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On the improvement in grey wolf optimization

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Abstract

Grey wolf optimization (GWO) is a recently developed nature-inspired global optimization method which mimics the social behaviour and hunting mechanism of grey wolves. Though the algorithm is very competitive and has been applied to various fields of research, it has poor exploration capability and suffers from local optima stagnation. So, in order to improve the explorative abilities of GWO, an extended version of grey wolf optimization (GWO-E) algorithm is presented. This newly proposed algorithm consists of two modifications: Firstly, it is able to explore new areas in the search space because of diverse positions assigned to the leaders. This helps in increasing the exploration and avoids local optima stagnation problem. Secondly, an opposition-based learning method has been used in the initial half of iterations to provide diversity among the search agents. The proposed approach has been tested on standard benchmarking functions for different population and dimension sizes to prove its effectiveness over other state-of-the-art algorithms. Experimental results show that the GWO-E algorithm performs better than GWO, bat algorithm, bat flower pollinator, chicken swarm optimization, differential evolution, firefly algorithm, flower pollination algorithm (FPA) and grasshopper optimization algorithm. Statistical testing of GWO-E has been done to prove its significance over other popular algorithms. Further, as a real-world application, the GWO-E is used to design non-uniform linear antenna array (LAA) for minimum possible sidelobe level and null control. Performance of GWO-E for the synthesis of LAA is evaluated by considering the several different case studies of LAA that exists in the literature, and the results are compared with the results of other popular meta-heuristic algorithms like genetic algorithm, ant lion algorithm, FPA, cat swarm optimization, GWO and many more. Numerical results further show the superior performance of GWO-E over original GWO and other popular algorithms.

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References

  1. Gutjahr WJ (2009) Convergence analysis of metaheuristics. In: Maniezzo V, Stützle T, Voß S (eds) Matheuristics. Springer, Boston, pp 159–187

    Google Scholar 

  2. Holland JH (1992) Genetic algorithms. Sci Am 267:66–72

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  4. Koza JR (1992) Genetic programming. MIT Press, Cambridge

    MATH  Google Scholar 

  5. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evolut Comput 3:82–102

    Google Scholar 

  6. Hansen N, Müller SD, Koumoutsakos P (1994) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMAES). Evolut Comput 2003(11):1–18

    Google Scholar 

  7. Rechenberg I (1994) Evolutionsstrategie'94. frommann-holzboog

  8. Webster B, Bernhard PJ (2006) A local search optimization algorithm based on natural principles of gravitation. In: Proceedings of the 2003 international conference on information and knowledge engineering (IKE’03), Las Vegas, Nevada, USA, 2003, pp 255–261

  9. Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37:106–111

    Google Scholar 

  10. Hatamlou A (2012) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184

    MathSciNet  Google Scholar 

  11. Zheng YJ (2015) Water wave optimization: a new nature-inspired metaheuristic. Comput Oper Res 55:1–11

    MathSciNet  MATH  Google Scholar 

  12. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    MATH  Google Scholar 

  13. Kennedy J, Eberhart R (1995) Particle swarm optimization, in neural networks. In: IEEE international conference on proceedings, pp 1942–1948

  14. Dorigo M, Birattari M, Stutzle T (2016) Ant colony optimization. IEEE Comput Intell Mag 2006(1):28–39

    Google Scholar 

  15. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74

    Google Scholar 

  16. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv En Softw 69:46–61

    Google Scholar 

  17. Salgotra R, Singh U (2016) A novel bat flower pollination algorithm for synthesis of linear antenna arrays. Neural Comput Appl 30(7):2269–2282

    Google Scholar 

  18. Yang XS (2012) Flower pollination algorithm for global optimization. In: International conference on unconventional computing and natural computation. Springer, Berlin, pp 240–249

  19. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Google Scholar 

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

    Google Scholar 

  21. Salgotra R, Singh U, Saha S (2018) New cuckoo search algorithms with enhanced exploration and exploitation properties. Expert Syst Appl 95(384–420):2018

