I-GWO and Ex-GWO: improved algorithms of the Grey Wolf Optimizer to solve global optimization problems

  • Amir SeyyedabbasiEmail author
  • Farzad Kiani
Original Article


In this paper, two novel meta-heuristic algorithms are introduced to solve global optimization problems inspired by the Grey Wolf Optimizer (GWO) algorithm. In the GWO algorithm, wolves are likely to be located in regions close to each other. Therefore, as they catch the hunt (approaching the solution), they may create an intensity in the same or certain regions. In this case, the mechanism to prevent the escape of the hunt may not work well. First, the proposed algorithm is the expanded model of the GWO algorithm that is called expanded Grey Wolf Optimizer. In this method, the same as GWO, alpha, beta, and delta play the role of the main three wolves. However, the next wolves select and update their positions according to the previous and the first three wolves in each iteration. Another proposed algorithm is based on the incremental model and is, therefore, called incremental Grey Wolf Optimizer. In this method, each wolf updates its own position based on all the wolves selected before it. There is the possibility of finding solutions (hunts) quicker than according to other algorithms in the same category. However, they may not always guarantee to find a good solution because of their act dependent on each other. Both algorithms focus on exploration and exploitation. In this paper, the proposed algorithms are simulated over 33 benchmark functions and the related results are compared with well-known optimization algorithms. The results of the proposed algorithms seem to be good solutions for various problems.


Grey wolf optimizer (GWO) Optimization algorithm Meta-heuristic Swarm intelligence 


Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.


