The paper describes a novel approach to the design of non-uniform planar circular antenna arrays for achieving maximal side lobe level suppression and directivity. The current excitation amplitudes and phase perturbations of the array elements are determined using an Adaptive Memetic algorithm resulting from a synergy of Differential Evolution (DE) and Learning Automata that is able to significantly outperform existing state-of-the-art approaches to the design problem. However, existing literature considers the design problem as a single-objective optimization task that is formulated as a linear sum of all the performance metrics. Due to the conflicting nature of the various design objectives, improvements in a certain design measure causes deterioration of the other measures. Following this observation, the single-objective design problem is reformulated as a constrained multi-objective optimization task. The proposed memetic algorithm is extended to the multi-objective framework to generate a set of nondominated solutions from which the best compromise solution is selected employing a fuzzy membership based approach. An instantiation of the design problem clearly depicts that the multi-objective approach provides simultaneous side lobe level suppression and directivity maximization in comparison to the single-objective scenario.
2. Dessouky, M., H. Sharshar, and Y. Albagory, "A novel tapered beamforming window for uniform concentric circular arrays," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2077-2089, 2006.
doi:10.1163/156939306779322701
3. Chandran, S. (ed.), Adaptive Antenna Arrays: Trends and Applications, Springer, 2004.
4. Tsoulos, G. V., Ed., Adaptive Antennas for Wireless Communications, IEEE Press, Piscataway, NJ, 2001.
5. Zhang, J., W. Wu, and D. G. Fang, "360°± scanning multi-beam antenna based on homogeneous ellipsoidal lens fed by circular array," Electronics Letters, 298-300, 2011.
doi:10.1049/el.2010.3646
6. Panduro, M., A. L. Mendez, R. Dominguez, and G. Romero, "Design of non-uniform circular antenna arrays for side lobe reduction using the method of genetic algorithms ," Int. J. of Electron. and Commun., AEU, Vol. 60, 713-717, 2006.
doi:10.1016/j.aeue.2006.03.006
7. Shihab, M., Y. Najjar, N. Dib, and M. Khodier, "Design of non-uniform circular antenna arrays using particle swarm optimization," Journal of Electrical Engineering, Vol. 59, No. 4, 216-220, 2008.
8. Panduro, M. A., C. A. Brizuela, L. I. Balderas, and D. A. Acosta, "A comparison of genetic algorithms, particle swarm optimization and the di®erential evolution method for the design of scannable circular antenna arrays," Progress In Electromagnetics Research B, Vol. 13, 171-186, 2009.
doi:10.2528/PIERB09011308
9. Roy, G. G., S. Das, P. Chakraborty, and P. N. Suganthan, "Design of non-uniform circular antenna arrays using a modified invasive weed optimization algorithm," IEEE Transactions on Antennas and Propagation, 110-118, 2011.
doi:10.1109/TAP.2010.2090477
10. Singh, U. and T. S. Kamal, "Design of non-uniform circular antenna arrays using biogeography-based optimization," IET Microwaves, Antennas & Propagation, 1365-1370, 2011.
doi:10.1049/iet-map.2010.0204
11. Mandal, A., H. Zafar, S. Das, and A. V. Vasilakos, "Efficient circular array synthesis with a memetic differential evolution algorithm ," Progress In Electromagnetics Research B, Vol. 38, 367-385, 2012.
12. Dawkins, R., The Selfish Gene, Oxford University Press, 1976.
13. Moscato, P., "On evolution, search, optimization, genetic algorithms and martial arts - Towards memetic algorithms," Caltech Concurrent Computation Program, Report 826, 1989.
14. Ong, Y.-S., M.-H. Lim, N. Zhu, and K.-W.Wong, "Classification of adaptive memetic algorithms: A comparative study," IEEE Trans. on Systems, Man and Cybernetics, Vol. 36, No. 1, Feb. 2006.
15. Kendall, G., P. Cowling, and E. Soubeiga, "Choice function and random hyperheuristics," Proc. 4th Asia-Pacific Conference on Simulated Evolution and Learning, 667-671, Singapore, Nov. 2002.
16. Storn, R. and K. V. Price, "Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces," J. Global Optimization, Vol. 11, No. 4, 341-359, 1997.
doi:10.1023/A:1008202821328
17. Storn, R., K. V. Price, and J. Lampinen, Differential Evolution: A Practical Approach to Global Optimization, Springer-Verlag, 2005.
18. Lampinen, J. and I. Zelinka, "On stagnation of the differential evolution algorithm," Proc. MENDEL 2000, 6th Int. Mendel Conf. Soft Computing, 76-78, Brno, Czech Republic, Jun. 2000.
