Skip to main content

Advertisement

Springer Nature Link
Log in

Equilibrium optimizer: a comprehensive survey

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Equilibrium optimizer (EO) is a recent optimization method inspired by the physical equation of the mass balance that provides the conservation of mass entering, leaving, and generating in a control volume and the system always reaches an equilibrium point. It is a fast-growing algorithm that has been adopted by several researchers due to its successful features, such as simplicity, parameter-less, derivative-free, and sound-and-complete. In this survey paper, a comprehensive analysis of EO and its evolution, since its introduction in 2020 until now, is provided. Its performance and convergence behavior are initially studied and compared against eight well-established methods using 23 mathematical optimization functions which reveals its superiority. Since EO is established to deal with a single objective and free optimization problems of the continuous domain, a comprehensive analysis of the different EO versions which are either modified versions or hybridized versions are introduced to deal with different search spaces of optimization problems. Furthermore, this research aims to provide a deep analysis of the applications of the EO algorithm, including the population type, the optimizer version used, and the main contribution. This is realized by its successful applications in different domains such as scheduling and planning, power and electrical engineering, civil and environmental engineering, communication and networking, image processing, etc. A discussion about the different EO versions and applications is provided to highlight the pros and cons of such algorithms. This discussion leads this survey to end up providing several possible research directions that can be followed in the future. Overall, this survey provides a comprehensive analysis of Equilibrium Optimizer performance and applications and contributes to the broader field of optimization algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. https://www.mathworks.com/matlabcentral/fileexchange/73352-equilibrium-optimizer-eo

  2. https://github.com/afshinfaramarzi/Equilibrium-Optimizer

  3. https://github.com/PengGui-N/United-Equilibrium-Optimizer

  4. https://github.com/ahmed-shameem/Feature_selection

  5. https://www.mathworks.com/matlabcentral/fileexchange/79074-equilibrium-optimizer-for-feature-selection/?s_tid=LandingPageTabfx

  6. https://www.mathworks.com/matlabcentral/fileexchange/100421-equilibrium-slime-mould-algorithm-esma-source-code

  7. https://github.com/arijitdey1/Hybrid-GREO

Abbreviations

AV:

Average Results

BA:

Bat Algorithm

EO:

Equilibrium Optimizer

FPA:

Flower Pollination Algorithm

JAYA:

JAYA Algorithm

LSTM:

Long Short-Term Memory

MFO:

Moth-Flame Optimization Algorithm

MOEO:

Multi-objective Equilibrium optimizer

PSO:

Particle Swarm Optimization

ROS:

Rat Swarm Optimizer

SCA:

Since Cosine Algorithm

SD:

Standard Deviation

SSA:

Salp Swarm Algorithm

WOA:

Whale Optimization Algorithm

References

  1. Simon D (2013) Evolutionary optimization algorithms. John Wiley & Sons

    Google Scholar 

  2. Kann V (1992) On the approximability of NP-complete optimization problems, Ph.D. thesis, Citeseer

  3. Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Comput Surv (CSUR), 35:268–308

  4. Zitar RA, Al-Betar MA, Awadallah MA, Doush IA, Assaleh K (2021) An intensive and comprehensive overview of jaya algorithm, its versions and applications, Archives of Computational Methods in Engineering 1–30

  5. Awadallah MA, Al-Betar MA, Doush IA, Makhadmeh SN, Al-Naymat G (2023) Recent versions and applications of sparrow search algorithm. Arch Comput Methods Eng, 1–28. https://doi.org/10.1007/s11831-023-09887-z

  6. Hussain K, Mohd Salleh MN, Cheng S, Shi Y (2019) Metaheuristic research: a comprehensive survey. Artif Intell Rev, 52:2191–2233

  7. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Sci, 220:671–680

  8. Glover F, Laguna M (1998) Tabu search, In: Handbook of combinatorial optimization, Springer, pp 2093–2229

  9. Al-Betar MA (2017) \(\beta \)-hill climbing: an exploratory local search. Neural Comput & Applic, 28:153–168

  10. Mladenovic N, Hansen P (1997) Variable neighborhood search. Comput & Oper Res, 24:1097–1100

  11. Doğan B, Ölmez T (2015) A new metaheuristic for numerical function optimization: Vortex search algorithm. Inf Sci 293:125–145

    Google Scholar 

  12. Lourenco HR, Martin OC, Stutzle T (2003) Iterated local search, In: Handbook of metaheuristics, Springer, pp 320–353

  13. Gabis AB, Meraihi Y, Mirjalili S, Ramdane-Cherif A (2021) A comprehensive survey of sine cosine algorithm: variants and applications, Artif Intell Rev, 1–72

  14. Sorensen K (2015) Metaheuristics–the metaphor exposed. Int Trans Oper Res 22:3–18

    MathSciNet  Google Scholar 

  15. Holland JH (1992) Genetic algorithms. Sci Am 267:66–73

    ADS  Google Scholar 

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

    Google Scholar 

  17. Koza JR, Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection, vol 1, MIT press

  18. Beyer H-G, Schwefel H-P (2002) Evolution strategies-a comprehensive introduction. Nat Comput 1:3–52

    MathSciNet  Google Scholar 

  19. Baluja S (1994) Population-based incremental learning. a method for integrating genetic search based function optimization and competitive learning, Technical Report, Carnegie-Mellon Univ Pittsburgh Pa Dept Of Computer Science

