Behavior of Grey Wolf Optimization (GWO) Algorithm using Meta-heuristics method

1. Introduction

     The GWO algorithm mimics the leadership hierarchy and hunting mechanism of gray wolves in nature proposed by Mirjalili et al. in 2014. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the leadership hierarchy. In addition, three main steps of hunting, searching for prey, encircling prey, and attacking prey, are implemented to perform optimization [1]. Meta-heuristic optimization methods have become extremely popular over the past two decades because of their simplicity, flexibility, derivation-free and local minima avoidance. These techniques have been mostly inspired by very simple concepts typically related to physical phenomena, animals’ behavior or evolutionary concepts. This simplicity attracts the researchers to develop and propose new meta-heuristics. The meta-heuristics can be separated into two main modules: single-solution based and population based [2]. Among these, the latter has some advantages than the primer which motivate the researcher to apply meta-heuristic techniques for solving various practical optimization problems. The techniques based on the swarm intelligence behavior belong to a branch of population based meta-heuristics. The exploration and exploitation phases are the common feature of swarm intelligence techniques.  Usually optimization techniques bring the control parameters of the non-linear problem to the edge, whereas, their mathematical methods are difficult to implement for better accuracy. So, an effective optimization technique is needed to solve non-linear problems [3].

  1. Hierarchy of grey wolf
Fig 1: Hierarchy of grey wolf

Grey wolf hunting is the principle stages which are as per the following:

  • Tracking, pursuing, and moving toward the prey
  •  Until it quits moving while seeking after, encompassing, and irritating the prey
  •  Attack towards the prey [4] 

2.   Grey Wolf Optimization Algorithm

Grey wolf belongs to Candidate family. Grey wolves are considered as apex predators, meaning that they are at the top of the food chain. Grey wolves mostly prefer to live in a pack. The group size is 5-12 on average. Of particular interest is that they have a very strict social dominant hierarchy. The leaders are a male and female, called alphas. The alpha is mostly responsible for making decisions about hunting, sleeping place, time to wake, and so on [5]. The alpha’s decisions are dictated to the pack. However, some kind of democratic behavior has also been observed, in which an alpha follows the other wolves in the pack. In gatherings, the entire pack acknowledges the alpha by holding their tails down. The alpha wolf is also called the dominant wolf since his/her orders should be followed by the pack. The alpha wolves are only allowed to mate in the pack. Interestingly, the alpha is not necessarily the strongest member of the pack but the best in terms of managing the pack [6]. This shows that the organization and discipline of a pack is much more important than its strength. The second level in the hierarchy of grey wolves is beta. The betas are subordinate wolves that help the alpha in decision-making or other pack activities. The beta wolf can be either male or female, and he/she is probably the best candidate to be the alpha in case one of the alpha wolves passes away or becomes very old. The beta wolf should respect the alpha, but commands the other lower-level wolves as well. It plays the role of an adviser to the alpha and discipliner for the pack. The beta reinforces the alpha’s commands throughout the pack and gives feedback to the alpha [7].

      The lowest ranking grey wolf is omega. The omega plays the role of scapegoat. Omega wolves always have to submit to all the other dominant wolves. They are the last wolves that are allowed to eat. It may seem the omega is not an important individual in the pack, but it has been observed that the whole pack face internal fighting and problems in case of losing the omega. This is due to the venting of violence and frustration of all wolves by the omega(s). This assists satisfying the entire pack and maintaining the dominance structure. In some cases the omega is also the babysitters in the pack. If a wolf is not an alpha, beta, or omega, he/she is called subordinate (or delta in some references). Delta wolves have to submit to alphas and betas, but they dominate the omega. Scouts, sentinels, elders, hunters, and caretakers belong to this category. Scouts are responsible for watching the boundaries of the territory and warning the pack in case of any danger. Sentinels protect and guarantee the safety of the pack. Elders are the experienced wolves who used to be alpha or beta. Hunter’s help the alphas and betas when hunting prey and providing food for the pack [8]. Finally, the caretakers are responsible for caring for the weak, ill, and wounded wolves in the pack. In addition to the social hierarchy of wolves, group hunting is another interesting social behavior of grey wolves. According to Muro et al. The main phases of gray wolf hunting are as follows:

  • Tracking, chasing, and approaching the prey
  • Pursuing, encircling, and harassing the prey until it stops moving
  • Attack towards the prey
Fig 2: Grey Wolf Optimization Algorithm
  1. Steps for GWO Algorithm
  • Social Hierarchy
  • Encircling prey
  • Hunting
  • Attaching the prey
  • Exploration

2.1.1 Social Hierarchy  

    The fitness solutions are structured according to the societal hierarchy of wolves. The best fitness solution is regarded as alpha (α) followed by beta (β), delta (δ) and omega (ω) wolves. Grey wolf belongs to Candidate family. Grey wolves are considered as apex predators, meaning that they are at the top of the food chain. Grey wolves mostly prefer to live in a pack [9]. Of particular interest is that they have a strict social dominant hierarchy from alpha, beta, delta, too mega.

2.1.2. Encircling prey

     A grey wolf can update its position inside the space around the prey in any random location. In addition to the social hierarchy of grey wolves described above, group hunting is another interesting social behavior of grey wolves. According to Muroetal. The main phases of grey wolf hunting include: Tracking, chasing, and approaching the prey; Encircling, pursuing, and harassing the prey until it stops moving; Attacking towards the prey [10].

2.1.3. Hunting

      In order to mathematically simulate the hunting behavior of grey wolves, the first three best solutions obtained so far are saved and oblige the other search agents (including the omegas) to update their positions according to the position of the best search agents [11].

2.2.Flow Chart of GWO algorithm   


Fig 3: Flowchart of GWO Algorithm

    3.Numerical Expression of GWO Algorithm

Grey wolves first find out the position of the prey, and then encircle it. In fact, the position of the optimal prey is unknown in a search space [14]. For the sake of simulating the hunting behavior of grey wolves, we suppose that the grey wolf Alpha, Beta and Delta are aware of the potential position of a prey. So, the first three best solutions gained so far are stored and the other members in the pack must update their positions in the light of the best three solutions [15]. Such behavior can be formulated as follows:

4. Applications of GWO Algorithm  

  • Training Algorithm for Multi-layer perception
  • Training q-Gaussian Radial Basis Functional-link nets[16]
  • Economic dispatch problems[17]
  • Feature Subset Selection
  • Power system grid
  • Evolutionary population dynamics[18]
  • Optimizing key values
Fig 4: Applications of GWO Algorithm

5. Advantages of GWO Algorithm

  • The GWO is a new optimization method which overcomes the limitations such as lower tracking efficiency, steady-state oscillations, and transients as encountered in perturb and observe (P&O) and improved PSO (IPSO) techniques [19].
  • To validate the performance of the GWO, statistical measures like best, mean, worst, standard deviation, epsilon, iter and sol-iter over 50 independent runs are taken [21].
  • The GWO algorithm can reveal an efficient performance compared to other well-established optimizers [22].
  • The great advantages of GWO are that the algorithm is simple, flexible, robust and easy to implement. Also there are fewer control parameters to tune [23].
  • Experimental results show the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration [24].


[1] Mirjalili, S., Mirjalili, S. and Lewis, A. (2014). Grey Wolf Optimizer. Advances in Engineering Software, 69, pp.46-61.

[2] Kohli, M. and Arora, S. (2018). Chaotic grey wolf optimization algorithm for constrained optimization problems. Journal of Computational Design and Engineering, 5(4), pp.458-472.

[3] Mohanty, S., Subudhi, B. and Ray, P. (2016). A New MPPT Design Using Grey Wolf Optimization Technique for Photovoltaic System Under Partial Shading Conditions. IEEE Transactions on Sustainable Energy, 7(1), pp.181-188.

[4] Jayakumar, N., Subramanian, S., Ganesan, S. and Elanchezhian, E. (2016). Grey wolf optimization for combined heat and power dispatch with cogeneration systems. International Journal of Electrical Power & Energy Systems, 74, pp.252-264.

[5] Heidari, A. and Pahlavani, P. (2017). An efficient modified grey wolf optimizer with Lévy flight for optimization tasks. Applied Soft Computing, 60, pp.115-134.

