TARU PUBLICATIONS
Journal of Information and Optimization Sciences cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

Powered by:Powered by

Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

Issues up to 2022 co-published with and available at:Taylor & Francis
submissions@tarupublications.com
Open Access Research Article

StableGWO : A grey wolf optimizer with von Neumann stability criteria

, , , *

* Corresponding author · click or hover a name for details

pp. 1401–1424Vol. 46Issue 5July 2025DOI: 10.47974/JIOS-1361XML
Received:
06 Dec 2022
Published Online:
03 Feb 2025
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1361
Pages:
1401–1424

Abstract

The Grey wolf optimizer (GWO) is a recent swarm intelligence-based algorithm. The performance of GWO highly depends on the choice of the controlling parameters. Finding the most suitable values of these parameters becomes a challenging task due to the stochastic nature of the position update process. Mathematical analysis of the position update mechanism can guide in finding the most appropriate range of these parameters. This paper attempts to use von Neumann stability criteria to find the most suitable value of these parameters. The objective of this study is also to check whether the original parameter setting is in line with the recommendation of mathematical analysis. Recommendations are further examined using numerical experiments over 23 classical benchmark functions. It is found that the parameters of GWO are within the stable range. It is also verified that GWO performs poorly if the parameters are set beyond the stable range.

Keywords

Subject Classifications

90C3190C3090C26

References

[1] A. Abraham, A. Konar, N. R. Samal, and S. Das, “Stability analysis of the ant system dynamics with non-uniform pheromone deposition rules,” in 2007 IEEE Congress on Evolutionary Computation, pp. 1103–1108 (2007).
[2] M. A. Al-Betar, M. A. Awadallah, H. Faris, I. Aljarah, and A. I. Hammouri, “Natural selection methods for grey wolf optimizer,” Expert Systems with Applications, vol. 113, pp. 481–498 (2018).
[3] J. C. Bansal, A. Gopal, and A. K. Nagar, “Analysing convergence, consistency, and trajectory of artificial bee colony algorithm,” IEEE Access, vol. 6, pp. 73593–73602 (2018).
[4] J. C. Bansal, A. Gopal, and A. K. Nagar, “Stability analysis of artificial bee colony optimization algorithm,” Swarm and Evolutionary Computation, vol. 41, pp. 9–19 (2018).
[5] J. C. Bansal, H. Sharma, S. S. Jadon, and M. Clerc, “Spider monkey optimization algorithm for numerical optimization,” Memetic Computing vol. 6, no. 1, pp. 31–47 (2014).
[6] J. C. Bansal and S. Singh, “A better exploration strategy in grey wolf optimizer,” Journal of Ambient Intelligence and Humanized Computing, pp. 1–20 (2020).
[7] A. Biswas, S. Das, A. Abraham, and S. Dasgupta, “Stability analysis of the reproduction operator in bacterial foraging optimization,” Theoretical Computer Science, vol. 411, no. 21, pp. 2127–2139 (2010).
[8] R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in MHS’95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43 (1995).
[9] E. Emary, H. M. Zawbaa, and A. E. Hassanien, “Binary grey wolf optimization approaches for feature selection,” Neurocomputing, vol. 172, pp. 371–381 (2016).
[10] A. Entesar, H. S. Mahmood, and O. S. Qasim, “Solving nonlinear differential equations using a hybrid method between the variational iteration method and grey wolf optimization algorithm,” Journal of Interdisciplinary Mathematics, vol. 25, no. 2, pp. 573–585 (2022).
[11] F. Farivar and M. A. Shoorehdeli, “Stability analysis of particle dynamics in gravitational search optimization algorithm,” Information Sciences, vol. 337, pp. 25–43 (2016).
[12] R. Ghosh, N. Sinha, S. K. Biswas, and S. Phadikar, “A modified grey wolf optimization based feature selection method from EEG for silent speech classification,” Journal of Information and Optimization Sciences, vol. 40, no. 8, pp. 1639–1652 (2019).
[13] A. Gopal and J. C. Bansal, “Stability analysis of differential evolution,” in 2016 International Workshop on Computational Intelligence (IWCI), pp. 221–223 (2016).
[14] A. Gopal, M. M. Sultani, and J. C. Bansal, “On stability analysis of particle swarm optimization algorithm,” Arabian Journal for Science and Engineering, pp. 1–10 (2019).