  20. 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  Google Scholar 

  21. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713

    Google Scholar 

  22. Karami H, Sanjari MJ, Gharehpetian GB (2014) Hyper-spherical search (hss) algorithm: a novel meta-heuristic algorithm to optimize nonlinear functions. Neural Comput & Applic 25:1455–1465

    Google Scholar 

  23. Salimi H (2015) Stochastic fractal search: a powerful metaheuristic algorithm. Knowl-Based Syst 75:1–18

    Google Scholar 

  24. Mirjalili S (2016) Sca: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Google Scholar 

  25. Zhao J, Tang D, Liu Z, Cai Y, Dong S (2019) Spherical search optimizer: a simple yet efficient meta-heuristic approach, Neural Comput & Applic, 1–32

  26. Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    ADS  MathSciNet  Google Scholar 

  27. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simul 76:60–68

    Google Scholar 

  28. Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition, In: IEEE congress on evolutionary computation, Ieee, pp 4661–4667

  29. Rao RV, Savsani VJ, Vakharia D (2011) Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315

    Google Scholar 

  30. Fadakar E, Ebrahimi M (2016) A new metaheuristic football game inspired algorithm, In: 1st Conference on Swarm Intelligence and Evolutionary Computation (CSIEC), IEEE, pp 6–11

  31. Moosavi SHS, Bardsiri VK (2019) Poor and rich optimization algorithm: A new human-based and multi populations algorithm. Eng Appl Artif Intell 86:165–181

    Google Scholar 

  32. Askari Q, Younas I, Saeed M (2020) Political optimizer: A novel socio-inspired meta-heuristic for global optimization. Knowl-Based Syst 195:105709

    Google Scholar 

  33. Al-Betar MA, Alyasseri ZAA, Awadallah MA, Doush IA (2020) Coronavirus herd immunity optimizer (chio). Neural Comput & Applic. https://doi.org/10.1007/s00521-020-05296-6

    Article  Google Scholar 

  34. Braik M, Ryalat MH, Al-Zoubi H (2022) A novel meta-heuristic algorithm for solving numerical optimization problems: Ali baba and the forty thieves. Neural Comput & Applic 34:409–455

    Google Scholar 

  35. Kennedy J, Eberhart R (1995) Particle swarm optimization, In: Proceedings of ICNN95-International Conference on Neural Networks, vol 4, IEEE pp. 1942–1948

  36. Dorigo M, Di Caro G (1999) Ant colony optimization: a new meta-heuristic, In: Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), vol 2, IEEE, pp 1470–1477

  37. Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17:4831–4845

    ADS  MathSciNet  Google Scholar 

  38. Yang X-S, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput, 29:464–483

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

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

  41. Yazdani M, Jolai F (2016) Lion optimization algorithm (loa): a nature-inspired metaheuristic algorithm. J Comput Des Eng. 3:24–36

    Google Scholar 

  42. Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput & Struct 169:1–12

    Google Scholar 

  43. Fathollahi-Fard AM, Hajiaghaei-Keshteli M, Tavakkoli-Moghaddam R (2020) Red deer algorithm (rda): a new nature-inspired meta-heuristic. Soft Comput 24:14637–14665

    Google Scholar 

  44. Xue J, Shen B (2020) A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci & Control Eng 8:22–34

    Google Scholar 

  45. Dhiman G, Garg M, Nagar A, Kumar V, Dehghani M (2021) A novel algorithm for global optimization: rat swarm optimizer. J Ambient Intell Hum Comput 12:8457–8482

    Google Scholar 

  46. Braik M, Hammouri A, Atwan J, Al-Betar MA, Awadallah MA (2022) White shark optimizer: A novel bio-inspired meta-heuristic algorithm for global optimization problems. Knowl-Based Syst 243:108457

    Google Scholar 

  47. Chen P, Zhou S, Zhang Q, Kasabov N (2022) A meta-inspired termite queen algorithm for global optimization and engineering design problems. Eng Appl Artif Intell, 111:104805

  48. Agushaka JO, Ezugwu AE, Abualigah L (2022) Dwarf mongoose optimization algorithm. Comput Methods Appl Mech Eng, 391:114570

  49. Irizarry R (2004) Lares: An artificial chemical process approach for optimization. Evol Comput 12:435–459

    PubMed  Google Scholar 

  50. Lam AY, Li VO (2009) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput, 14:381–399

  51. Alatas B (2011) Acroa: artificial chemical reaction optimization algorithm for global optimization. Expert Systems with Applications, Expert Syst Appl, 38:13170–13180

  52. Abdechiri M, Meybodi MR, Bahrami H (2013) Gases brownian motion optimization: an algorithm for optimization (gbmo). Appl Soft Comput, 13:2932–2946

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

  54. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294

    Google Scholar 

  55. Hatamlou A (2013) Black hole: A new heuristic optimization approach for data clustering. Inf Sci 222:175–184

    MathSciNet  Google Scholar 

  56. Kaveh A, Bakhshpoori T (2016) Water evaporation optimization: a novel physically inspired optimization algorithm. Comput Struct 167:69–85

    Google Scholar 

  57. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: A novel optimization algorithm. Knowl-Based Syst 191:105190

