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Synthesis of Linear Antenna Arrays Using Enhanced Firefly Algorithm

  • Research Article - Electrical Engineering
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Abstract

Nature inspired algorithms are finding extensive applications in real-world applications. Firefly algorithm (FA) is one such swarm intelligent algorithm introduced in the recent past. This algorithm has proved its competitiveness over standard benchmark and real-world applications, but suffers from the problem of slow convergence speed. So, in order to overcome this problem, a modified FA approach called enhanced firefly algorithm (EFA) is proposed. The performance of the proposed EFA with respect to FA and other algorithms has been evaluated for eleven benchmark functions. The numerical results show that the novel method consistently provides better solution at a faster rate. Moreover, as a real-world application, EFA has been used for synthesis of linear antenna array for both equally and unequally spaced arrays. The results demonstrate that EFA provides reduced sidelobe level and faster convergence in comparison with algorithms like FA, biogeography-based optimization, cuckoo search, differential evolution, genetic algorithm, particle swarm optimization, tabu search and Taguchi method.

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References

  1. Dorigo, M.; Birattari, M.; Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)

    Article  Google Scholar 

  2. Storn, R.; Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Karaboga, D.: An Idea Based on Honey Bee Swarm for Numerical Optimization, Vol. 200. Technical Report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)

  4. Kennedy, J.; Eberhart, R.C.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ, pp. 1942–1948 (1995)

  5. Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12(6), 702–713 (2008)

    Article  Google Scholar 

  6. Yang, X.-S.: Flower pollination algorithm for global optimization. In: UCNC, pp. 240–249 (2012)

  7. Yao, X.; Liu, Y.; Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)

    Article  Google Scholar 

  8. Mezura-Montes, E.; Velázquez-Reyes, J.; Coello, C.A.: A comparative study of differential evolution variants for global optimization. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 485–492. ACM (2006)

  9. Lampinen, J.; Zelinka, I.: On stagnation of the differential evolution algorithm. In: Proceedings of MENDEL, pp. 76–83 (2000)

  10. Shi, Y.; Eberhart, R.C.: Parameter selection in particle swarm optimization. In: International Conference on Evolutionary Programming, pp. 591–600. Springer, Berlin (1998)

  11. Karaboga, D.; Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214(1), 108–132 (2009)

    MathSciNet  MATH  Google Scholar 

  12. Babayigit, B.; Ozdemir, R.: A modified artificial bee colony algorithm for numerical function optimization. In: 2012 IEEE Symposium on Computers and Communications (ISCC), pp. 000245–000249. IEEE (2012)

  13. Babayigit, B.; Ozdemir, R.: Enhancing artificial bee colony algorithm using inversely proportional mutation. Int. J. Reason. Based Intell. Syst. 5(2), 104–112 (2013)

    Google Scholar 

  14. Zhu, G.; Kwong, S.: Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl. Math. Comput. 217(7), 3166–3173 (2010)

    MathSciNet  MATH  Google Scholar 

  15. Yang, X.-S.: Firefly algorithms for multimodal optimization. In: International Symposium on Stochastic Algorithms, pp. 169–178. Springer, Berlin (2009)

  16. Fister Jr., I.; Yang, X.-S.; Fister, I.; Brest, J.: Memetic firefly algorithm for combinatorial optimization. ArXiv preprint arXiv:1204.5165 (2012)

  17. Hassanzadeh, T.; Faez, K.; Seyfi, G.: A speech recognition system based on structure equivalent fuzzy neural network trained by firefly algorithm. In: 2012 International Conference on Biomedical Engineering (ICoBE), pp. 63–67. IEEE (2012)

  18. Hassanzadeh, T.; Meybodi, M.R.: A new hybrid algorithm based on Firefly Algorithm and cellular learning automata. In: 2012 20th Iranian Conference on Electrical Engineering (ICEE), pp. 628–633. IEEE (2012)

  19. Kannan, G.; Subramanian, D.P.; Shankar, R.T.U.: Reactive power optimization using firefly algorithm. In: Power Electronics and Renewable Energy Systems, pp. 83–90. Springer, New Delhi (2015)

  20. Bharathi, R.S.; Pramod, C.V.S.; Krishna, K.V.; Ragunathan, A.; Vinesh, S.: Optimization of electrical discharge machining parameters on hardened die steel using firefly algorithm. Eng. Comput. 31(1), 1–9 (2015)

    Article  Google Scholar 

  21. Abdelaziz, A.Y.; Hegazy, Y.G.; El-Khattam, W.; Othman, M.M.: Optimal planning of distributed generators in distribution networks using modified firefly method. Electr. Power Compon. Syst. 43(3), 320–333 (2015)

