Conference on Neural Networks, Vol. 4, 1942-1948, 1995. doi:10.1109/ICNN.1995.488968
28. Shi, Y. and R. C. Eberhart, "A modified particle swarm optimizer," Proceedings of IEEE International Conference on Evolutionary Computation, 69-73, 1998.
29. Mehrabian, A. R. and C. Lucas, "A novel numerical optimization algorithm inspired from weed colonization," Ecological Informatics, Vol. 1, 355-366, 2006. doi:10.1016/j.ecoinf.2006.07.003
31. García, S., D. Molina, M. Lozano, and F. Herrera, "A study on the use of non-parametric tests for analyzing the evolutionary algorithms' behavior: A case study on the CEC'2005 special session on real parameter optimization," Journal of Heuristics, Vol. 15, No. 6, 617-644, Dec. 2009. doi:10.1007/s10732-008-9080-4