    Google Scholar 

  58. Karami H, Anaraki MV, Farzin S, Mirjalili S (2021) Flow direction algorithm (fda): A novel optimization approach for solving optimization problems. Comput Ind Eng 156:107224

    Google Scholar 

  59. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: A novel optimization algorithm, Knowl-Based Syst, vol 191

  60. Gao Y, Zhou Y, Luo Q (2020) An efficient binary equilibrium optimizer algorithm for feature selection. IEEE Access 8:140936–140963

    Google Scholar 

  61. Wang J, Yang B, Li D, Zeng C, Chen Y, Guo Z, Zhang X, Tan T, Shu H, Yu T (2021) Photovoltaic cell parameter estimation based on improved equilibrium optimizer algorithm, Energy Convers Manag, vol 236

  62. Zhao J, Gao Z-M (2020) The improved equilibrium optimization algorithm with levy flight, In: 5th International Conference on Computer and Communication Systems (ICCCS), pp 352–355. https://doi.org/10.1109/ICCCS49078.2020.9118502

  63. Zhang X, Lin Q (2022) Information-utilization strengthened equilibrium optimizer. Artif Intell Rev 55:4241–4274. https://doi.org/10.1007/s10462-021-10105-0

    Article  Google Scholar 

  64. Sayed GI, Khoriba G, Haggag MH (2021) A novel chaotic equilibrium optimizer algorithm with s-shaped and v-shaped transfer functions for feature selection, J Ambient Intell Humanized Comput, p 1–26

  65. Wansasueb K, Panmanee S, Panagant N, Pholdee N, Bureerat S, Yildiz A (2022) Hybridised differential evolution and equilibrium optimiser with learning parameters for mechanical and aircraft wing design, Knowl-Based Syst, vol 239

  66. El-Shorbagy MA, Mousa A (2021) Constrained multiobjective equilibrium optimizer algorithm for solving combined economic emission dispatch problem, Complexity vol 2021

  67. Hu P, Chu S-C, Snášl V, Pan J-S (2022) Binary equilibrium optimizer algorithm. J Netw Intell 7:45–58

    Google Scholar 

  68. Guo Z (2002) Review of indoor emission source models. part 1. overview. Environ Pollut 120:533–549

    CAS  PubMed  Google Scholar 

  69. Parouha RP, Das KN (2016) A memory based differential evolution algorithm for unconstrained optimization. Appl Soft Comput 38:501–517

    Google Scholar 

  70. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: A bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191

    Google Scholar 

  71. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Soft 95:51–67

    Google Scholar 

  72. Awadallah MA, Al-Betar MA, Doush IA, Makhadmeh SN, Alyasseri ZAA, Abasi AK, Alomari OA (2022) Ccsa: Cellular crow search algorithm with topological neighborhood shapes for optimization. Expert Syst Appl 194:116431

    Google Scholar 

  73. Yang X-S (2012) Flower pollination algorithm for global optimization In: International conference on unconventional computing and natural computation, Springer, p 240–249

  74. Rao R (2016) Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7:19–34

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

    Google Scholar 

  76. Wunnava A, Naik M, Panda R, Jena B, Abraham A (2020) A novel interdependence based multilevel thresholding technique using adaptive equilibrium optimizer, Eng Appl Artif Intell, vol 94

  77. Kardani N, Bardhan A, Gupta S, Samui P, Nazem M, Zhang Y, Zhou A (2021) Predicting permeability of tight carbonates using a hybrid machine learning approach of modified equilibrium optimizer and extreme learning machine, Acta Geotech, p 1–17

  78. Gao Z, Zhao J, Tian X (2020) The improved equilibrium optimization algorithm with averaged candidates, vol 1575

  79. Rostami M, Berahmand K, Nasiri E, Forouzandeh S (2021) Review of swarm intelligence-based feature selection methods. Eng Appl Artif Intell 100:104210

    Google Scholar 

  80. Lim TY, Al-Betar MA, Khader AT (2016) Taming the 0/1 knapsack problem with monogamous pairs genetic algorithm. Expert Syst Appl 54:241–250

    Google Scholar 

  81. Saberi-Movahed F, Rostami M, Berahmand K, Karami S, Tiwari P, Oussalah M, Band SS (2022) Dual regularized unsupervised feature selection based on matrix factorization and minimum redundancy with application in gene selection. Knowl-Based Syst 256:109884

    Google Scholar 

  82. Minocha S, Singh B (2022) A novel phishing detection system using binary modified equilibrium optimizer for feature selection, Comput Electr Eng, vol 98

  83. Gao Z-M, Zhao J, Li S-R (2020) The binary equilibrium optimization algorithm with sigmoid transfer functions, pp 193–197

  84. Abdel-Basset M, Mohamed R, Mirjalili S (2021) A binary equilibrium optimization algorithm for 0–1 knapsack problems, Comput Ind Eng, vol 151

  85. Ouadfel S, Abd Elaziz M (2022) Efficient high-dimension feature selection based on enhanced equilibrium optimizer, Expert Syst Appl, vol 187

  86. Ahmed S, Ghosh K, Mirjalili S, Sarkar R (2021) Aieou: Automata-based improved equilibrium optimizer with u-shaped transfer function for feature selection, Knowl-Based Syst, vol 228