  1. 1.
    Winston PH (1992) Artificial intelligence, 3rd edn. Addison-Wesley, BostonzbMATHGoogle Scholar
  2. 2.
    Yao X, Yong L (1997) Fast evolution strategies. In: International conference on evolutionary programming. Springer, BerlinGoogle Scholar
  3. 3.
    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61Google Scholar
  4. 4.
    Talbi EG (2009) Metaheuristics: from design to implementation, vol 74. Wiley, HobokenzbMATHGoogle Scholar
  5. 5.
    Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98Google Scholar
  6. 6.
    Jamil M, Xin-She Y (2013) A literature survey of benchmark functions for global optimization problems. arXiv preprint arXiv.1308-4008Google Scholar
  7. 7.
    Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73Google Scholar
  8. 8.
    Chawla P, Chana I, Rana A (2015) A novel strategy for automatic test data generation using soft computing technique. Front Comput Sci 9(3):346–363Google Scholar
  9. 9.
    Gomes GF, de Almeida FA, Junqueira DM, da Cunha Jr SS, Ancelotti AC Jr (2019) Optimized damage identification in CFRP plates by reduced mode shapes and GA-ANN methods. Eng Struct 181:111–123Google Scholar
  10. 10.
    Kilinc M, Caicedo JM (2019) Finding plausible optimal solutions in engineering problems using an adaptive genetic algorithm. Adv Civ Eng 2019:1–9Google Scholar
  11. 11.
    Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetzbMATHGoogle Scholar
  12. 12.
    Sharma R, Vashisht V, Singh AV, Kumar S (2019) Analysis of existing clustering algorithms for wireless sensor networks. System Performance and Management Analytics. Springer, Singapore, pp 259–277Google Scholar
  13. 13.
    Mann PS, Singh S (2019) Improved metaheuristic-based energy-efficient clustering protocol with optimal base station location in wireless sensor networks. Soft Comput 23(3):1021–1037zbMATHGoogle Scholar
  14. 14.
    Sahu RK, Sekhar GC, Priyadarshani S (2019) Differential evolution algorithm tuned tilt integral derivative controller with filter controller for automatic generation control. Evol Intell. Google Scholar
  15. 15.
    Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102Google Scholar
  16. 16.
    Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. Wiley-IEEE Press, HobokenzbMATHGoogle Scholar
  17. 17.
    Zhang X, Luo J, Sun X, Xie J (2019) Optimal reservoir flood operation using a decomposition-based multi-objective evolutionary algorithm. Eng Optim 51(1):42–62MathSciNetGoogle Scholar
  18. 18.
    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713Google Scholar
  19. 19.
    Kasilingam F, Pasupuleti J, Bharatiraja C, Adedayo Y (2019) Power system stabilizer optimization using BBO algorithm for a better damping of rotor oscillations owing to small disturbances. FME Trans 47(1):166–176Google Scholar
  20. 20.
    Kumar M, Om H (2019) A Hybrid bio-inspired algorithm for protein domain problems. In: Advances in nature-inspired computing and applications. Springer, Cham, pp 291–311Google Scholar
  21. 21.
    Bhattacharya A, Chattopadhyay PK (2010) Solving complex economic load dispatch problems using biogeography-based optimization. Expert Syst Appl 37(5):3605–3615Google Scholar
  22. 22.
    Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248zbMATHGoogle Scholar
  23. 23.
    Naserbegi A, Aghaie M, Minuchehr A, Alahyarizadeh G (2018) A novel exergy optimization of Bushehr nuclear power plant by gravitational search algorithm (GSA). Energy 148:373–385Google Scholar
  24. 24.
    Marzband M, Ghadimi M, Sumper A, Domínguez-García JL (2014) Experimental validation of a real-time energy management system using multi-period gravitational search algorithm for microgrids in islanded mode. Appl Energy 128:164–174Google Scholar
  25. 25.
    Chakraborti T, Sharma KD, Chatterjee A (2014) A novel local extrema based gravitational search algorithm and its application in face recognition using one training image per class. Eng Appl Artif Intell 34:13–22Google Scholar
  26. 26.
    Erol OK, Eksin I (2006) A new optimization method: big bang–big crunch. Adv Eng Softw 37(2):106–111Google Scholar
  27. 27.
    Sakthivel S, Pandiyan SA, Marikani S, Selvi SK (2013) Application of big bang big crunch algorithm for optimal power flow problems. Int J Eng Sci 2(4):41–47Google Scholar
  28. 28.
    Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3–4):267–289zbMATHGoogle Scholar
  29. 29.
    Özyön S, Temurtaş H, Durmuş B, Kuvat G (2012) Charged system search algorithm for emission constrained economic power dispatch problem. Energy 46(1):420–430Google Scholar
  30. 30.
    Lam AY, Li VO (2010) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput 14(3):381–399Google Scholar
  31. 31.
    Xu J, Lam AY, Li VO (2011) Chemical reaction optimization for task scheduling in grid computing. IEEE Trans Parallel Distrib Syst 22(10):1624–1631Google Scholar
  32. 32.
    Li Z, Li Y, Yuan T, Chen S, Jiang S (2019) Chemical reaction optimization for virtual machine placement in cloud computing. Appl Intell 49(1):220–232Google Scholar
  33. 33.
    Kabir R, Islam R (2019) Chemical reaction optimization for RNA structure prediction. Appl Intell 49(2):352–375Google Scholar
  34. 34.
    Formato RA (2007) Central force optimization: a new metaheuristic with applications in applied electromagnetics. Prog Electromagn Res 77:425–491Google Scholar
  35. 35.
    Haghighi A, Ramos HM (2012) Detection of leakage freshwater and friction factor calibration in drinking networks using central force optimization. Water Resour Manag 26(8):2347–2363Google Scholar
  36. 36.
    Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184MathSciNetGoogle Scholar
  37. 37.
    Hatamlou A (2018) Solving travelling salesman problem using black hole algorithm. Soft Comput 22(24):8167–8175Google Scholar
  38. 38.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95 - international conference on neural networks, Australia, pp 1942–1948Google Scholar
  39. 39.
    Pattanayak S, Agarwal S, Choudhury BB, Sahoo SC (2019) Path planning of mobile robot using PSO algorithm. In: Information and communication technology for intelligent systems. Springer, Singapore, pp 515–522Google Scholar
  40. 40.
    Syahputra R, Robandi I, Ashari M (2015) Reconfiguration of distribution network with distributed energy resources integration using PSO algorithm. Telkomnika 13(3):759Google Scholar
  41. 41.
    Dorigo M, Birattari M (2010) Ant colony optimization. Springer, New York, pp 36–39Google Scholar
  42. 42.
    Okdem S, Karaboga D (2009) Routing in wireless sensor networks using an ant colony optimization (ACO) router chip. Sensors 9(2):909–921Google Scholar
  43. 43.
    Yi W, Kumar A (2007) Ant colony optimization for disaster relief operations. Transp Res Part E Logist Transp Rev 43(6):660–672Google Scholar
  44. 44.
    Tian J, Yu W, Xie S (2008) An ant colony optimization algorithm for image edge detection. In: 2008 IEEE congress on evolutionary computation (IEEE World Congress on Computational Intelligence). IEEE, pp 751–756Google Scholar
  45. 45.
    Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697Google Scholar
  46. 46.
    Gong D, Han Y, Sun J (2018) A novel hybrid multi-objective artificial bee colony algorithm for blocking lot-streaming flow shop scheduling problems. Knowl Based Syst 148:115–130Google Scholar
  47. 47.
    Singh A (2009) An artificial bee colony algorithm for the leaf-constrained minimum spanning tree problem. Appl Soft Comput 9(2):625–631Google Scholar
  48. 48.
    Yang XS (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, New York, pp 65–74Google Scholar
  49. 49.
    Osaba E, Yang XS, Diaz F, Lopez-Garcia P, Carballedo R (2016) An improved discrete bat algorithm for symmetric and asymmetric traveling salesman problems. Eng Appl Artif Intell 48:59–71Google Scholar
  50. 50.
    Sathya MR, Ansari MMT (2015) Load frequency control using Bat inspired algorithm based dual mode gain scheduling of PI controllers for interconnected power system. Int J Electr Power Energy Syst 64:365–374Google Scholar
  51. 51.
    Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspir Comput 2:78–84Google Scholar
  52. 52.
    Banati H, Bajaj M (2011) Fire fly based feature selection approach. Int J Comput Sci Issues (IJCSI) 8(4):473Google Scholar
  53. 53.
    Talatahari S, Gandomi AH, Yun GJ (2014) Optimum design of tower structures using firefly algorithm. Struct Des Tall Spec Build 23(5):350–361Google Scholar
  54. 54.
    Tuba E, Tuba M, Beko M (2017) Mobile wireless sensor networks coverage maximization by firefly algorithm. In: 2017 27th international conference Radioelektronika (RADIOELEKTRONIKA). IEEE, pp 1–5Google Scholar
  55. 55.
    Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World congress on nature and biologically inspired computing (NaBIC), pp 210–214Google Scholar
  56. 56.
    Mohamad A, Zain AM, Bazin NEN, Udin A (2013) Cuckoo search algorithm for optimization problems-a literature review. Applied mechanics and materials, vol 421. Trans Tech Publications, Zurich, pp 502–506Google Scholar
  57. 57.
    Rath A, Samantaray S, Swain PC (2019) Optimization of the cropping pattern using cuckoo search technique. Smart techniques for a smarter planet. Springer, Cham, pp 19–35Google Scholar
  58. 58.
    Arif MA, Mohamad MS, Latif MSA, Deris S, Remli MA, Daud KM, Corchado JM (2018) A hybrid of cuckoo search and minimization of metabolic adjustment to optimize metabolites production in genome-scale models. Comput Biol Med 102:112–119Google Scholar
  59. 59.
    Dhivya M, Sundarambal M (2011) Cuckoo search for data gathering in wireless sensor networks. Int J Mob Commun 9(6):642–656Google Scholar
  60. 60.
    Mucherino A, Seref O (2007) Monkey search: a novel metaheuristic search for global optimization. AIP Conf Proc 953(1):162–173Google Scholar
  61. 61.
    Zhou Y, Chen X, Zhou G (2016) An improved monkey algorithm for a 0–1 knapsack problem. Appl Soft Comput 38:817–830Google Scholar
  62. 62.
    Yi TH, Li HN, Zhang XD (2015) Health monitoring sensor placement optimization for Canton Tower using immune monkey algorithm. Struct Control Health Monit 22(1):123–138Google Scholar
  63. 63.
    Khairuzzaman AKM, Chaudhury S (2017) Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Syst Appl 86:64–76Google Scholar
  64. 64.
    Li Q, Chen H, Huang H, Zhao X, Cai Z, Tong C, Tian X (2017) An enhanced grey wolf optimization based feature selection wrapped kernel extreme learning machine for medical diagnosis. Comput Math Methods Med 2017:1–15Google Scholar
  65. 65.
    Fahad M, Aadil F, Khan S, Shah PA, Muhammad K, Lloret J, Mehmood I (2018) Grey wolf optimization based clustering algorithm for vehicular ad-hoc networks. Comput Electr Eng 70:853–870Google Scholar
  66. 66.
    Mousavi S, Mosavi A, Varkonyi-Koczy AR (2017) A load balancing algorithm for resource allocation in cloud computing. In: International conference on global research and education. Springer, Cham, pp 289–296Google Scholar
  67. 67.
    Mittal N, Singh U, Sohi BS (2016) Modified grey wolf optimizer for global engineering optimization. Appl Comput Intell Soft Comput 8:1–16Google Scholar
  68. 68.
    Faris H, Aljarah I, Al-Betar MA, Mirjalili S (2018) Grey wolf optimizer: a review of recent variants and applications. Neural Comput Appl 30(2):413–435Google Scholar
  69. 69.
    Joshi H, Arora S (2017) Enhanced grey wolf optimization algorithm for global optimization. Fundam Inform 153(3):235–264MathSciNetzbMATHGoogle Scholar
  70. 70.
    Liang JJ, Qu BY, Suganthan PN (2013) 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, vol 635Google Scholar
  71. 71.
    Liang JJ, Qu BY, Suganthan PN, Chen Q (2014) Problem definitions and evaluation criteria for the CEC 2015 competition on learning-based real-parameter single objective optimization. Technical Report201411A, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, vol 29, pp 625–640Google Scholar
  72. 72.
    Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Computer Engineering Department, Engineering and Natural Sciences FacultyIstanbul Sabahattin Zaim UniversityIstanbulTurkey
  2. 2.Computer Engineering Department, Engineering and Architecture FacultyIstanbul Arel UniversityIstanbulTurkey

Personalised recommendations