Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 19,343

The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.

Grey Wolf Optimizer

Open access
Mirjalili, Seyedali, Mirjalili, Seyed Mohammad, Lewis, Andrew·2014·Advances in Engineering Software
DOI 10.1016/j.advengsoft.2013.12.007
Open this paper in CoChat — free account

Abstract

This work proposes a new meta-heuristic called Grey Wolf Optimizer (GWO) inspired by grey wolves (Canis lupus). The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Four types of grey wolves such as alpha, beta, delta, and omega are employed for simulating the leadership hierarchy. In addition, the three main steps of hunting, searching for prey, encircling prey, and attacking prey, are implemented. The algorithm is then benchmarked on 29 well-known test functions, and the results are verified by a comparative study with Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Differential Evolution (DE), Evolutionary Programming (EP), and Evolution Strategy (ES). The results show that the GWO algorithm is able to provide very competitive results compared to these well-known meta-heuristics. The paper also considers solving three classical engineering design problems (tension/compression spring, welded beam, and pressure vessel designs) and presents a real application of the proposed method in the field of optical engineering. The results of the classical engineering design problems and real application prove that the proposed algorithm is applicable to challenging problems with unknown search spaces.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1016/j.advengsoft.2013.12.007

Cites

4 of 4 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 4 references

Research works printed but not linked: 71

  1. Bonabeau E, Dorigo M, Theraulaz G. Swarm intelligence: from natural to artificial systems: OUP USA; 1999. · DOI
  2. Dorigo, 2006, Ant colony optimization, Comput Intell Magaz, IEEE, 1, 28, 10.1109/CI-M.2006.248054 · DOI · Paper page
  3. Kennedy J, Eberhart R. Particle swarm optimization, in Neural Networks, 1995. In: Proceedings, IEEE international conference on; 1995. p. 1942–1948. · DOI · Paper page
  4. Kirkpatrick S, Jr. DG, Vecchi MP. Optimization by simulated annealing. Science, vol. 220; 1983. p. 671–80. · DOI · Paper page
  5. Beni G, Wang J. Swarm intelligence in cellular robotic systems. In: Robots and biological systems: towards a new bionics?, ed. Springer; 1993. p. 703–12. · DOI · Paper page
  6. Basturk B, Karaboga D. An artificial bee colony (ABC) algorithm for numeric function optimization. In: IEEE swarm intelligence symposium; 2006. p. 12–4.
  7. Olorunda O, Engelbrecht AP. Measuring exploration/exploitation in particle swarms using swarm diversity. In: Evolutionary computation, 2008. CEC 2008 (IEEE World Congress on Computational Intelligence). IEEE Congress on; 2008. p. 1128–34. · DOI · Paper page
  8. Alba, 2005, The exploration/exploitation tradeoff in dynamic cellular genetic algorithms, Evolut Comput, IEEE Trans, 9, 126, 10.1109/TEVC.2005.843751 · DOI · Paper page
  9. Lin, 2009, Auto-tuning strategy for evolutionary algorithms: balancing between exploration and exploitation, Soft Comput, 13, 157, 10.1007/s00500-008-0303-2 · DOI
  10. Mirjalili S, Hashim SZM. A new hybrid PSOGSA algorithm for function optimization. In: Computer and information application (ICCIA), 2010 international conference on; 2010. p. 374–77. · DOI · Paper page
  11. Mirjalili, 2012, Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm, Appl Math Comput, 218, 11125, 10.1016/j.amc.2012.04.069 · DOI · Paper page
  12. Goldberg D. Genetic Algorithms in optimization, search and machine learning, Addison Wesley, New York. In: Eiben AE, Smith JE, editors. 2003 Introduction to evolutionary computing. Springer. Jacq J, Roux C (1995) Registration of non-segmented images using a genetic algorithm. Lecture notes in computer science, vol. 905; 1989. p. 205–11. · DOI
  13. Yao, 1999, Evolutionary programming made faster, Evolut Comput, IEEE Trans, 3, 82, 10.1109/4235.771163 · DOI
  14. Rechenberg, 1994, Evolution strategy, Comput Intel Imitat Life, 1
  15. Koza JR. Genetic programming; 1992. · DOI
  16. Simon, 2008, Biogeography-based optimization, Evolut Comput IEEE Trans, 12, 702, 10.1109/TEVC.2008.919004 · DOI · Paper page
  17. Webster B, Bernhard PJ. 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. p. 255–61.
  18. Erol, 2006, A new optimization method: big bang–big crunch, Adv Eng Softw, 37, 106, 10.1016/j.advengsoft.2005.04.005 · DOI · Paper page