  87. Zhao J, Gao Z-M (2020) Simulation research on the binary equilibrium optimization algorithm, pp 140–144

  88. Joshi PM, Verma HK (2021) Binary equilibrium optimizer based weak bus constrained pmu placement, In: Emerging Trends in Industry 4.0 (ETI 4.0), pp 1–8. https://doi.org/10.1109/ETI4.051663.2021.9619191

  89. Elmanakhly D, Saleh M, Rashed E (2021) An improved equilibrium optimizer algorithm for features selection: Methods and analysis. IEEE Access 9:120309–120327

    Google Scholar 

  90. Houssein EH, Çelik E, Mahdy MA, Ghoniem RM (2022) Self-adaptive equilibrium optimizer for solving global, combinatorial, engineering, and multi-objective problems, Expert Syst Appl, 195:116552. https://www.sciencedirect.com/science/article/pii/S0957417422000513. https://doi.org/10.1016/j.eswa.2022.116552

  91. Gui P, He F, Ling BWK, Zhang D (2021) United equilibrium optimizer for solving multimodal image registration. Knowl-Based Syst 233:107552. https://doi.org/10.1016/j.knosys.2021.107552

    Article  Google Scholar 

  92. Mahmoodjanloo M, Tavakkoli-Moghaddam R, Baboli A, Bozorgi-Amiri A (2022) Distributed job-shop rescheduling problem considering reconfigurability of machines: a self-adaptive hybrid equilibrium optimiser. Int J Prod Res 60:4973–4994. https://doi.org/10.1080/00207543.2021.1946193

    Article  Google Scholar 

  93. Mostafa A, Ebeed M, Kamel S, Abdel-Moamen M (2021) Optimal power flow solution using levy spiral flight equilibrium optimizer with incorporating cupfc. IEEE Access 9:69985–69998

    Google Scholar 

  94. Liu J, Li W, Li Y (2022) Lwmeo: An efficient equilibrium optimizer for complex functions and engineering design problems. Expert Syst Appl 198:116828. https://doi.org/10.1016/j.eswa.2022.116828

    Article  Google Scholar 

  95. Zhou Z, Yang X, Zhu Z, Wang Y, Liu D (2022) Color constancy with an optimized regularized random vector functional link based on an improved equilibrium optimizer. J Opt Soc Am A Opt Image Sci Vis 39:482–493

    ADS  PubMed  Google Scholar 

  96. Elgamal ZM, Yasin NM, Sabri AQM, Sihwail R, Tubishat M, Jarrah H (2021) Improved equilibrium optimization algorithm using elite opposition-based learning and new local search strategy for feature selection in medical datasets. Comput 9. https://doi.org/10.3390/computation9060068

  97. Dinkar S, Deep K, Mirjalili S, Thapliyal S (2021) Opposition-based laplacian equilibrium optimizer with application in image segmentation using multilevel thresholding, Expert Syst Appl, vol 174

  98. Naik M, Panda R, Abraham A (2021) An opposition equilibrium optimizer for context-sensitive entropy dependency based multilevel thresholding of remote sensing images, Swarm & Evol Comput, vol 65

  99. Shankar N, Saravanakumar N, Kumar C, Kamatchi Kannan V, Indu Rani B (2021) Opposition-based equilibrium optimizer algorithm for identification of equivalent circuit parameters of various photovoltaic models. J Comput Electron 20:1560–1587

    Google Scholar 

  100. Fan Q, Huang H, Yang K, Zhang S, Yao L, Xiong Q (2021) A modified equilibrium optimizer using opposition-based learning and novel update rules. Expert Systems with Applications 170:114575. https://doi.org/10.1016/j.eswa.2021.114575

    Article  Google Scholar 

  101. Ates A, Chen Y (2021) Fractional order chaotic model based enhanced equilibrium optimization algorithm for controller design of 3 dof hover flight system, vol 7

  102. Lan P, Xia K, Pan Y, Fan S (2021) An improved equilibrium optimizer algorithm and its application in lstm neural network, Symmetry vol 13

  103. Mousa A, El-Shorbagy M, Mustafa I, Alotaibi H (2021) Chaotic search based equilibrium optimizer for dealing with nonlinear programming and petrochemical application. Processes 9:1–20

    Google Scholar 

  104. Gupta S, Deep K, Mirjalili S (2020) An efficient equilibrium optimizer with mutation strategy for numerical optimization. Appl Soft Comput 96:106542. https://doi.org/10.1016/j.asoc.2020.106542

    Article  Google Scholar 

  105. Abdel-Basset M, Mohamed R, Mirjalili S, Chakrabortty R, Ryan M (2020) Solar photovoltaic parameter estimation using an improved equilibrium optimizer. Sol Energy 209:694–708

    ADS  Google Scholar 

  106. Bardhan A, GuhaRay A, Gupta S, Pradhan B, Gokceoglu C (2022) A novel integrated approach of elm and modified equilibrium optimizer for predicting soil compression index of subgrade layer of dedicated freight corridor, Transp Geotech, vol 32

  107. Malik MM, Haouassi H (2022) Efficient sequential covering strategy for classification rules mining using a discrete equilibrium optimization algorithm. J King Saud Univ - Comput Inf Sci 34:7559–7569. https://doi.org/10.1016/j.jksuci.2021.08.032

    Article  Google Scholar 

  108. Guha D, Roy PK, Banerjee S (2021) Equilibrium optimizer-tuned cascade fractional-order 3dof-pid controller in load frequency control of power system having renewable energy resource integrated. Int Trans Electr Energy Syst 31:e12702

