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A Critical Review of Moth-Flame Optimization Algorithm and Its Variants: Structural Reviewing, Performance Evaluation, and Statistical Analysis

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Abstract

A growing trend of introducing new metaheuristic algorithms and their improvements is observed with almost the same inherited weaknesses. The main reason is that a few studies have been performed to analyze the algorithms and their variants before improving them. This paper aims to review and analyze the moth-flame optimization (MFO) algorithm and its variants to show the structural reviewing, performance evaluation, and statistical analysis required before improving a metaheuristic algorithm. First, the MFO is described, and then its eligible variants are selected and reviewed in three categories: improved, hybrid, and adapted. Then, the outstanding developments of the eligible MFO variants are reviewed from a structural point of view. Next, to show the weaknesses and strengths of the MFO, its behavior, convergence, and balance ability are qualitatively analyzed. This paper quantitatively measures the performance of the MFO and its state-of-the-art variants. It also uses well-regarded criteria to conduct statistical tests among the algorithms. The results show that IMFO achieves the highest solution quality in dimensions 10 and 30, while m-DMFO achieves the highest in dimension 100. Overall, m-DMFO outperforms MFO and its state-of-the-art variants, with an overall effectiveness of 39.08%. Moreover, the results show that CMFO is the quickest MFO variant among the other algorithms regarding execution time. The findings of this study demonstrate that despite their claims, most MFO variants have not tackled the weaknesses and still inherently suffer from the same shortcomings. Thus, it is recommended to consider structural reviewing, performance evaluation, and statistical analysis performed in this study before improving other metaheuristic algorithms.

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References

  1. Deb K, Myburgh C (2017) A population-based fast algorithm for a billion-dimensional resource allocation problem with integer variables. Eur J Oper Res 261:460–474

    Article  MathSciNet  Google Scholar 

  2. Talbi E-G (2009) Metaheuristics: from design to implementation. Wiley

    Book  Google Scholar 

  3. Sayarshad HR (2010) Using bees algorithm for material handling equipment planning in manufacturing systems. Int J Adv Manuf Technol 48:1009–1018

    Article  Google Scholar 

  4. Zamani H, Nadimi-Shahraki MH, Gandomi AH (2022) Starling murmuration optimizer: a novel bio-inspired algorithm for global and engineering optimization. Comput Method Appl Methods 392:114616

    Article  MathSciNet  Google Scholar 

  5. Zamani H, Nadimi-Shahraki MH, Gandomi AH (2021) QANA: quantum-based avian navigation optimizer algorithm. Eng Appl Artif Intell 104:104314

    Article  Google Scholar 

  6. Qiao W, Yang Z (2019) Modified dolphin swarm algorithm based on chaotic maps for solving high-dimensional function optimization problems. IEEE Access 7:110472–110486

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Shayanfar H, Gharehchopogh FS (2018) Farmland fertility: a new metaheuristic algorithm for solving continuous optimization problems. Appl Soft Comput 71:728–746

    Article  Google Scholar 

  9. Zamani H, Nadimi-Shahraki MH, Gandomi AH (2019) CCSA: conscious neighborhood-based crow search algorithm for solving global optimization problems. Appl Soft Comput 85:105583

    Article  Google Scholar 

  10. Soleimanpour-Moghadam M, Nezamabadi-Pour H, Farsangi MM (2014) A quantum inspired gravitational search algorithm for numerical function optimization. Inform Sci 267:83–100

    Article  MathSciNet  Google Scholar 

  11. Javidy B, Hatamlou A, Mirjalili S (2015) Ions motion algorithm for solving optimization problems. Appl Soft Comput 32:72–79

    Article  Google Scholar 

  12. Xu J, Xu L (2021) Optimal stochastic process optimizer: a new metaheuristic algorithm with adaptive exploration-exploitation property. IEEE Access 9:108640–108664