    Google Scholar 

  22. Kamboj VK, Bath SK, Dhillon JS (2016) Solution of non-convex economic load dispatch problem using grey wolf optimizer. Neural Comput Appl 27(5):1301–1316

    Google Scholar 

  23. Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381

    Google Scholar 

  24. Komaki GM, Kayvanfar V (2015) Grey wolf optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time. J Comput Sci 8:109–120

    Google Scholar 

  25. Recioui A et al (2008) Synthesis of linear arrays with sidelobe level reduction constraint using genetic algorithms. Int J Microw Opt Technol 3(5):524–530

    Google Scholar 

  26. Zaman MA (2011) Phased array synthesis using modified particle swarm optimization. J Eng Sci Technol Rev 4(1):68–73

    Google Scholar 

  27. Hansen RC (2009) Phased array antennas, vol 213. Wiley, New York

    Google Scholar 

  28. Kurup DG, Himdi M, Rydberg A (2003) Synthesis of uniform amplitude unequally spaced antenna arrays using the differential evolution algorithm. IEEE Trans Antennas Propag 51(9):2210–2217

    Google Scholar 

  29. Chen K, He Z, Han C (2006) A modified real GA for the sparse linear array synthesis with multiple constraints. IEEE Trans Antennas Propag 54(7):2169

    Google Scholar 

  30. Rattan M, Patterh MS and Sohi BS (2007) Synthesis of aperiodic linear antenna arrays using genetic algorithm. In: 19th IEEE international conference on applied electromagnetics and communications. Dubrovnik, Croatia, pp 1–4

  31. Cengiz Y, Tokat H (2008) Linear antenna array design with use of genetic, memetic and tabu search optimization algorithms. Prog Electromagn Res C 1:63–72

    Google Scholar 

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

    Google Scholar 

  33. Murino V, Trucco A, Regazzoni CS (1996) Synthesis of unequally spaced arrays by simulated annealing. IEEE Trans Signal Process 44(1):119–122

    Google Scholar 

  34. Guney K, Onay M (2011) Optimal synthesis of linear antenna arrays using a harmony search algorithm. Expert Syst Appl 38(12):15455–15462

    Google Scholar 

  35. Rajo-Iglesias E, Quevedo-Teruel O (2007) Linear array synthesis using an ant-colony-optimization-based algorithm. IEEE Antennas Propag Mag 49(2):70–79

    Google Scholar 

  36. Saxena P, Kothari A (2016) Linear antenna array optimization using flower pollination algorithm. SpringerPlus 5(1):306

    Google Scholar 

  37. Singh U, Salgotra R (2016) Synthesis of linear antenna array using flower pollination algorithm. Neural Comput Appl 29(2):435–445

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  41. Saxena P, Kothari A (2016) 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  44. Saxena P, Kothari A (2016) Optimal pattern synthesis of linear antenna array using grey wolf optimization algorithm. Int J Antennas Propag 2016:1205970

    Google Scholar 

  45. Mangaraj BB, Swain P (2017) An optimal LAA subsystem designed using Gravitational Search Algorithm. Eng Sci Technol Int J 20(2):494–501

    Google Scholar 

  46. Guney K, Durmus A (2015) Pattern nulling of linear antenna arrays using backtracking search optimization algorithm. Int J Antennas Propag 2015:713080

    Google Scholar 

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

    Google Scholar 

  48. Oraizi H, Fallahpour M (2008) Nonuniformly spaced linear array design for the specified beamwidth/sidelobe level or specified directivity/sidelobe level with coupling consideration. Prog Electromagn Res M 4:185–209

    Google Scholar 

  49. Pal S, Qu B, Das S, Suganthan PN (2010) Linear antenna array synthesis with constrained multi-objective differential evolution. Prog Electromagn Res B 21:87–111

    Google Scholar 

  50. Goudos SK, Moysiadou V, Samaras T, Siakavara K, Sahalos JN (2010) 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