    Google Scholar 

  109. Fu Z, Hu P, Li W, Pan J-S, Chu S (2021) Parallel equilibrium optimizer algorithm and its application in capacitated vehicle routing problem. Intell Autom Soft Comput 27:233–247

    Google Scholar 

  110. Too J, Mirjalili S (2021) General learning equilibrium optimizer: a new feature selection method for biological data classification. Appl Artif Intell 35:247–263

    Google Scholar 

  111. Xu XW, Pan TS, Song PC, Hu CC, Chu SC (2021) Multi-cluster based equilibrium optimizer algorithm with compact approach for power system network. J. Network Intell 6:117–142

    Google Scholar 

  112. Shao Z-Y, Pan J-S, Hu P, Chu S-C (2021) Equilibrium optimizer of interswarm interactive learning strategy, Enterp Inf Syst, p 1–25

  113. Pan JS, Zhuang J, Liao L, Chu SC (2021) Advanced equilibrium optimizer for electric vehicle routing problem with time windows. J Netw Intell 6:216–237

    Google Scholar 

  114. Sun Y, Pan J-S, Hu P, Chu S-C (2023) Enhanced equilibrium optimizer algorithm applied in job shop scheduling problem. J Intell Manuf 34:1639–1665

    Google Scholar 

  115. Abdel-Basset M, Chang V, Mohamed R (2021) A novel equilibrium optimization algorithm for multi-thresholding image segmentation problems. Neural Comput & Applic 33:10685–10718

    Google Scholar 

  116. Gao Z-M, Zhao J, Li S-R, Hu Y-R (2020) The improved equilibrium optimization algorithm, pp 26–30

  117. Nguyen T, Nguyen T, Duong M (2022) An improved equilibrium optimizer for optimal placement of photovoltaic systems in radial distribution power networks. Neural Comput & Applic 34:6119–6148

    Google Scholar 

  118. Dey A, Chattopadhyay S, Singh P, Ahmadian A, Ferrara M, Sarkar R (2020) A hybrid meta-heuristic feature selection method using golden ratio and equilibrium optimization algorithms for speech emotion recognition. IEEE Access 8:200953–200970

    Google Scholar 

  119. Özkaya H, Yildiz M, Yildiz A, Bureerat S, Yildiz B, Sait S (2020) The equilibrium optimization algorithm and the response surface-based metamodel for optimal structural design of vehicle components. Materialpruefung/Materials Testing 62:492–496

    ADS  Google Scholar 

  120. Ismael O, Qasim M, Noaman M (2021) Equilibrium optimizer-based robust sliding mode control of magnetic levitation system. J Euro des Syst Autom 54:131–138

    Google Scholar 

  121. Seleem S, Hasanien H, El-Fergany A (2021) Equilibrium optimizer for parameter extraction of a fuel cell dynamic model. Renew Energy 169:117–128

    CAS  Google Scholar 

  122. Elsayed S, Otaibi S, Ahmed Y, Hendawi E, Elkalashy N, Hoballah A (2021) Probabilistic modeling and equilibrium optimizer solving for energy management of renewable micro-grids incorporating storage devices, Energies, vol. 14

  123. Chen H, Li W, Cui W (2020) Disruption-based multiobjective equilibrium optimization algorithm, Comput Intell Neurosci, vol. 2020

  124. Nusair K, Alhmoud L (2020) Application of equilibrium optimizer algorithm for optimal power flow with high penetration of renewable energy, Energies vol. 13

  125. Jia H, Peng X (2021) High equilibrium optimizer for global optimization. J Intell & Fuzzy Syst 40:5583–5594

    Google Scholar 

  126. Qi H, Zhang G, Jia H, Xing Z (2021) A hybrid equilibrium optimizer algorithm for multi-level image segmentation. Math Biosci Eng 18:4648–4678

    MathSciNet  PubMed  Google Scholar 

  127. Chattopadhyay S, Dey A, Singh P, Ahmadian A, Sarkar R (2022) A feature selection model for speech emotion recognition using clustering-based population generation with hybrid of equilibrium optimizer and atom search optimization algorithm, Multimed Tools Appl,

  128. Tang A-D, Han T, Zhou H, Xie L (2021) An improved equilibrium optimizer with application in unmanned aerial vehicle path planning. Sensors 21:1–21

    CAS  Google Scholar 

  129. Sayed EA, Sameh MA, Badr AO, Attia MA (2021) Hybrid optimization of pv system for enhanced performance using teaching learning based optimization (tlbo) and equilibrium optimizer (eo), In: 16th International Conference on Computer Engineering and Systems (ICCES), pp 1–6. https://doi.org/10.1109/ICCES54031.2021.9686130

  130. Nguyen Q, Bui M-P (2021) Performance of equilibrium optimizer for the traveling salesman problem. Int J Intell Eng & Syst 14:46–55

  131. Ansingkar N, Patil R, Deshmukh P (2022) An efficient multi class alzheimer detection using hybrid equilibrium optimizer with capsule auto encoder. Multimed Tools Appl 81:6539–6570

    Google Scholar 

  132. Zhao X, Cui Y, Guo Z, Hao Z (2020) An energy–efficient coverage enhancement strategy for wireless sensor networks based on a dynamic partition algorithm for cellular grids and an improved vampire bat optimizer, Sensors (Switzerland), vol. 20