19. Ronkkonen, J., S. Kukkonen, and K. V. Price, "Real parameter optimization with differential evolution," Proc. IEEE Congr. Evol. Comput. (CEC-2005), Vol. 1, 506-513, 2001.
20. Narendra, K. S. and M. A. L. Thathachar, "Learning automata - A survey," IEEE Trans. on Systems, Man and Cybernetics, Vol. 4, No. 4, Jul. 1974.
21. Meybodi, M. R. and H. Beigy, "A note on learning automata based schemes for adaptation of BP parameters," Journal of Neurocomputing,, Vol. 48, No. 4, 957-974, 2002.
doi:10.1016/S0925-2312(01)00686-5
22. Unsal, C., P. Kachroo, and J. S. Bay, "Multiple stochastic learning automata for vehicle path control in an automated highway system," IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, Vol. 29, No. 1, Jan. 1999.
doi:10.1109/3468.736368
23. Flury, B., A First Course in Multivariate Statistics, 28, Springer, 1997.
24. Das, S. and P. N. Suganthan, "Differential evolution: A survey of the state-of-the-Art," IEEE Transactions on Evolutionary Computation, Vol. 15, No. 1, 4-31, 2011.
doi:10.1109/TEVC.2010.2059031
25. Chen, X., Y.-S. Ong, M.-H. Lim, and K. C. Tan, "A multi-facet survey on memetic computation," IEEE Transactions on Evolutionary Computation, Vol. 15, No. 5, 591-607, 2011.
doi:10.1109/TEVC.2011.2132725
26. Robic, T. and B. Filipic, "DEMO: Differential evolution for multiobjective optimization," Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization - EMO 2005, Vol. 3410, 520-533, Ser. Lecture Notes in Computer Science, Springer, 2005.
doi:10.1007/978-3-540-31880-4_36
27. Knowles, J., L. Thiele, and E. Zitzler, "A tutorial on the performance assessment of stochastic multiobjective optimizers,", Revised Version,-Computer Engineering and Networks Laboratory (TIK), 214, ETH Zurich, Switzerland, Feb. 2006.
28. Deb, K., S. Agrawal, A. Pratab, T. Meyarivan, M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J. J. Merelo, and H.-P. Schwefel, Eds, "A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II," Proceedings of the Parallel Problem Solving from Nature VI Conference, No. 1917, 849- 858, Ser. Lecture Notes in Computer Science, Springer, Paris, France, 2000.
doi:10.1007/3-540-45356-3_83
29. Zitzler, E., M. Laumanns, and L. Thiele, K. C. Gian, nakoglou, D. T. Tsahalis, J. Periaux, K. D. Papailiou, and T. Fogarty, (eds.), "SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective opmization," Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, 95-100, International Center for Numerical Methods in Engineering , (Cmine), Athens, Greece, 2001.
30. Zitzler, E., S. Künzli, and , "Indicator-based selection in multiobjective search," Parallel Problem Solving from Nature (PPSN VIII), X. Yao et al., Eds., 832-842, Springer-Verlag, Berlin, Germany, 2004.
31. Pal, S., B. Y. Qu, S. Das, and P. N. Suganthan, "Optimal synthesis of linear antenna arrays with multi-objective differential evolution," Progress In Electromagnetics Research B, Vol. 21, 87-111, 2010.
32. Pal, S., S. Das, A. Basak, and P. N. Suganthan, "Synthesis of difference patterns for monopulse antennas with optimal combination of array-size and number of subarrays - A multi-objective optimization approach," Progress In Electromagnetics Research B, Vol. 21, 257-280, 2010.
33. Rocca, P., G. Oliveri, and G. Massa, "Differential evolution as applied to electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 1, 38-49, 2011.
34. Abido, M. A., "A novel multiobjective evolutionary algorithm for environmental/economic power dispatch," Electric Power Systems Research, Vol. 65, No. 1, 71-81, Elsevier, 2003.
doi:10.1016/S0378-7796(02)00221-3
35. Deb, K., "An efficient constraint handling method for genetic algorithms," Computer Methods in Applied Mechanics and Engineering, Vol. 186, 311-338, 2000.
doi:10.1016/S0045-7825(99)00389-8
36. Das, S., A. Abraham, U. K. Chakraborty, and A. Konar, "Differential evolution using a neighborhood-based mutation operator," IEEE Transactions on Evolutionary Computation, Vol. 13, No. 3, 526-553, 2009.
doi:10.1109/TEVC.2008.2009457
37. Balanis, C. A., Antenna Theory: Analysis and Design, Harper Row, New York, 1982.
38. Bogdan, L. and C. Comsa, "Analysis of circular arrays as smart antennas for cellular networks," Proc. IEEE Int. Symp. Signals, Circuits and Systems, SCS03, Vol. 2, 525-528, Jul. 2003.
Submit