    Article  Google Scholar 

  13. Nadimi-Shahraki MH (2023) An effective hybridization of quantum-based avian navigation and bonobo optimizers to solve numerical and mechanical engineering problems. J Bionic Eng 20:1361–1385

    Article  Google Scholar 

  14. Asghari K, Masdari M, Gharehchopogh FS, Saneifard R (2021) A chaotic and hybrid gray wolf-whale algorithm for solving continuous optimization problems. Lect Notes Artif Intell 10:1–26

    Google Scholar 

  15. Ziadeh A, Abualigah L, Abd Elaziz M, Şahin CB et al (2021) Augmented grasshopper optimization algorithm by differential evolution: a power scheduling application in smart homes. Multimed Tools Appl 80:31569–31597

    Article  Google Scholar 

  16. Gharehchopogh FS, Nadimi-Shahraki MH, Barshandeh S, Abdollahzadeh B et al (2023) Cqffa: A chaotic quasi-oppositional farmland fertility algorithm for solving engineering optimization problems. J Bionic Eng 20:158–183

    Article  Google Scholar 

  17. Fard ES, Monfaredi K, Nadimi MH (2014) An area-optimized chip of ant colony algorithm design in hardware platform using the address-based method. Int J Electr Comput Eng 2088–8708:4

    Google Scholar 

  18. Gharehchopogh FS, Abdollahzadeh B (2021) An efficient harris hawk optimization algorithm for solving the travelling salesman problem. Clust Comput 25:1–25

    Google Scholar 

  19. Gharehchopogh FS, Maleki I, Dizaji ZA (2021) Chaotic vortex search algorithm: metaheuristic algorithm for feature selection. Evol Intell 1–32

  20. Dezfouli MB, Shahraki MHN, Zamani H (2018) A novel tour planning model using big data. In: 2018 International Conference on Artificial Intelligence and Data Processing (IDAP). IEEE, pp 1–6

  21. Yousri D, Abd Elaziz M, Abualigah L, Oliva D et al (2021) COVID-19 X-ray images classification based on enhanced fractional-order cuckoo search optimizer using heavy-tailed distributions. Appl Soft Comput 101:107052

    Article  Google Scholar 

  22. Nadimi-Shahraki MH, Asghari Varzaneh Z, Zamani H, Mirjalili S (2022) Binary starling murmuration optimizer algorithm to select effective features from medical data. Appl Sci 13:564

    Article  Google Scholar 

  23. Nadimi-Shahraki MH, Fatahi A, Zamani H, Mirjalili S (2022) Binary approaches of quantum-based avian navigation optimizer to select effective features from high-dimensional medical data. Mathematics 10:2770

    Article  Google Scholar 

  24. Taghian S, Nadimi-Shahraki MH, Zamani H (2018) Comparative analysis of transfer function-based binary Metaheuristic algorithms for feature selection. In: 2018 International Conference on Artificial Intelligence and Data Processing (IDAP). IEEE, pp 1–6

  25. Nadimi-Shahraki MH, Taghian S, Mirjalili S, Zamani H et al (2022) GGWO: Gaze cues learning-based grey wolf optimizer and its applications for solving engineering problems. J Comput Sci 61:101636

    Article  Google Scholar 

  26. Fatahi A, Nadimi-Shahraki MH, Zamani H (2023) An improved binary quantum-based avian navigation optimizer algorithm to select effective feature subset from medical data: a COVID-19 case study. J Bionic Eng. https://doi.org/10.1007/s42235-023-00433-y

    Article  Google Scholar 

  27. Nadimi-Shahraki MH, Zamani H, Asghari Varzaneh Z, Mirjalili S (2023) A systematic review of the whale optimization algorithm: theoretical foundation, improvements, and hybridizations. Arch Comput Methods Eng. https://doi.org/10.1007/s11831-023-09928-7

    Article  Google Scholar 

  28. Hussien AG, Amin M, Abd El Aziz M (2020) A comprehensive review of moth-flame optimisation: variants, hybrids, and applications. J Exp Theor Artif Intell 32:705–725