  133. Ćalasan M, Micev M, Radulović M, Zobaa A, Hasanien H, Abdel Aleem S (2021) Optimal pid controllers for avr system considering excitation voltage limitations using hybrid equilibrium optimizer, Mach, vol. 9

  134. Agnihotri S, Atre A, Verma HK (2020) Equilibrium optimizer for solving economic dispatch problem, In: 2020 IEEE 9th Power India International Conference (PIICON), pp 1–5. https://doi.org/10.1109/PIICON49524.2020.9113048

  135. Pandya SB, Jariwala HR (2021) Equilibrium optimizer: Insights, balance, diversity for renewable energy resources based optimal power flow with multiple scenarios. Smart Science 9:257–274

    Google Scholar 

  136. Abdul-hamied DT, Shaheen AM, Salem WA, Gabr WI, El-sehiemy RA (2020) Equilibrium optimizer based multi dimensions operation of hybrid ac/dc grids. Alex Eng J 59:4787–4803

    Google Scholar 

  137. Micev M, Ćalasan M, Oliva D (2021) Design and robustness analysis of an automatic voltage regulator system controller by using equilibrium optimizer algorithm. Comput & Electr Eng 89:106930

    Google Scholar 

  138. Kharrich M, Kamel S, Abdeen M, Mohammed OH, Akherraz M, Khurshaid T, Rhee S-B (2021) Developed approach based on equilibrium optimizer for optimal design of hybrid pv/wind/diesel/battery microgrid in dakhla, morocco. IEEE Access 9:13655–13670

    Google Scholar 

  139. Heidari E, Movaghar A, Motameni H, Barzegar B (2022) A novel approach for clustering and routing in wsn using genetic algorithm and equilibrium optimizer. Int J Commun Syst 35. https://doi.org/10.1002/dac.5148

  140. Dinh P-H (2021) Multi-modal medical image fusion based on equilibrium optimizer algorithm and local energy functions. Appl Intell 51:8416–8431

    Google Scholar 

  141. Gabr AR, Roy B, Kaloop MR, Kumar D, Arisha A, Shiha M, Shwally S, Hu JW, El-Badawy SM (2021) A novel approach for resilient modulus prediction using extreme learning machine-equilibrium optimiser techniques, Int J Pavement Eng, p 1–11

  142. Bardhan A, Manna P, Kumar V, Burman A, Žlender B, Samui P (2021) Reliability analysis of piled raft foundation using a novel hybrid approach of ann and equilibrium optimizer. CMES - Computer Modeling in Engineering and Sciences 128:1033–1067

    Google Scholar 

  143. Menesy AS, Sultan HM, Kamel S (2020) Extracting model parameters of proton exchange membrane fuel cell using equilibrium optimizer algorithm, In: International Youth Conference on Radio Electronics, Electrical and Power Engineering (REEPE), pp 1–7. https://doi.org/10.1109/REEPE49198.2020.9059219

  144. Nguyen TNA, Pham DC, Thanh NHC, Nguyen AN (2021) Implementation of equilibrium optimizer algorithm for mppt in a wind turbine with pmsg. WSEAS Transactions on Systems and Control 16:216–223

    Google Scholar 

  145. Tiachacht S, Khatir S, Slimani M, Behtani A, Le Thanh C, Abdel Wahab M (2021) Model updating of frame structure using equilibrium optimizer (eo) and cuckoo search (cs) algorithms, Lecture Notes in Civil Engineering, 148 LNCE:19–28

  146. Aval S, Mohebian P (2022) Joint damage identification in frame structures by integrating a new damage index with equilibrium optimizer algorithm. International Journal of Structural Stability and Dynamics 22. https://doi.org/10.1142/S0219455422500560

  147. Mansoor M, Mirza A, Duan S, Zhu J, Yin B, Ling Q (2021) Maximum energy harvesting of centralized thermoelectric power generation systems with non-uniform temperature distribution based on novel equilibrium optimizer, Energy Conversion and Management vol. 246

  148. Chen M-R, Huang Y-Y, Zeng G-Q, Lu K-D, Yang L-Q (2021) An improved bat algorithm hybridized with extremal optimization and boltzmann selection, Expert Syst Appl, vol. 175

  149. Wu X, Hirota K, Tang B, Dai Y, Jia Z (2021) Ameliorated frenet trajectory optimization method based on artificial emotion and equilibrium optimizer. J Adv Comput Intell & Intell Inf 25:110–120

  150. Houssein E, Dirar M, Abualigah L, Mohamed W (2022) An efficient equilibrium optimizer with support vector regression for stock market prediction. Neural Comput Appl 34:3165–3200

    Google Scholar 

  151. Yin S, Luo Q, Zhou Y (2022) Eosma: An equilibrium optimizer slime mould algorithm for engineering design problems. Arab J Sci Eng 47:10115–10146

    Google Scholar 

  152. Elsheikh A, Shehabeldeen T, Zhou J, Showaib E, Abd Elaziz M (2021) Prediction of laser cutting parameters for polymethylmethacrylate sheets using random vector functional link network integrated with equilibrium optimizer. J Intell Manuf 32:1377–1388