    Article  Google Scholar 

  22. Yazdani, D.; Nasiri, B.; Sepas-Moghaddam, A.; Meybodi, M.R.: A novel multi-swarm algorithm for optimization in dynamic environments based on particle swarm optimization. Appl. Soft Comput. 13(4), 2144–2158 (2013)

    Article  Google Scholar 

  23. Yang, X.-S.; Deb, S.: Eagle strategy using Lévy walk and firefly algorithms for stochastic optimization. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 101–111 (2010)

  24. Abdullah, A.; Deris, S.; Mohamad, M.S.; Hashim, S.Z.M.: A new hybrid firefly algorithm for complex and nonlinear problem. In: DCAI, pp. 673–680 (2012)

  25. dos Santos Coelho, L.; de Andrade Bernert, D.L.; Mariani, V.C.: A chaotic firefly algorithm applied to reliability-redundancy optimization. In: 2011 IEEE Congress on Evolutionary Computation (CEC), pp. 517–521. IEEE (2011)

  26. Gandomi, A.H.; Yang, X.-S.; Talatahari, S.; Alavi, A.H.: Firefly algorithm with chaos. Commun. Nonlinear Sci. Numer. Simul. 18(1), 89–98 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  27. Subutic, M.; Tuba, M.; Stanarevic, N.: Parallelization of the firefly algorithm for unconstrained optimization problems. Latest Adv. Inf. Sci. Appl. 22(3), 264–269 (2012)

    Google Scholar 

  28. Husselmann, A.V.; Hawick, K.A.: Parallel parametric optimisation with firefly algorithms on graphical processing units. In: Proceedings of the International Conference on Genetic and Evolutionary Methods (GEM), p. 1. The Steering Committee of The World Congress in Computer Science, Computer Engineering and Applied Computing (WorldComp) (2012)

  29. Wang, H.; Cui, Z.; Sun, H.; Rahnamayan, S.; Yang, X.-S.: Randomly attracted firefly algorithm with neighborhood search and dynamic parameter adjustment mechanism. Soft Comput. 21, 1–15 (2016)

    Google Scholar 

  30. Bidar, M.; Kanan, H.R.: Jumper firefly algorithm. In: 2013 3th International eConference on Computer and Knowledge Engineering (ICCKE), pp. 267–271. IEEE (2013)

  31. Wang, G.-G.; Gandomi, A.H.; Alavi, A.H.; Dong, Y.-Q.: A hybrid meta-heuristic method based on firefly algorithm and krill herd. In: Handbook of Research on Advanced Computational Techniques for Simulation-Based Engineering, pp. 505–524. IGI Global (2016)

  32. Osaba, E.; Yang, X.-S.; Diaz, F.; Onieva, E.; Masegosa, A.D.; Perallos, A.: A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy. Soft. Comput. 21(18), 5295–5308 (2017)

    Article  Google Scholar 

  33. Pereira, C.; Yang, X.-S.: Learning parameters in deep belief networks through firefly algorithm. In: Proceedings of Artificial Neural Networks in Pattern Recognition: 7th IAPR TC3 Workshop, ANNPR 2016, Ulm, Germany, September 28–30, 2016, Vol. 9896, p. 138. Springer (2016)

  34. Sekhar, G.T.C.; Sahu, R.K.; Baliarsingh, A.K.; Panda, S.: Load frequency control of power system under deregulated environment using optimal firefly algorithm. Int. J. Electr. Power Energy Syst. 74, 195–211 (2016)

    Article  Google Scholar 

  35. Ajiatmo, D.; Robandi, I.: A hybrid fuzzy logic controller-firefly algorithm (FLC-FA) based for MPPT photovoltaic (PV) system in solar car. In: IEEE International Conference on Power and Power and Renewable Energy (ICPRE), pp. 606–610. IEEE (2016)

  36. Balanis, C.A.: Antenna theory: a review. Proc. IEEE 80(1), 7–23 (1992)

    Article  Google Scholar 

  37. Rattan, M.; Patterh, M.S.; Sohi, B.S.: Synthesis of aperiodic linear antenna arrays using genetic algorithm. In: 19th International Conference on Applied Electromagnetics and Communications, 2007. ICECom 2007, pp. 1–4. IEEE (2007)

  38. Dib, N.I.; Goudos, S.K.; Muhsen, H.: Application of Taguchi’s optimization method and self-adaptive differential evolution to the synthesis of linear antenna arrays. Prog. Electromagn. Res. 102, 159–180 (2010)

    Article  Google Scholar 

  39. Lin, C.; Qing, A.; Feng, Q.: Synthesis of unequally spaced antenna arrays by using differential evolution. IEEE Trans. Antennas Propag. 58(8), 2553–2561 (2010)

    Article  Google Scholar 

  40. Merad, L.; Bendimerad, F.; Meriah, S.: Design of linear antenna arrays for side lobe reduction using the tabu search method. Int. Arab J. Inf. Technol. 5(3), 219–222 (2008)

    Google Scholar 

  41. Zaman, M.A.; Matin, Md.A.: Nonuniformly spaced linear antenna array design using firefly algorithm. Int. J. Microw Sci. Technol. 2012, 256759 (2012)

  42. Khodier, M.: Optimisation of antenna arrays using the cuckoo search algorithm. IET Microw. Antennas Propag. 7(6), 458–464 (2013)

    Article  Google Scholar 

  43. Jin, N.; Rahmat-Samii, Y.: Advances in particle swarm optimization for antenna designs: real-number, binary, single-objective and multiobjective implementations. IEEE Trans. Antennas Propag. 55(3), 556–567 (2007)

    Article  Google Scholar 

  44. Khodier, M.M.; Christodoulou, C.G.: Linear array geometry synthesis with minimum sidelobe level and null control using particle swarm optimization. IEEE Trans. Antennas Propag. 53(8), 2674–2679 (2005)

    Article  Google Scholar 

  45. Khodier, M.M.; Al-Aqeel, M.: Linear and circular array optimization: a study using particle swarm intelligence. Prog. Electromagn. Res. B 15, 347–373 (2009)

    Article  Google Scholar 

  46. Singh, U.; Salgotra, R.: Pattern synthesis of linear antenna arrays using enhanced flower pollination algorithm. Int. J. Antennas Propag. 2017, 7158752 (2017)

    Article  Google Scholar 

  47. Singh, U.; Salgotra, R.: Synthesis of linear antenna array using flower pollination algorithm. Neural Comput. Appl. 29, 1–11 (2016)

    Google Scholar 

  48. Salgotra, R.; Singh, U.: A novel bat flower pollination algorithm for synthesis of linear antenna arrays. Neural Comput. Appl. (2016). https://doi.org/10.1007/s00521-016-2833-3

  49. Singh, U.; Salgotra, R.: Optimal synthesis of linear antenna arrays using modified spider monkey optimization. Arab. J. Sci. Eng. 41(8), 2957–2973 (2016)

    Article  Google Scholar 

  50. Sharaqa, A.; Dib, N.: Design of linear and elliptical antenna arrays using biogeography based optimization. Arab. J. Sci. Eng. 39(4), 2929–2939 (2014)

    Article  Google Scholar 

  51. Singh, U.; Kamal, T.S.: Optimal synthesis of thinned arrays using biogeography based optimization. Prog. Electromagn. Res. M 24, 141–155 (2012)

    Article  Google Scholar 

  52. Singh, U.; Kumar, H.; Kamal, T.S.: Linear array synthesis using biogeography based optimization. Prog. Electromagn. Res. M 11, 25–36 (2010)

    Article  Google Scholar 

  53. Singh, U.; Rattan, M.: Design of linear and circular antenna arrays using cuckoo optimization algorithm. Prog. Electromagn. Res. C 46, 1–11 (2014)

    Article  Google Scholar 

  54. Babayigit, B.; Senyigit, E.: Application of the Taguchi method to the design of circular antenna arrays. In: 2015 9th International Conference on Electrical and Electronics Engineering (ELECO), pp. 342–345. IEEE (2015)

  55. Babayigit, B.; Senyigit, E.: Design optimization of circular antenna arrays using Taguchi method. Neural Comput. Appl. 28(6), 1443–1452 (2017)

    Article  Google Scholar 

  56. Zaharis, Z.D.; Lazaridis, P.I.; Cosmas, J.; Skeberis, C.; Xenos, T.D.: Synthesis of a near-optimal high-gain antenna array with main lobe tilting and null filling using Taguchi initialized invasive weed optimization. IEEE Trans. Broadcast. 60(1), 120–127 (2014)

    Article  Google Scholar 

  57. Zaharis, Z.D.: A modified Taguchi’s optimization algorithm for beamforming applications. Prog. Electromagn. Res. 127, 553–569 (2012)

    Article  Google Scholar 

  58. Pelosi, G.; Selleri, S.; Taddei, R.: A novel multiobjective Taguchi’s optimization technique for multibeam array synthesis. Microw. Opt. Technol. Lett. 55(8), 1836–1840 (2013)

    Article  Google Scholar 

  59. Guney, K.; Akdagli, A.; Babayigit, B.: Shaped-beam pattern synthesis of linear antenna arrays with the use of a clonal selection algorithm. Neural Netw. World 16(6), 489 (2006)

    MATH  Google Scholar 

  60. Akdagli, A.; Guney, K.; Babayigit, B.: Clonal selection algorithm for design of reconfigurable antenna array with discrete phase shifters. J. Electromag. Waves Appl. 21(2), 215–227 (2007)

    Article  Google Scholar 

  61. Babayigit, B.; Akdagli, A.; Guney, K.: A clonal selection algorithm for null synthesizing of linear antenna arrays by amplitude control. J. Electromagn. Waves Appl. 20(8), 1007–1020 (2006)

    Article  MATH  Google Scholar 

  62. Guney, K.; Babayigit, B.; Akdagli, A.: Position only pattern nulling of linear antenna array by using a clonal selection algorithm (CLONALG). Electr. Eng. 90(2), 147–153 (2007)

    Article  Google Scholar 

  63. Guney, K.; Babayigit, B.; Akdagli, A.: Interference suppression of linear antenna arrays by phase-only control using a clonal selection algorithm. J. Franklin Inst. 345(3), 254–266 (2008)

    Article  MATH  Google Scholar 

  64. Guney, K.; Babayigit, B.: Amplitude-only pattern nulling of linear antenna arrays with the use of an immune algorithm. Int. J. RF Microw. Comput. Aided Eng. 18(5), 397–409 (2008)

    Article  Google Scholar 

  65. Goudos, S.K.; Moysiadou, V.; Samaras, T.; Siakavara, K.; Sahalos, J.N.: Application of a comprehensive learning particle swarm optimizer to unequally spaced linear array synthesis with sidelobe level suppression and null control. IEEE Antennas Wirel. Propag. Lett. 9, 125–129 (2010)

    Article  Google Scholar 

  66. Wang, W.-B.; Feng, Q.; Liu, D.: Application of chaotic particle swarm optimization algorithm to pattern synthesis of antenna arrays. Prog. Electromagn. Res. 115, 173–189 (2011)

    Article  Google Scholar 

  67. Saxena, P.; Kothari, A.: Ant Lion Optimization algorithm to control side lobe level and null depths in linear antenna arrays. AEU Int. J. Electron. Commun. 70(9), 1339–1349 (2016)

    Article  Google Scholar 

  68. Pappula, L.; Ghosh, D.: Linear antenna array synthesis using cat swarm optimization. AEU Int. J. Electron. Commun. 68(6), 540–549 (2014)

    Article  Google Scholar 

  69. Liu, C.; Gao, F.; Jin, N.: Design and simulation of a modified firefly algorithm. In: 2014 Seventh International Joint Conference on Computational Sciences and Optimization (CSO), pp. 21–25. IEEE (2014)

  70. Mantegna, R.N.: Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes. Phys. Rev. E 49(5), 4677 (1994)

    Article  Google Scholar 

  71. Yang, X.-S.; Deb, S.: Cuckoo search via Lévy flights. In: World Congress on Nature and Biologically Inspired Computing, 2009. NaBIC 2009, pp. 210–214. IEEE (2009)

  72. Soneji, H.; Sanghvi, R.C.: Towards the improvement of cuckoo search algorithm. In: 2012 World Congress on Information and communication technologies (wict), pp. 878–883. IEEE (2012)

  73. Jamil, M.; Yang, X.-S.: A literature survey of benchmark functions for global optimisation problems. Int. J. Math. Model. Numer. Optim. 4(2), 150–194 (2013)

    MATH  Google Scholar 

  74. Liang, J.J.; Qu, B.Y.; Suganthan, P.N.: Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore (2013)

  75. Salgotra, R.; Singh, U.: Application of mutation operators to flower pollination algorithm. Expert Syst. Appl. 79, 112–129 (2017)

    Article  Google Scholar 

  76. Zhang, J.; Sanderson, A.C.: JADE: self-adaptive differential evolution with fast and reliable convergence performance. In: IEEE Congress on Evolutionary Computation, 2007. CEC 2007, pp. 2251–2258. IEEE (2007)

  77. Derrac, J.; García, S.; Molina, D.; Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut. Comput. 1(1), 3–18 (2011)

    Article  Google Scholar 

  78. Salgotra, R.; Singh, U.; Saha, S.: New cuckoo search algorithms with enhanced exploration and exploitation properties. Expert Syst. Appl. 95, 384–420 (2017)

    Article  Google Scholar 

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Acknowledgements

This work is funded under Inspire Fellowship (IF-160215) by Directorate of Science and Technology, Government of India.

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Correspondence to Urvinder Singh.

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Singh, U., Salgotra, R. Synthesis of Linear Antenna Arrays Using Enhanced Firefly Algorithm. Arab J Sci Eng 44, 1961–1976 (2019). https://doi.org/10.1007/s13369-018-3214-2

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