  19. Rashedi, 2009, GSA: a gravitational search algorithm, Inf Sci, 179, 2232, 10.1016/j.ins.2009.03.004 · DOI
  20. Kaveh, 2010, A novel heuristic optimization method: charged system search, Acta Mech, 213, 267, 10.1007/s00707-009-0270-4 · DOI · Paper page
  21. Formato, 2007, Central force optimization: a new metaheuristic with applications in applied electromagnetics, Prog Electromag Res, 77, 425, 10.2528/PIER07082403 · DOI
  22. Alatas, 2011, ACROA: artificial chemical reaction optimization algorithm for global optimization, Expert Syst Appl, 38, 13170, 10.1016/j.eswa.2011.04.126 · DOI
  23. Hatamlou, 2012, Black hole: a new heuristic optimization approach for data clustering, Inf Sci
  24. Kaveh, 2012, A new meta-heuristic method: ray optimization, Comput Struct, 112, 283, 10.1016/j.compstruc.2012.09.003 · DOI · Paper page
  25. Du H, Wu X, Zhuang J. Small-world optimization algorithm for function optimization. In: Advances in Natural Computation, ed.: Springer; 2006. p. 264–73. · DOI
  26. Shah-Hosseini, 2011, Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation, Int J Comput Sci Eng, 6, 132, 10.1504/IJCSE.2011.041221 · DOI
  27. Moghaddam FF, Moghaddam RF, Cheriet M. Curved space optimization: a random search based on general relativity theory. arXiv, preprint arXiv:1208.2214; 2012. · arXiv
  28. Yang X-S. A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010), ed.: Springer; 2010. p. 65–74. · DOI · Paper page
  29. Abbass HA. MBO: Marriage in honey bees optimization – a haplometrosis polygynous swarming approach. In: Evolutionary computation, 2001. Proceedings of the 2001 congress on; 2001. p. 207–214. · DOI
  30. Li X. A new intelligent optimization-artificial fish swarm algorithm. Doctor thesis, Zhejiang University of Zhejiang, China; 2003.
  31. Pinto PC, Runkler TA, Sousa JM. Wasp swarm algorithm for dynamic MAX-SAT problems. In: Adaptive and Natural Computing Algorithms, ed.: Springer; 2007. p. 350–57. · DOI
  32. Mucherino A, Seref O. Monkey search: a novel metaheuristic search for global optimization. In: AIP conference proceedings; 2007. p. 162. · DOI
  33. Lu X, Zhou Y. A novel global convergence algorithm: bee collecting pollen algorithm. In: Advanced intelligent computing theories and applications. With Aspects of Artificial Intelligence, ed.: Springer; 2008. p. 518–25. · DOI
  34. Yang X-S, Deb S. Cuckoo search via Lévy flights. In: Nature & Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on; 2009. p. 210–14. · DOI
  35. Shiqin Y, Jianjun J, Guangxing Y. A dolphin partner optimization. In: Intelligent systems, 2009. GCIS’09. WRI Global Congress on; 2009. p. 124–28. · DOI
  36. Yang, 2010, Firefly algorithm, stochastic test functions and design optimisation, Int J Bio-Inspired Comput, 2, 78, 10.1504/IJBIC.2010.032124 · DOI · Paper page
  37. Askarzadeh, 2012, A new heuristic optimization algorithm for modeling of proton exchange membrane fuel cell: bird mating optimizer, Int J Energy Res
  38. Gandomi, 2012, Krill Herd: a new bio-inspired optimization algorithm, Commun Nonlinear Sci Numer Simul, 10.1016/j.cnsns.2012.05.010 · DOI · Paper page
  39. Pan, 2012, A new fruit fly optimization algorithm: taking the financial distress model as an example, Knowl-Based Syst, 26, 69, 10.1016/j.knosys.2011.07.001 · DOI · Paper page
  40. Mech, 1999, Alpha status, dominance, and division of labor in wolf packs, Can J Zool, 77, 1196, 10.1139/z99-099 · DOI · Paper page
  41. Muro, 2011, Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations, Behav Process, 88, 192, 10.1016/j.beproc.2011.09.006 · DOI · Paper page
  42. Digalakis, 2001, On benchmarking functions for genetic algorithms, Int J Comput Math, 77, 481, 10.1080/00207160108805080 · DOI
  43. Yang X-S. Test problems in optimization, arXiv, preprint arXiv:1008.0549; 2010. · arXiv
  44. Mirjalili, 2013, S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization, Swarm Evolut Comput, 9, 1, 10.1016/j.swevo.2012.09.002 · DOI · Paper page
  45. Liang J, Suganthan P, Deb K. Novel composition test functions for numerical global optimization. In: Swarm intelligence symposium, 2005. SIS 2005. Proceedings 2005 IEEE; 2005. p. 68–75. · DOI · Paper page
  46. van den Bergh, 2006, A study of particle swarm optimization particle trajectories, Inf Sci, 176, 937, 10.1016/j.ins.2005.02.003 · DOI · Paper page
  47. Belegundu, 1985, A Study of mathematical programming methods for structural optimization. Part I: Theory, Int J Numer Meth Eng, 21, 1583, 10.1002/nme.1620210904 · DOI