    Google Scholar 

  153. Bastawy M, Ebeed M, Rashad A, Alghamdi AS, Kamel S (2020) Micro-grid dynamic economic dispatch with renewable energy resources using equilibrium optimizer, In: 2020 IEEE Electric Power and Energy Conference (EPEC), IEEE, pp 1–5

  154. Zayed M, Zhao J, Li W, Elsheikh A, Elaziz M (2021) A hybrid adaptive neuro-fuzzy inference system integrated with equilibrium optimizer algorithm for predicting the energetic performance of solar dish collector, Energy, vol 235

  155. Ahanch M, McCann R (2021) Integrated volt/var control and conservation voltage reduction in unbalanced distribution networks considering smart pv inverter control using equilibrium optimizer algorithm

  156. Al-Akayshee A, Kuznetsov O, Sultan H (2021) Application of equilibrium optimization algorithm for optimal design of pv/hydroelectric pumped storage energy system, case study-iraq, pp 1354–1359

  157. Hamdy A, Hasanien H, Abdelaziz A (2021) Development of optimal pi controllers of an inverter-based decentralized energy generation system based on equilibrium optimization algorithm. Int J Renew Energy Res 11:1095–1106

    Google Scholar 

  158. Xia Y (2022) Comments to “maximum energy harvesting of centralized thermoelectric power generation systems with non-uniform temperature distribution based on novel equilibrium optimizer”, Energy Convers Manag, vol. 251

  159. Sun F, Yu J, Zhao A, Zhou M (2021) Optimizing multi-chiller dispatch in hvac system using equilibrium optimization algorithm. Energy Reports 7:5997–6013

    Google Scholar 

  160. Shaheen A, Elsayed A, El-Sehiemy R, Abdelaziz A (2021) Equilibrium optimization algorithm for network reconfiguration and distributed generation allocation in power systems, Appl Soft Comput, vol 98

  161. Rabehi A, Nail B, Helal H, Douara A, Ziane A, Amrani M, Akkal B, Benamara Z (2020) Optimal estimation of schottky diode parameters using a novel optimization algorithm: Equilibrium optimizer, Superlattice Microst, vol 146

  162. Cikan M, Kekezoglu B (2022) Comparison of metaheuristic optimization techniques including equilibrium optimizer algorithm in power distribution network reconfiguration. Alex Eng J 61:991–1031

    Google Scholar 

  163. Ndi F, Perabi S, Ndjakomo S, Ondoua Abessolo G, Mengounou Mengata G (2021) Estimation of single-diode and two diode solar cell parameters by equilibrium optimizer method. Energy Reports 7:4761–4768

    Google Scholar 

  164. Behera S, Parida S, Panda S, Behera S (2021) Voltage control optimization by equilibrium optimizer for unity power factor operation of grid-connected three-phase photovoltaic inverter, pp 209–214

  165. Ali Shaik M, Mareddy P, Visali N (2022) Enhancement of voltage profile in the distribution system by reconfiguring with dg placement using equilibrium optimizer: Enhancement of voltage profile in the distribution system. Alex Eng J 61:4081–4093

    Google Scholar 

  166. Paliwal N, Srivastava L, Pandit M (2021) Equilibrium optimizer tuned novel fopid-dn controller for automatic voltage regulator system, Int Trans Electr Energy Syst, vol 31

  167. Khadanga R, Kumar A, Panda S (2021) Application of interval type-2 fuzzy pid controller for frequency regulation of ac islanded microgrid using modified equilibrium optimization algorithm. Arab J Sci Eng 46:9831–9847

    Google Scholar 

  168. Soliman MA, Al-Durra A, Hasanien HM (2021) Electrical parameters identification of three-diode photovoltaic model based on equilibrium optimizer algorithm. IEEE Access 9:41891–41901

    Google Scholar 

  169. Tabak A (2021) A novel fractional order pid plus derivative controller for avr system using equilibrium optimizer. COMPEL - The Int J Comput & Math Electr Electro Eng 40:722743

    Google Scholar 

  170. Abderazek H, Riza Yildiz A, Sait S (2021) Optimization of constrained mechanical design problems using the equilibrium optimization algorithm. Materialpruefung/Materials Testing 63:552–559

    ADS  Google Scholar 

  171. Rezk H, Aly M, Fathy A (2021) A novel strategy based on recent equilibrium optimizer to enhance the performance of pem fuel cell system through optimized fuzzy logic mppt, Energy vol 234

  172. Wang W, Kang J, Li K, Fan Y, Lin P (2022) A novel intelligent inversion method of hydrogeological parameters based on the disturbance-inspired equilibrium optimizer, Sustainability (Switzerland), vol 14

  173. Roy B, Singh M, Kaloop M, Kumar D, Hu J-W, Kumar R, Hwang W-S (2021) Data-driven approach for rainfall-runoff modelling using equilibrium optimizer coupled extreme learning machine and deep neural network, Applied Sciences (Switzerland), vol 11

  174. Durmus A, Kurban R (2021) Optimum design of linear and circular antenna arrays using equilibrium optimization algorithm. Int J Microw Wirel Technol 13:986–997

    Google Scholar 

  175. Hemalatha R, Umamaheswari R, Jothi S (2021) Lf distribution and equilibrium optimizer based fuzzy logic for multipath routing in manet. Wirel Pers Commun 120:1837–1861

    Google Scholar 

  176. Dinh P-H (2021) Combining gabor energy with equilibrium optimizer algorithm for multi-modality medical image fusion, Biomed Signal Proc Control, vol 68

  177. Premkumar M, Jangir P, Sowmya R, Alhelou H, Mirjalili S, Kumar B (2022) Multi-objective equilibrium optimizer: Framework and development for solving multi-objective optimization problems. J Comput Des Eng 9:24–50

    Google Scholar 

  178. Hou C, Shi J, Zhang B (2021) Evolving dendritic neuron model by equilibrium optimizer algorithm, pp 14–18

  179. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82

    Google Scholar 

  180. Al-Betar M, Awadallah M (2018) Island bat algorithm for optimization. Expert Syst Appl 107:126–145

    Google Scholar 

  181. Awadallah MA, Al-Betar MA, Bolaji AL, Doush IA, Hammouri AI, Mafarja M (2020) Island artificial bee colony for global optimization. Soft Computing 24:13461–13487

    Google Scholar 

  182. Al-Betar MA, Awadallah MA, Abu Doush I, Hammouri AI, Mafarja M, Alyasseri ZAA (2019) Island flower pollination algorithm for global optimization. The J Supercomput 75:5280–5323

    Google Scholar 

  183. El Moiz Dahi Z, Mezioud C, Draa A (2017) A 0–1 bat algorithm for cellular network optimisation: A systematic study on mapping techniques. Int J Reason-based Intell Syst 9:22–42

    Google Scholar 

  184. Lim TY (2014) Structured population genetic algorithms: A literature survey. Artif Intell Rev 41:385–399

    Google Scholar 

  185. Eiben ÁE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3:124–141

    Google Scholar 

  186. Nasiri E, Berahmand K, Li Y (2023) Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks. Multimed Tools Appl 82:3745–3768

    Google Scholar 

  187. Abu Doush I, El-Abd M, Hammouri AI, Bataineh MQ (2021) The effect of different stopping criteria on multi-objective optimization algorithms, Neural Comput & Applic, 1–31

  188. Al Bataineh A, Kaur D (2021) Immunocomputing-based approach for optimizing the topologies of lstm networks. IEEE Access 9:78993–79004

    Google Scholar 

  189. Abu Doush I, Awadallah MA, Al-Betar MA, Alomari OA, Makhadmeh SN, Abasi AK, Alyasseri ZAA (2023) Archive-based coronavirus herd immunity algorithm for optimizing weights in neural networks, Neural Comput & Applic 1–19

  190. Ali A, Zhu Y, Zakarya M (2022) Exploiting dynamic spatio-temporal graph convolutional neural networks for citywide traffic flows prediction. Neural Netw 145:233–247

    PubMed  Google Scholar 

  191. Ali A, Zhu Y, Zakarya M (2021) Exploiting dynamic spatio-temporal correlations for citywide traffic flow prediction using attention based neural networks. Inf Sci 577:852–870

    MathSciNet  Google Scholar 

  192. Ali A, Zhu Y, Zakarya M (2021) A data aggregation based approach to exploit dynamic spatio-temporal correlations for citywide crowd flows prediction in fog computing, Multimed Tools & Appl, p 1–33

  193. Ali A, Zhu Y, Chen Q, Yu J, Cai H (2019) Leveraging spatio-temporal patterns for predicting citywide traffic crowd flows using deep hybrid neural networks, In: IEEE 25th international conference on parallel and distributed systems (ICPADS), IEEE, pp 125–132

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, College of Engineering and Information Technology, Ajman University, P.O.Box 346, Ajman, United Arab Emirates

    Mohammed Azmi Al-Betar & Ghazi Al-Naymat

  2. Artificial Intelligence Research Center (AIRC), Ajman University, P.O.Box 346, Ajman, United Arab Emirates

    Mohammed Azmi Al-Betar, Sharif Naser Makhadmeh, Ghazi Al-Naymat & Mohammed A. Awadallah

  3. Department of Information Technology, Al-Huson University College, Al-Balqa Applied University, P.O.Box 50, Irbid, Jordan

    Mohammed Azmi Al-Betar

  4. Computer Science Department, Yarmouk University, Irbid, Jordan

    Iyad Abu Doush

  5. Computing Department College of Engineering and Applied Sciences, American University of Kuwait, Salmiya, Kuwait

    Iyad Abu Doush

  6. Department of Data Science and Artificial Intelligence, University of Petra, P.O.Box 11196, Amman, Jordan

    Sharif Naser Makhadmeh

  7. Department of Computer Science and Information Technology, College of Engineering, Abu Dhabi University, Abu Dhabi, United Arab Emirates

    Osama Ahmad Alomari

  8. Department of Computer Science, Al-Aqsa University, P.O. Box 4051, Gaza, Palestine

    Mohammed A. Awadallah

Authors
  1. Mohammed Azmi Al-Betar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iyad Abu Doush
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sharif Naser Makhadmeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ghazi Al-Naymat
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Osama Ahmad Alomari
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mohammed A. Awadallah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammed Azmi Al-Betar.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Al-Betar, M.A., Abu Doush, I., Makhadmeh, S.N. et al. Equilibrium optimizer: a comprehensive survey. Multimed Tools Appl 83, 29617–29666 (2024). https://doi.org/10.1007/s11042-023-16764-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-16764-1

Keywords