[15] M. Gopal, Digital Control & State Variable Methods, Tata McGraw-Hill Education (2012).
[16] D. Guha, P. K. Roy, and S. Banerjee, “Load frequency control of interconnected power system using grey wolf optimization,” Swarm and Evolutionary Computation, vol. 27, pp. 97–115 (2016).
[17] W. Hahn, H. H. Hosenthien, and H. Lehnigk, Theory and Application of Liapunov’s Direct Method, vol. 3, Prentice-Hall Englewood Cliffs (1963).
[18] Y. He and W. Sun, “Stability and convergence of the Crank–Nicolson/Adams–Bashforth scheme for the time-dependent Navier–Stokes equations,” SIAM Journal on Numerical Analysis, vol. 45, no. 2, pp. 837–869 (2007).
[19] D. Karaboga and B. Basturk, “A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm,” Journal of Global Optimization, vol. 39, no. 3, pp. 459–471 (2007).
[20] G. M. Komaki and V. Kayvanfar, “Grey wolf optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time,” Journal of Computational Science, vol. 8, pp. 109–120 (2015).
[21] N. Li, D.-B. Sun, T. Zou, Y.-Q. Qin, and Y. Wei, “An analysis for a particle’s trajectory of PSO based on difference equation,” Jisuanji Xuebao/Chinese Journal of Computers, vol. 29, no. 11, pp. 2052–2061 (2006).
[22] Q. Liu, “Order-2 stability analysis of particle swarm optimization,” Evolutionary Computation, vol. 23, no. 2, pp. 187–216 (2015).
[23] W. Long, J. Jiao, X. Liang, and M. Tang, “An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization,” Engineering Applications of Artificial Intelligence, vol. 68, pp. 63–80 (2018).
[24] A. Madadi and M. M. Motlagh, “Optimal control of DC motor using grey wolf optimizer algorithm,” Tech J Eng Appl Sci, vol. 4, no. 4, pp. 373–379 (2014).
[25] K. Meidani, A. H. Hemmasian, S. Mirjalili, and A. B. Farimani, “Adaptive grey wolf optimizer,” Neural Computing and Applications, pp. 1–21 (2022).
[26] S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Advances in Engineering Software vol. 69, pp. 46–61 (2014).
[27] C. Muro, R. Escobedo, L. Spector, and R. P. Coppinger, “Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations,” Behavioural Processes, vol. 88, no. 3, pp. 192–197 (2011).
[28] M. H. Nadimi-Shahraki, S. Taghian, and S. Mirjalili, “An improved grey wolf optimizer for solving engineering problems,” Expert Systems with Applications, vol. 166, p. 113917 (2021).
[29] E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “GSA: A gravitational search algorithm,” Information Sciences, vol. 179, no. 13, pp. 2232–2248 (2009).
[30] L. Rodríguez, O. Castillo, J. Soria, P. Melin, F. Valdez, C. I. Gonzalez, G. E. Martinez, and J. Soto, “A fuzzy hierarchical operator in the grey wolf optimizer algorithm,” Applied Soft Computing, vol. 57, pp. 315–328 (2017).
[31] N. R. Samal, A. Konar, S. Das, and A. Abraham, “A closed loop stability analysis and parameter selection of the particle swarm optimization dynamics for faster convergence,” in 2007 IEEE Congress on Evolutionary Computation, pp. 1769–1776 (2007).
[32] S. Singh and J. C. Bansal, “Grey wolf optimizer with crossover and opposition-based learning,” in International Conference on Harmony Search Algorithm, pp. 401–410 (2020).
[33] S. Singh and J. C. Bansal, “Mutation-driven grey wolf optimizer with modified search mechanism,” Expert Systems with Applications, p. 116450 (2022).
[34] M. H. Sulaiman, Z. Mustaffa, M. R. Mohamed, and O. Aliman, “Using the grey wolf optimizer for solving optimal reactive power dispatch problem,” Applied Soft Computing, vol. 32, pp. 286–292 (2015).
[35] M. Vidyasagar, Nonlinear Systems Analysis, SIAM (2002).
[36] R. F. Warming and B. J. Hyett, “The modified equation approach to the stability and accuracy analysis of finite-difference methods,” Journal of Computational Physics, vol. 14, no. 2, pp. 159–179 (1974).
[37] X.-S. Yang, “Firefly algorithm, stochastic test functions and design optimisation,” International Journal of Bio-inspired Computation, vol. 2, no. 2, pp. 78–84 (2010).
[38] X.-S. Yang and S. Deb, “Cuckoo search via Lévy flights,” in 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), pp. 210–214 (2009).
[39] X. Yao, Y. Liu, and G. Lin, “Evolutionary programming made faster,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 2, pp. 82–102 (1999).

Views: 278Downloads: 136Citations: 0