    Article  Google Scholar 

  29. Shehab M, Abualigah L, Al Hamad H, Alabool H et al (2020) Moth–flame optimization algorithm: variants and applications. Neural Comput Appl 32:9859–9884

    Article  Google Scholar 

  30. Li Z, Zhou Y, Zhang S, Song J (2016) Lévy-flight moth-flame algorithm for function optimization and engineering design problems. Math Probl Eng 2016:1–22

    Google Scholar 

  31. Khalilpourazari S, Khalilpourazary S (2019) An efficient hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems. Soft Comput 23:1699–1722

    Article  Google Scholar 

  32. Hongwei L, Jianyong L, Liang C, Jingbo B et al (2019) Chaos-enhanced moth-flame optimization algorithm for global optimization. J Syst Eng Electron 30:1144–1159

    Article  Google Scholar 

  33. Xu Y, Chen H, Heidari AA, Luo J et al (2019) An efficient chaotic mutative moth-flame-inspired optimizer for global optimization tasks. Expert Syst Appl 129:135–155

    Article  Google Scholar 

  34. Pelusi D, Mascella R, Tallini L, Nayak J et al (2020) An improved Moth-flame optimization algorithm with hybrid search phase. Knowl-Based Syst 191:105277

    Article  Google Scholar 

  35. Xu Y, Chen H, Luo J, Zhang Q et al (2019) Enhanced Moth-flame optimizer with mutation strategy for global optimization. Inform Sciences 492:181–203

    Article  MathSciNet  Google Scholar 

  36. Zhifu L, Junhai Z, Yangquan C, Ge M et al (2021) Death mechanism-based moth–flame optimization with improved flame generation mechanism for global optimization tasks. Expert Syst Appl 183:115436

    Article  Google Scholar 

  37. Chen C, Wang X, Yu H, Wang M et al (2021) Dealing with multi-modality using synthesis of Moth-flame optimizer with sine cosine mechanisms. Math Comput Simulat 188:291–318

    Article  MathSciNet  Google Scholar 

  38. Nadimi-Shahraki MH, Taghian S, Mirjalili S, Ewees AA et al (2021) Mtv-mfo: multi-trial vector-based moth-flame optimization algorithm. Symmetry 13:2388

    Article  Google Scholar 

  39. Sahoo SK, Saha AK, Sharma S, Mirjalili S et al (2022) An enhanced moth flame optimization with mutualism scheme for function optimization. Soft Comput 26:1–28

    Article  Google Scholar 

  40. Nadimi-Shahraki MH, Fatahi A, Zamani H, Mirjalili S et al (2022) Hybridizing of whale and moth-flame optimization algorithms to solve diverse scales of optimal power flow problem. Electronics 11:831

    Article  Google Scholar 

  41. Nadimi-Shahraki MH, Zamani H, Fatahi A, Mirjalili S (2023) MFO-SFR: an enhanced moth-flame optimization algorithm using an effective stagnation finding and replacing strategy. Mathematics 11:862

    Article  Google Scholar 

  42. Sahoo SK, Saha AK, Nama S, Masdari M (2023) An improved moth flame optimization algorithm based on modified dynamic opposite learning strategy. Artif Intell Rev 56:2811–2869

    Article  Google Scholar 

  43. NH Awad MZA, Suganthan PN, Liang JJ, Qu BY (2016) Problem Definitions and Evaluation Criteria for the CEC 2017 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization. Technical Report, Nanyang Technological University, Singapore

  44. Harzing AW (2007) Publish or Perish. http://www.harzing.com/pop.htm.

  45. Ouzzani M, Hammady H, Fedorowicz Z, Elmagarmid A (2016) Rayyan—a web and mobile app for systematic reviews. Syst Rev 5:1–10

    Article  Google Scholar 

  46. Nadimi-Shahraki MH, Zamani H, Mirjalili S, Soleimanian Gharehchopogh, et al. (2023) MFO papers. https://www.researchgate.net/publication/369196829_MFOpapers