[6] Song, X., Tang, L., Zhao, S., Zhang, X., Li, L., Huang, J. and Cai, W. (2015). Grey Wolf Optimizer for parameter estimation in surface waves. Soil Dynamics and Earthquake Engineering, 75, pp.147-157.

[7] Mohanty, S., Subudhi, B. and Ray, P. (2017). A Grey Wolf-Assisted Perturb & Observe MPPT Algorithm for a PV System. IEEE Transactions on Energy Conversion, 32(1), pp.340-347.

[8] Ibrahim, R., Elaziz, M. and Lu, S. (2018). Chaotic opposition-based grey-wolf optimization algorithm based on differential evolution and disruption operator for global optimization. Expert Systems with Applications, 108, pp.1-27.

[9] Zhu, A., Xu, C., Li, Z., Wu, J. and Liu, Z. (2015). Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC. Journal of Systems Engineering and Electronics, 26(2), pp.317-328.

[10] Mohanty, S., Subudhi, B. and Ray, P. (2017). A Grey Wolf-Assisted Perturb & Observe MPPT Algorithm for a PV System. IEEE Transactions on Energy Conversion, 32(1), pp.340-347.

[11] Daniel, E., Anitha, J. and Gnanaraj, J. (2017). Optimum laplacian wavelet mask based medical image using hybrid cuckoo search – grey wolf optimization algorithm. Knowledge-Based Systems, 131, pp.58-69.

[12] Khairuzzaman, A. and Chaudhury, S. (2017). Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Systems with Applications, 86, pp.64-76.

[13] Mahdad, B. and Srairi, K. (2015). Blackout risk prevention in a smart grid based flexible optimal strategy using Grey Wolf-pattern search algorithms. Energy Conversion and Management, 98, pp.411-429.

[14] Long, W., Liang, X., Cai, S., Jiao, J. and Zhang, W. (2016). A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems. Neural Computing and Applications, 28(S1), pp.421-438.

[15] Yang, B., Zhang, X., Yu, T., Shu, H. and Fang, Z. (2017). Grouped grey wolf optimizer for maximum power point tracking of doubly-fed induction generator based wind turbine. Energy Conversion and Management, 133, pp.427-443.

[16] Wong, L., Sulaiman, M. and Mohamed, M. (2015). Solving Economic Dispatch Problems with Practical Constraints Utilizing Grey Wolf Optimizer. Applied Mechanics and Materials, 785, pp.511-515.

[17] Sultana, U., Khairuddin, A., Mokhtar, A., Zareen, N. and Sultana, B. (2016). Grey wolf optimizer based placement and sizing of multiple distributed generation in the distribution system. Energy, 111, pp.525-536.

[18] de Moura Oliveira, P., Freire, H. and Solteiro Pires, E. (2016). Grey wolf optimization for PID controller design with prescribed robustness margins. Soft Computing, 20(11), pp.4243-4255.

[19] Garg, A. and Kumar Agarwal, S. (2012). Dynamic Stability Enhancement of Power Transmission System Using Artificial Neural Network Controlled Static Var Compensator. International Journal of Computer Applications, 53(9), pp.21-29.

[20] Radmanesh, M., Kumar, M. and Sarim, M. (2018). Grey wolf optimization based sense and avoid algorithm in a Bayesian framework for multiple UAV path planning in an uncertain environment. Aerospace Science and Technology, 77, pp.168-179.

[21] Energy-Efficient Routing Protocol for Wireless Sensor Networks Based on Improved Grey Wolf Optimizer. (2018). KSII Transactions on Internet and Information Systems, 12(6).

[22] Gupta, S. and Deep, K. (2019). Enhanced leadership-inspired grey wolf optimizer for global optimization problems. Engineering with Computers.

[23] Pradhan, M., Roy, P. and Pal, T. (2018). Oppositional based grey wolf optimization algorithm for economic dispatch problem of power system. Ain Shams Engineering Journal, 9(4), pp.2015-2025.

[24] Jaafari, A., Panahi, M., Pham, B., Shahabi, H., Bui, D., Rezaie, F. and Lee, S. (2019). Meta optimization of an adaptive neuro-fuzzy inference system with grey wolf optimizer and biogeography-based optimization algorithms for spatial prediction of landslide susceptibility. CATENA, 175, pp.430-445.

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