  48. Coello Coello, 2002, Constraint-handling in genetic algorithms through the use of dominance-based tournament selection, Adv Eng Inform, 16, 193, 10.1016/S1474-0346(02)00011-3 · DOI · Paper page
  49. He, 2007, An effective co-evolutionary particle swarm optimization for constrained engineering design problems, Eng Appl Artif Intell, 20, 89, 10.1016/j.engappai.2006.03.003 · DOI · Paper page
  50. Mezura-Montes, 2008, An empirical study about the usefulness of evolution strategies to solve constrained optimization problems, Int J Gen Syst, 37, 443, 10.1080/03081070701303470 · DOI
  51. Coello Coello, 2000, Use of a self-adaptive penalty approach for engineering optimization problems, Comput Ind, 41, 113, 10.1016/S0166-3615(99)00046-9 · DOI · Paper page
  52. Mahdavi, 2007, An improved harmony search algorithm for solving optimization problems, Appl Math Comput, 188, 1567, 10.1016/j.amc.2006.11.033 · DOI · Paper page
  53. Huang, 2007, An effective co-evolutionary differential evolution for constrained optimization, Appl Math Comput, 186, 340, 10.1016/j.amc.2006.07.105 · DOI
  54. Carlos, 2000, Constraint-handling using an evolutionary multiobjective optimization technique, Civil Eng Syst, 17, 319, 10.1080/02630250008970288 · DOI
  55. Deb, 1991, Optimal design of a welded beam via genetic algorithms, AIAA J, 29, 2013, 10.2514/3.10834 · DOI
  56. Deb, 2000, An efficient constraint handling method for genetic algorithms, Comput Methods Appl Mech Eng, 186, 311, 10.1016/S0045-7825(99)00389-8 · DOI
  57. Lee, 2005, A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Comput Methods Appl Mech Eng, 194, 3902, 10.1016/j.cma.2004.09.007 · DOI · Paper page
  58. Ragsdell, 1976, Optimal design of a class of welded structures using geometric programming, ASME J Eng Indust, 98, 1021, 10.1115/1.3438995 · DOI
  59. Deb K, Gene AS. A robust optimal design technique for mechanical component design. In: Presented at the Dasgupta D, Michalewicz Z, editors. Evolutionary algorithms in engineering applications, Berlin; 1997. · DOI
  60. Kaveh, 2010, An improved ant colony optimization for constrained engineering design problems, Eng Comput Int J Comput-Aided Eng, 27, 155
  61. Kannan, 1994, An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design, J Mech Des, 116, 405, 10.1115/1.2919393 · DOI
  62. Sandgren E. Nonlinear integer and discrete programming in mechanical design; 1988. p. 95–105. · DOI
  63. Caer, 2011, Dispersion engineering of wide slot photonic crystal waveguides by Bragg-like corrugation of the slot, Photonics Technol Lett, IEEE, 23, 1298, 10.1109/LPT.2011.2158996 · DOI
  64. Baba, 2008, Slow light in photonic crystals, Nat Photonics, 2, 465, 10.1038/nphoton.2008.146 · DOI
  65. Zhai, 2011, Slow light property improvement and optical buffer capability in ring-shape-hole photonic crystal waveguide, Light Technol J, 29, 3083, 10.1109/JLT.2011.2165334 · DOI
  66. Wang, 2011, Slow light engineering in polyatomic photonic crystal waveguides based on square lattice, Optics Commun, 284, 5829, 10.1016/j.optcom.2011.07.080 · DOI
  67. Mirjalili SM, Mirjalili S. Light property and optical buffer performance enhancement using Particle Swarm Optimization in Oblique Ring-Shape-Hole Photonic Crystal Waveguide. In: Photonics global conference (PGC); 2012. p. 1–4 [2012]. · DOI
  68. Mirjalili, 2013, Optical buffer performance enhancement using Particle Swarm Optimization in Ring-Shape-Hole Photonic Crystal Waveguide, Optik – Int J Light Elect Optics, 124, 5989, 10.1016/j.ijleo.2013.04.114 · DOI
  69. Mirjalili, 2014, A novel multi-objective optimization framework for designing photonic crystal waveguides, Photonics Technol Lett IEEE, 26, 146, 10.1109/LPT.2013.2290318 · DOI
  70. Wu, 2010, Wideband and low dispersion slow light in slotted photonic crystal waveguide, Optics Commun, 283, 2815, 10.1016/j.optcom.2010.03.037 · DOI
  71. Mirjalili S, Mirjalili SM, Yang X. Binary bat algorithm. Neural Comput Appl, in press, DOI: 10.1007/s00521-013-1525-5. · DOI · Paper page

Cited by

Metadata

Authors
Mirjalili, S., Mirjalili, S. M., & Lewis, A.
Venue
Advances in Engineering Software
Publisher
Elsevier BV
Published
2014-03
Volume
69
Pages
46-61
ISSN
0965-9978 (ISSN-L)
DOI
10.1016/j.advengsoft.2013.12.007
OpenAlex
W2061438946
Cited by
19,343
References
4
FWCI
238.00
Type
journal article
Language
en
Open access
green

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.