  47. van Geffen K (2015) Moths in illuminated nights: artificial night light effects on moth ecology. Moths in illuminated nights: artificial night light effects on moth ecology

  48. Khodadadi N, Mirjalili SM, Mirjalili S (2022) Multi-objective moth-flame optimization algorithm for engineering problems. Handbook of moth-flame optimization algorithm. CRC Press, Boca Raton, pp 79–96

    Book  Google Scholar 

  49. Sapre S, Mini S (2019) Opposition-based moth flame optimization with Cauchy mutation and evolutionary boundary constraint handling for global optimization. Soft Comput 23:6023–6041

    Article  Google Scholar 

  50. Oliva D, Esquivel-Torres S, Hinojosa S, Pérez-Cisneros M et al (2021) Opposition-based moth swarm algorithm. Expert Syst Appl 184:115481

    Article  Google Scholar 

  51. Shah YA, Habib HA, Aadil F, Khan MF et al (2018) CAMONET: Moth-flame optimization (MFO) based clustering algorithm for VANETs. IEEE Access 6:48611–48624

    Article  Google Scholar 

  52. Shaikh MS, Raj S, Babu R, Kumar S et al (2023) A hybrid moth–flame algorithm with particle swarm optimization with application in power transmission and distribution. Decis Anal J 6:100182

    Article  Google Scholar 

  53. Taher MA, Kamel S, Jurado F, Ebeed M (2019) An improved moth-flame optimization algorithm for solving optimal power flow problem. Int Trans Electr Energy 29:e2743

    Article  Google Scholar 

  54. Talaat M, Alsayyari AS, Farahat MA, Said T (2018) Moth-flame algorithm for accurate simulation of a non-uniform electric field in the presence of dielectric barrier. IEEE Access 7:3836–3847

    Article  Google Scholar 

  55. Tumar I, Hassouneh Y, Turabieh H, Thaher T (2020) Enhanced binary moth flame optimization as a feature selection algorithm to predict software fault prediction. IEEE Access 8:8041–8055

    Article  Google Scholar 

  56. Zhang H, Li R, Cai Z, Gu Z et al (2020) Advanced orthogonal moth flame optimization with Broyden–Fletcher–Goldfarb–Shanno algorithm: framework and real-world problems. Expert Syst Appl 159:113617

    Article  Google Scholar 

  57. Wang M, Chen H, Yang B, Zhao X et al (2017) Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses. Neurocomputing 267:69–84

    Article  Google Scholar 

  58. Elsakaan AA, El-Sehiemy RA, Kaddah SS, Elsaid MI (2018) An enhanced moth-flame optimizer for solving non-smooth economic dispatch problems with emissions. Energy 157:1063–1078

    Article  Google Scholar 

  59. Xu L, Li Y, Li K, Beng GH et al (2018) Enhanced moth-flame optimization based on cultural learning and Gaussian mutation. J Bionic Eng 15:751–763

    Article  Google Scholar 

  60. Li WK, Wang WL, Li L (2018) Optimization of water resources utilization by multi-objective moth-flame algorithm. Water Resour Manag 32:3303–3316

    Article  MathSciNet  Google Scholar 

  61. Reddy S, Panwar LK, Panigrahi BK, Kumar R (2018) Solution to unit commitment in power system operation planning using binary coded modified moth flame optimization algorithm (BMMFOA): a flame selection based computational technique. J Comput Sci-Neth 25:298–317

    Article  MathSciNet  Google Scholar 

  62. Li C, Niu Z, Song Z, Li B et al (2018) A double evolutionary learning moth-flame optimization for real-parameter global optimization problems. IEEE Access 6:76700–76727

    Article  Google Scholar 

  63. Buch H, Trivedi IN (2019) An efficient adaptive moth flame optimization algorithm for solving large-scale optimal power flow problem with POZ, multifuel and valve-point loading effect. Iran J Sci Technol Trans Electr Eng 43:1031–1051

    Article  Google Scholar 

  64. Wu Z, Shen D, Shang M, Qi S (2019) Parameter Identification of single-phase inverter based on improved moth flame optimization algorithm. Electr Pow Compo Sys 47:456–469

    Article  Google Scholar 

  65. Helmi A, Alenany A (2020) An enhanced Moth-flame optimization algorithm for permutation-based problems. Evol Intel 13:741–764

    Article  Google Scholar 

  66. Nguyen T-T, Wang H-J, Dao T-K, Pan J-S et al (2020) A scheme of color image multithreshold segmentation based on improved moth-flame algorithm. IEEE Access 8:174142–174159

    Article  Google Scholar 

  67. Zhang H, Heidari AA, Wang M, Zhang L et al (2020) Orthogonal Nelder-Mead moth flame method for parameters identification of photovoltaic modules. Energy Convers Manag 211:112764

    Article  Google Scholar 

  68. Bhadoria A, Marwaha S, Kamboj VK (2020) BMFO-SIG: a novel binary moth flame optimizer algorithm with sigmoidal transformation for combinatorial unit commitment and numerical optimization problems. Trans Indian Natl Acad Eng 5:789–826

    Article  Google Scholar 

  69. Li Y, Zhu X, Liu J (2020) An improved moth-flame optimization algorithm for engineering problems. Symmetry 12:1234

    Article  Google Scholar 

  70. Kaur K, Singh U, Salgotra R (2020) An enhanced moth flame optimization. Neural Comput Appl 32:2315–2349

    Article  Google Scholar 

  71. Zhang Z, Qin H, Yao L, Liu Y et al (2020) Improved multi-objective moth-flame optimization algorithm based on R-domination for cascade reservoirs operation. J Hydrol 581:124431

    Article  Google Scholar 

  72. Kotary DK, Nanda SJ (2020) Distributed robust data clustering in wireless sensor networks using diffusion moth flame optimization. Eng Appl Artif Intell 87:103342

    Article  Google Scholar 

  73. Sapre S, Mini S (2021) Emulous mechanism based multi-objective moth–flame optimization algorithm. J Parallel Distrib Computi 150:15–33

    Article  Google Scholar 

  74. Zhang B, Tan R, Lin C-J (2021) Forecasting of e-commerce transaction volume using a hybrid of extreme learning machine and improved moth-flame optimization algorithm. Appl Intell 51:952–965

    Article  Google Scholar 

  75. Zouache D, Abdelaziz FB, Lefkir M, Chalabi NE-H (2021) Guided Moth-Flame optimiser for multi-objective optimization problems. Ann Oper Res 296:877–899

    Article  MathSciNet  Google Scholar 

  76. Abu Khurmaa R, Aljarah I, Sharieh A (2021) An intelligent feature selection approach based on moth flame optimization for medical diagnosis. Neural Comput Appl 33:7165–7204

    Article  Google Scholar 

  77. Ma L, Wang C, Xie N-g, Shi M et al (2021) Moth-flame optimization algorithm based on diversity and mutation strategy. Appl Intell 51:1–37

    Article  Google Scholar 

  78. Shan W, Qiao Z, Heidari AA, Chen H et al (2021) Double adaptive weights for stabilization of moth flame optimizer: balance analysis, engineering cases, and medical diagnosis. Knowl-Based Syst 214:106728

    Article  Google Scholar 

  79. Singh P, Bishnoi S (2021) Modified moth-Flame optimization for strategic integration of fuel cell in renewable active distribution network. Electr Pow Syst Res 197:107323

    Article  Google Scholar 

  80. Xu Y, Huang H, Heidari AA, Gui W et al (2021) MFeature: towards high performance evolutionary tools for feature selection. Expert Syst Appl 186:115655

    Article  Google Scholar 

  81. Nadimi-Shahraki MH, Fatahi A, Zamani H, Mirjalili S et al (2021) An improved moth-flame optimization algorithm with adaptation mechanism to solve numerical and mechanical engineering problems. Entropy 23:1637

    Article  MathSciNet  Google Scholar 

  82. Kigsirisin S, Miyauchi H (2021) Short-term operational scheduling of unit commitment using binary alternative moth-flame optimization. IEEE Access 9:12267–12281

    Article  Google Scholar 

  83. Hou G, Gong L, Hu B, Su H et al (2022) Application of fast adaptive moth-flame optimization in flexible operation modeling for supercritical unit. Energy 239:121843

    Article  Google Scholar 

  84. Ma M, Wu J, Shi Y, Yan L et al (2022) Research on multiaircrafts cooperative arraying to jam based on multiobjective moth-flame optimization algorithm. IEEE Access 10:80539–80554

    Article  Google Scholar 

  85. Zhang Y, Wang P, Yang H, Cui Q (2022) Optimal dispatching of microgrid based on improved moth-flame optimization algorithm based on sine mapping and Gaussian mutation. Syst Sci Control Eng 10:115–125

    Article  Google Scholar 

  86. Qaraad M, Amjad S, Hussein NK, Badawy M et al (2023) Photovoltaic parameter estimation using improved moth flame algorithms with local escape operators. Comput Electr Eng 106:108603

    Article  Google Scholar 

  87. Yang Z (2023) FMFO: Floating flame moth-flame optimization algorithm for training multi-layer perceptron classifier. Appl Intell 53:251–271

    Article  Google Scholar 

  88. Wang C, Ma L, Ma L, Lai JW et al (2023) Identification of influential users with cost minimization via an improved moth flame optimization. J Comput Sci 67:101955

    Article  Google Scholar 

  89. Wu X-J, Xu L, Zhen R, Wu X-L (2023) Global and local moth-flame optimization algorithm for UAV formation path planning under multi-constraints. Int J Control Autom Syst 67:1–16

    Google Scholar 

  90. Sarma A, Bhutani A, Goel L (2017) Hybridization of moth flame optimization and gravitational search algorithm and its application to detection of food quality. In: 2017 Intelligent Systems Conference (IntelliSys). IEEE, pp 52–60

  91. Sayed GI, Hassanien AE (2018) A hybrid SA-MFO algorithm for function optimization and engineering design problems. Complex Intell Syst 4:195–212

    Article  Google Scholar 

  92. Yu C, Heidari AA, Chen H (2020) A quantum-behaved simulated annealing algorithm-based moth-flame optimization method. Appl Math Model 87:1–19

    Article  MathSciNet  Google Scholar 

  93. Bandopadhyay J, Roy PK (2020) Application of hybrid multi-objective moth flame optimization technique for optimal performance of hybrid micro-grid system. Appl Soft Comput 95:106487

    Article  Google Scholar 

  94. Wu Y, Chen R, Li C, Zhang L et al (2020) An adaptive sine-cosine moth-flame optimization algorithm for parameter identification of hybrid active power filters in power systems. IEEE Access 8:156378–156393

    Article  Google Scholar 

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

    Article  Google Scholar 

  96. Abd Elaziz M, Ewees AA, Ibrahim RA, Lu S (2020) Opposition-based moth-flame optimization improved by differential evolution for feature selection. Math Comput Simul 168:48–75

    Article  MathSciNet  Google Scholar 

  97. Zhao X, Fang Y, Liu L, Xu M et al (2020) Ameliorated moth-flame algorithm and its application for modeling of silicon content in liquid iron of blast furnace based fast learning network. Appl Soft Comput 94:106418

    Article  Google Scholar 

  98. Wu Y, Chen R, Li C, Zhang L et al (2020) Hybrid symbiotic differential evolution moth-flame optimization algorithm for estimating parameters of photovoltaic models. IEEE Access 8:156328–156346

    Article  Google Scholar 

  99. Zhao X, Fang Y, Liu L, Li J et al (2020) An improved moth-flame optimization algorithm with orthogonal opposition-based learning and modified position updating mechanism of moths for global optimization problems. Appl Intell 50:4434–4458

    Article  Google Scholar 

  100. Dash SP, Subhashini K, Satapathy J (2020) Optimal location and parametric settings of FACTS devices based on JAYA blended moth flame optimization for transmission loss minimization in power systems. Microsyst Technol 26:1543–1552

    Article  Google Scholar 

  101. Xia J, Zhang H, Li R, Chen H et al (2021) Generalized oppositional moth flame optimization with crossover strategy: an approach for medical diagnosis. J Bionic Eng 18:991–1010

    Article  Google Scholar 

  102. Shehab M, Alshawabkah H, Abualigah L, AL-Madi N, (2021) Enhanced a hybrid moth-flame optimization algorithm using new selection schemes. Eng Comput 37:2931–2956

    Article  Google Scholar 

  103. Abd Elaziz M, Yousri D, Mirjalili S (2021) A hybrid Harris hawks-moth-flame optimization algorithm including fractional-order chaos maps and evolutionary population dynamics. Adv Eng Softw 154:102973

    Article  Google Scholar 

  104. Nadimi-Shahraki MH, Fatahi A, Zamani H, Mirjalili S et al (2021) Migration-based moth-flame optimization algorithm. Processes 9:2276

    Article  Google Scholar 

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

    Article  Google Scholar 

  106. Le Chau N, Tran NT, Dao T-P (2021) A hybrid approach of density-based topology, multilayer perceptron, and water cycle-moth flame algorithm for multi-stage optimal design of a flexure mechanism. Eng Comput 38:2833–2865

    Article  Google Scholar 

  107. Ahmed OH, Lu J, Xu Q, Ahmed AM et al (2021) Using differential evolution and Moth-Flame optimization for scientific workflow scheduling in fog computing. Appl Soft Comput 112:107744

    Article  Google Scholar 

  108. Taleb SM, Meraihi Y, Mirjalili S, Acheli D et al. (2023) Mesh Router Nodes Placement for Wireless Mesh Networks Based on an Enhanced Moth–Flame Optimization Algorithm. Mobile Networks and Applications:1–24

  109. Nadimi-Shahraki MH, Moeini E, Taghian S, Mirjalili S (2021) DMFO-CD: a discrete moth-flame optimization algorithm for community detection. Algorithms 14:314

    Article  Google Scholar 

  110. Nadimi-Shahraki MH, Banaie-Dezfouli M, Zamani H, Taghian S et al (2021) B-MFO: A binary moth-flame optimization for feature selection from medical datasets. Computers 10:136

    Article  Google Scholar 

  111. Sadrishojaei M, Jafari Navimipour N, Reshadi M, Hosseinzadeh M (2021) Clustered routing method in the internet of things using a moth-flame optimization algorithm. Int J Commun Syst 34:e4964

    Article  Google Scholar 

  112. Hazra S, Roy PK (2020) Optimal dispatch using moth-flame optimization for hydro-thermal-wind scheduling problem. Int Trans Electr Energy 30:e12460

    Google Scholar 

  113. Yang L, Nguyen H, Bui X-N, Nguyen-Thoi T et al (2021) Prediction of gas yield generated by energy recovery from municipal solid waste using deep neural network and moth-flame optimization algorithm J. Clean Prod 311:127672

    Article  Google Scholar 

  114. Hassanien AE, Gaber T, Mokhtar U, Hefny H (2017) An improved moth flame optimization algorithm based on rough sets for tomato diseases detection. Comput Electron Agr 136:86–96

    Article  Google Scholar 

  115. Mei RNS, Sulaiman MH, Mustaffa Z, Daniyal H (2017) Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique. Appl Soft Comput 59:210–222

    Article  Google Scholar 

  116. Savsani V, Tawhid MA (2017) Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems. Eng Appl Artif Intel 63:20–32

    Article  Google Scholar 

  117. Zheng C, Wu W-Z, Xie W, Li Q (2021) A MFO-based conformable fractional nonhomogeneous grey Bernoulli model for natural gas production and consumption forecasting. Appl Soft Comput 99:106891

    Article  Google Scholar 

  118. Gupta D, Ahlawat AK, Sharma A, Rodrigues JJ (2020) Feature selection and evaluation for software usability model using modified moth-flame optimization. Computing 102:1503–1520

    Article  MathSciNet  Google Scholar 

  119. Wang Y, Li F, Yu H, Wang Y et al (2020) Optimal operation of microgrid with multi-energy complementary based on moth flame optimization algorithm. Energ Source Part A 42:785–806

    Article  Google Scholar 

  120. Yin T, Li Y, Fan J, Wang T et al (2021) A novel gated recurrent unit network based on svm and moth-flame optimization algorithm for behavior decision-making of autonomous vehicles. IEEE Access 9:20410–20422

    Article  Google Scholar 

  121. Pandya S, Jangir P, Trivedi NI (2022) Multi-objective Moth flame optimizer: a fundamental visions for wind power integrated optimal power flow with FACTS devices. Smart Sci 10:118–141

    Article  Google Scholar 

  122. Seyfollahi A, Moodi M, Ghaffari A (2022) MFO-RPL: A secure RPL-based routing protocol utilizing moth-flame optimizer for the IoT applications. Comput Stand Interface 82:103622

    Article  Google Scholar 

  123. Salehnia T, Seyfollahi A, Raziani S, Noori A, et al. (2023) An optimal task scheduling method in IoT-Fog-Cloud network using multi-objective moth-flame algorithm. Multimedia Tools and Applications:1–22

  124. Gadekallu TR, Kumar N, Baker T, Natarajan D, et al. (2023) Moth Flame Optimization based ensemble classification for intrusion detection in intelligent transport system for smart cities. Microprocessors and Microsystems:104935

  125. Nouri NA, Aliouat Z, Naouri A, Sa H (2023) An efficient mesh router nodes placement in wireless mesh networks based on moth-flame optimization algorithm. Int J Commun Syst 36:e5468

    Article  Google Scholar 

  126. Liu L, Sheng J, Liang H, Yang J, et al. (2023) Moth‐flame‐optimisation based parameter estimation for model‐predictive‐controlled superconducting magnetic energy storage‐battery hybrid energy storage system. IET Smart Grid

  127. Morales-Castañeda B, Zaldivar D, Cuevas E, Fausto F et al (2020) A better balance in metaheuristic algorithms: does it exist? Swarm Evol Comput 54:100671

    Article  Google Scholar 

  128. Xu J, Zhang J (2014) Exploration-exploitation tradeoffs in metaheuristics: Survey and analysis. In: Proceedings of the 33rd Chinese control conference. IEEE, pp 8633–8638

  129. Hussain K, Salleh MNM, Cheng S, Shi Y (2019) On the exploration and exploitation in popular swarm-based metaheuristic algorithms. Neural Comput Appl 31:7665–7683

    Article  Google Scholar 

  130. Olorunda O, Engelbrecht AP (2008) Measuring exploration/exploitation in particle swarms using swarm diversity. In: 2008 IEEE congress on evolutionary computation (IEEE world congress on computational intelligence). IEEE, pp 1128–1134

  131. Wu X, Zhang S, Xiao W, Yin Y (2019) The exploration/exploitation tradeoff in whale optimization algorithm. IEEE Access 7:125919–125928

    Article  Google Scholar 

  132. Nadimi-Shahraki MH, Zamani H (2022) DMDE: Diversity-maintained multi-trial vector differential evolution algorithm for non-decomposition large-scale global optimization. Expert Syst Appl 198:116895

    Article  Google Scholar 

  133. Morrison RW (2004) Designing evolutionary algorithms for dynamic environments. Springer, Berlin

    Book  Google Scholar 

  134. Fister I, