Advertisement

Synthesis of Linear Antenna Arrays Using Enhanced Firefly Algorithm

  • Urvinder Singh
  • Rohit Salgotra
Research Article - Electrical Engineering
  • 30 Downloads

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.

Keywords

Swarm intelligence Firefly algorithm Enhanced firefly algorithm Linear antenna arrays Side lobe level 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

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

References

  1. 1.
    Dorigo, M.; Birattari, M.; Stutzle, T.: Ant colony optimization. IEEE Comput. Intell. Mag. 1(4), 28–39 (2006)CrossRefGoogle Scholar
  2. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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)Google Scholar
  4. 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)Google Scholar
  5. 5.
    Simon, D.: Biogeography-based optimization. IEEE Trans. Evol. Comput. 12(6), 702–713 (2008)CrossRefGoogle Scholar
  6. 6.
    Yang, X.-S.: Flower pollination algorithm for global optimization. In: UCNC, pp. 240–249 (2012)Google Scholar
  7. 7.
    Yao, X.; Liu, Y.; Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)CrossRefGoogle Scholar
  8. 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)Google Scholar
  9. 9.
    Lampinen, J.; Zelinka, I.: On stagnation of the differential evolution algorithm. In: Proceedings of MENDEL, pp. 76–83 (2000)Google Scholar
  10. 10.
    Shi, Y.; Eberhart, R.C.: Parameter selection in particle swarm optimization. In: International Conference on Evolutionary Programming, pp. 591–600. Springer, Berlin (1998)Google Scholar
  11. 11.
    Karaboga, D.; Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214(1), 108–132 (2009)MathSciNetzbMATHGoogle Scholar
  12. 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)Google Scholar
  13. 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. 14.
    Zhu, G.; Kwong, S.: Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl. Math. Comput. 217(7), 3166–3173 (2010)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Yang, X.-S.: Firefly algorithms for multimodal optimization. In: International Symposium on Stochastic Algorithms, pp. 169–178. Springer, Berlin (2009)Google Scholar
  16. 16.
    Fister Jr., I.; Yang, X.-S.; Fister, I.; Brest, J.: Memetic firefly algorithm for combinatorial optimization. ArXiv preprint arXiv:1204.5165 (2012)
  17. 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)Google Scholar
  18. 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)Google Scholar
  19. 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)Google Scholar
  20. 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)CrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 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)Google Scholar
  24. 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)Google Scholar
  25. 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)Google Scholar
  26. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 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. 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)Google Scholar
  29. 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. 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)Google Scholar
  31. 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)Google Scholar
  32. 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)CrossRefGoogle Scholar
  33. 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)Google Scholar
  34. 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)CrossRefGoogle Scholar
  35. 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)Google Scholar
  36. 36.
    Balanis, C.A.: Antenna theory: a review. Proc. IEEE 80(1), 7–23 (1992)CrossRefGoogle Scholar
  37. 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)Google Scholar
  38. 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)CrossRefGoogle Scholar
  39. 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)CrossRefGoogle Scholar
  40. 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. 41.
    Zaman, M.A.; Matin, Md.A.: Nonuniformly spaced linear antenna array design using firefly algorithm. Int. J. Microw Sci. Technol. 2012, 256759 (2012)Google Scholar
  42. 42.
    Khodier, M.: Optimisation of antenna arrays using the cuckoo search algorithm. IET Microw. Antennas Propag. 7(6), 458–464 (2013)CrossRefGoogle Scholar
  43. 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)CrossRefGoogle Scholar
  44. 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)CrossRefGoogle Scholar
  45. 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)CrossRefGoogle Scholar
  46. 46.
    Singh, U.; Salgotra, R.: Pattern synthesis of linear antenna arrays using enhanced flower pollination algorithm. Int. J. Antennas Propag. 2017, 7158752 (2017)CrossRefGoogle Scholar
  47. 47.
    Singh, U.; Salgotra, R.: Synthesis of linear antenna array using flower pollination algorithm. Neural Comput. Appl. 29, 1–11 (2016)Google Scholar
  48. 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. 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)CrossRefGoogle Scholar
  50. 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)CrossRefGoogle Scholar
  51. 51.
    Singh, U.; Kamal, T.S.: Optimal synthesis of thinned arrays using biogeography based optimization. Prog. Electromagn. Res. M 24, 141–155 (2012)CrossRefGoogle Scholar
  52. 52.
    Singh, U.; Kumar, H.; Kamal, T.S.: Linear array synthesis using biogeography based optimization. Prog. Electromagn. Res. M 11, 25–36 (2010)CrossRefGoogle Scholar
  53. 53.
    Singh, U.; Rattan, M.: Design of linear and circular antenna arrays using cuckoo optimization algorithm. Prog. Electromagn. Res. C 46, 1–11 (2014)CrossRefGoogle Scholar
  54. 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)Google Scholar
  55. 55.
    Babayigit, B.; Senyigit, E.: Design optimization of circular antenna arrays using Taguchi method. Neural Comput. Appl. 28(6), 1443–1452 (2017)CrossRefGoogle Scholar
  56. 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)CrossRefGoogle Scholar
  57. 57.
    Zaharis, Z.D.: A modified Taguchi’s optimization algorithm for beamforming applications. Prog. Electromagn. Res. 127, 553–569 (2012)CrossRefGoogle Scholar
  58. 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)CrossRefGoogle Scholar
  59. 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)zbMATHGoogle Scholar
  60. 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)CrossRefGoogle Scholar
  61. 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)CrossRefzbMATHGoogle Scholar
  62. 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)CrossRefGoogle Scholar
  63. 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)CrossRefzbMATHGoogle Scholar
  64. 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)CrossRefGoogle Scholar
  65. 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)CrossRefGoogle Scholar
  66. 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)CrossRefGoogle Scholar
  67. 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)CrossRefGoogle Scholar
  68. 68.
    Pappula, L.; Ghosh, D.: Linear antenna array synthesis using cat swarm optimization. AEU Int. J. Electron. Commun. 68(6), 540–549 (2014)CrossRefGoogle Scholar
  69. 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)Google Scholar
  70. 70.
    Mantegna, R.N.: Fast, accurate algorithm for numerical simulation of Levy stable stochastic processes. Phys. Rev. E 49(5), 4677 (1994)CrossRefGoogle Scholar
  71. 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)Google Scholar
  72. 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)Google Scholar
  73. 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)zbMATHGoogle Scholar
  74. 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)Google Scholar
  75. 75.
    Salgotra, R.; Singh, U.: Application of mutation operators to flower pollination algorithm. Expert Syst. Appl. 79, 112–129 (2017)CrossRefGoogle Scholar
  76. 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)Google Scholar
  77. 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)CrossRefGoogle Scholar
  78. 78.
    Salgotra, R.; Singh, U.; Saha, S.: New cuckoo search algorithms with enhanced exploration and exploitation properties. Expert Syst. Appl. 95, 384–420 (2017)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of ECEThapar UniversityPatialaIndia

Personalised recommendations