    Google Scholar 

  51. Cen L, Yu ZL, Ser W, Cen W (2012) Linear aperiodic array synthesis using an improved genetic algorithm. IEEE Trans Antennas Propag 60(2):895–902

    MathSciNet  MATH  Google Scholar 

  52. Chowdhury A, Giri R, Ghosh A, Das S, Abraham A, Snasel V (2010) Linear antenna array synthesis using fitness-adaptive differential evolution algorithm. In: 2010 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–8

  53. Subhashini KR, Satapathy JK (2017) Development of an enhanced ant lion optimization algorithm and its application in antenna array synthesis. Appl Soft Comput 59:153–173

    Google Scholar 

  54. Pappula L, Ghosh D (2013). Large array synthesis using invasive weed optimization. In: 2013 International conference on microwave and photonics (ICMAP). IEEE, pp 1–6

  55. Pappula L, Ghosh D (2014) Constraint-based synthesis of linear antenna array using modified invasive weed optimization. Prog Electromagn Res M 36:9–22

    Google Scholar 

  56. Guney K, Basbug S (2014) Linear antenna array synthesis using mean variance mapping method. Electromagnetics 34(2):67–84

    Google Scholar 

  57. Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26(5):1257–1263

    Google Scholar 

  58. Lewis A, Mostaghim S, Randall M (2008) Evolutionary population dynamics and multi-objective optimisation problems. In: Multi-objective optimization in computational intelligence: theory and practice. IGI Global, pp 185–206

  59. Rodríguez L, Castillo O, Soria J (2016) Grey wolf optimizer with dynamic adaptation of parameters using fuzzy logic. In: 2016 IEEE congress on evolutionary computation (CEC). IEEE, pp 3116–3123

  60. Emary E, Zawbaa HM, Grosan C, Hassenian AE (2015) Feature subset selection approach by gray-wolf optimization. In: Afro-European conference for industrial advancement. Springer International Publishing, pp 1–13

  61. Eiben AE, Raue PE, Ruttkay Z (1994) Genetic algorithms with multi-parent recombination. In: International conference on parallel problem solving from nature. Springer, Berlin, pp 78–87

  62. Mahdad B, Srairi K (2015) Blackout risk prevention in a smart grid based flexible optimal strategy using Grey Wolf-pattern search algorithms. Energy Convers Manag 98:411–429

    Google Scholar 

  63. Zhu A, Xu C, Li Z, Wu J, Liu Z (2015) Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC. J Syst Eng Electron 26(2):317–328

    Google Scholar 

  64. Yang B, Zhang X, Yu T, Shu H, Fang Z (2017) Grouped grey wolf optimizer for maximum power point tracking of doubly-fed induction generator based wind turbine. Energy Convers Manag 133:427–443

    Google Scholar 

  65. Vrionis TD, Koutiva XI, Vovos NA (2014) A genetic algorithm-based low voltage ride-through control strategy for grid connected doubly fed induction wind generators. IEEE Trans Power Syst 29(3):1325–1334

    Google Scholar 

  66. Bekakra Y, Attous DB (2014) Optimal tuning of PI controller using PSO optimization for indirect power control for DFIG based wind turbine with MPPT. Int J Syst Assur Eng Manag 5(3):219–229

    Google Scholar 

  67. Muangkote N, Sunat K, Chiewchanwattana S (2014) An improved grey wolf optimizer for training q-Gaussian radial basis functional-link nets. In: Computer science and engineering conference (ICSEC), 2014 international. IEEE, pp 209–214

  68. Chandra M, Agrawal A, Kishor A, Niyogi R (2016) Web service selection with global constraints using modified gray wolf optimizer. In: 2016 international conference on advances in computing, communications and informatics (ICACCI). IEEE, pp 1989–1994

  69. Kishor A, Singh PK (2016) Empirical study of grey wolf optimizer. In: Proceedings of 5th international conference on soft computing for problem solving. Springer, Singapore, pp 1037–1049

  70. Canfora G, Di Penta M, Esposito R, Villani ML (2005) An approach for QoS-aware service composition based on genetic algorithms. In Proceedings of the 7th annual conference on genetic and evolutionary computation. ACM, pp 1069–1075

  71. Sharma Y, Saikia LC (2015) Automatic generation control of a multi-area ST–thermal power system using grey wolf optimizer algorithm based classical controllers. Int J Electr Power Energy Syst 73:853–862

    Google Scholar 

  72. Lal DK, Barisal AK, Tripathy M (2016) Grey wolf optimizer algorithm based Fuzzy PID controller for AGC of multi-area power system with TCPS. Procedia Comput Sci 92:99–105

    Google Scholar 

  73. Das KR, Das D, Das J (2015). Optimal tuning of PID controller using GWO algorithm for speed control in DC motor. In: 2015 international conference on soft computing techniques and implementations (ICSCTI). IEEE, pp 108–112

  74. Sodeifian G, Ardestani NS, Sajadian SA, Ghorbandoost S (2016) Application of supercritical carbon dioxide to extract essential oil from Cleome coluteoides Boiss: experimental, response surface and grey wolf optimization methodology. J Supercrit Fluids 114:55–63

    Google Scholar 

  75. Mohanty S, Subudhi B, Ray PK (2016) A new MPPT design using grey wolf optimization technique for photovoltaic system under partial shading conditions. IEEE Trans Sustain Energy 7(1):181–188

    Google Scholar 

  76. Song X, Tang L, Zhao S, Zhang X, Li L, Huang J, Cai W (2015) Grey wolf optimizer for parameter estimation in surface waves. Soil Dyn Earthq Eng 75:147–157

    Google Scholar 

  77. Zhang S, Zhou Y, Li Z, Pan W (2016) Grey wolf optimizer for unmanned combat aerial vehicle path planning. Adv Eng Softw 99:121–136

    Google Scholar 

  78. Elhariri, E., El-Bendary, N., Hassanien, A. E., & Abraham, A. (2015, November). Grey wolf optimization for one-against-one multi-class support vector machines. In: 2015 7th international conference on soft computing and pattern recognition (SoCPaR). IEEE, pp 7–12

  79. Medjahed SA, Saadi TA, Benyettou A, Ouali M (2016) Gray wolf optimizer for hyperspectral band selection. Appl Soft Comput 40:178–186

    Google Scholar 

  80. Mirjalili S (2015) How effective is the Grey Wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161

    Google Scholar 

  81. Guha D, Roy PK, Banerjee S (2016) Load frequency control of interconnected power system using grey wolf optimization. Swarm Evolut Comput 27:97–115

    Google Scholar 

  82. Jayakumar N, Subramanian S, Ganesan S, Elanchezhian EB (2016) Grey wolf optimization for combined heat and power dispatch with cogeneration systems. Int J Electr Power Energy Syst 74:252–264

    Google Scholar 

  83. Sultana U, Khairuddin AB, Mokhtar AS, Zareen N, Sultana B (2016) Grey wolf optimizer based placement and sizing of multiple distributed generation in the distribution system. Energy 111:525–536

    Google Scholar 

  84. Sulaiman MH, Mustaffa Z, Mohamed MR, Aliman O (2015) Using the gray wolf optimizer for solving optimal reactive power dispatch problem. Appl Soft Comput 32:286–292

    Google Scholar 

  85. Chaman-Motlagh A (2015) Superdefect photonic crystal filter optimization using grey wolf optimizer. IEEE Photonics Technol Lett 27(22):2355–2358

    Google Scholar 

  86. Shakarami MR, Davoudkhani IF (2016) Wide-area power system stabilizer design based on grey wolf optimization algorithm considering the time delay. Electr Power Syst Res 133:149–159

    Google Scholar 

  87. Yusof Y, Mustaffa Z (2015) Time series forecasting of energy commodity using grey wolf optimizer. In: Proceedings of the international multi conference of engineers and computer scientists (IMECS'15) (Vol. 1, No. 1)

  88. Precup RE, David RC, Petriu EM (2017) Grey wolf optimizer algorithm-based tuning of fuzzy control systems with reduced parametric sensitivity. IEEE Trans Ind Electron 64(1):527–534

    Google Scholar 

  89. Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. In: 2005 and international conference on intelligent agents, web technologies and internet commerce, international conference on computational intelligence for modelling, control and automation, vol 1. IEEE, pp 695–701

  90. Nasrabadi MS, Sharafi Y, Tayari M (2016) A parallel grey wolf optimizer combined with opposition based learning. In: 2016 1st conference on swarm intelligence and evolutionary computation (CSIEC). IEEE, pp 18–23

  91. Meng X, Liu Y, Gao X, Zhang H (2014) A new bio-inspired algorithm: chicken swarm optimization. In: International conference in swarm intelligence. Springer, Cham, pp 86–94

  92. Mirjalili SZ, Mirjalili S, Saremi S, Faris H, Aljarah I (2017) Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48(4):805–820

    Google Scholar 

  93. Fister I, Fister I Jr, Yang XS, Brest J (2013) A comprehensive review of firefly algorithms. Swarm Evolut Comput 13:34–46

    Google Scholar 

  94. Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126

    Google Scholar 

  95. Derrac J, García S, Molina D, Herrera F (2011) 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

    Google Scholar 

  96. Balanis CA (2005) Antenna theory: analysis and design. Wiley, New York

    Google Scholar 

  97. Yang XH, Yang ZF, Yin XA, Li JQ (2008) Chaos gray-coded genetic algorithm and its application for pollution source identifications in convection-diffusion equation. Commun Nonlinear Sci Numer Simul 13(8):1676–1688

    Google Scholar 

  98. Kaur K, Singh U, Salgotra R (2018) An enhanced moth flame optimization. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3821-6

    Article  Google Scholar 

  99. Sharma SK, Mittal N, Salgotra R, Singh U (2017) Linear antenna array synthesis using bat flower pollinator. In: 2017 international conference on innovations in information, embedded and communication systems (ICIIECS). IEEE, pp 1–4

  100. Yang XH, Li YQ, Wang KW, Sun BY, Ye Y, Li MS (2017) Improved gray-encoded evolution algorithm based on chaos cluster for parameter optimization of moisture movement. Therm Sci 21(4):15–20

    Google Scholar 

  101. Salgotra R, Singh U, Saha S (2018). Improved Cuckoo search with better search capabilities for solving CEC2017 benchmark problems. In: 2018 IEEE congress on evolutionary computation (CEC). IEEE, pp 1–7

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

    Google Scholar 

  103. Yang Xiao-Hua, Di Chong-Li, Mei Ying, Li Yu-Qi, Li Jian-Qiang (2014) Refined gray-encoded evolution algorithm for parameter optimization in convection-diffusion equations. Int J Numer Methods Heat Fluid Flow 24(6):1275–1289

    MathSciNet  MATH  Google Scholar 

  104. Shao BD, Wang LF, Li JY, Cheng HM (2011) Multi-objective optimization design of a micro-channel heat sink using adaptive genetic algorithm. Int J Numer Methods Heat Fluid Flow 21(3–4):353–364

    Google Scholar 

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Acknowledgements

This research has been funded under Inspire Fellowship (IF-160215) by Directorate of Science & Technology, Government of India.

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  1. Electronics and Communication Engineering Department, Thapar University, Patiala, Punjab, India

    Rohit Salgotra, Urvinder Singh & Sakshi Sharma

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  1. Rohit Salgotra
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Salgotra, R., Singh, U. & Sharma, S. On the improvement in grey wolf optimization. Neural Comput & Applic 32, 3709–3748 (2020). https://doi.org/10.1007/s00521-019-04456-7

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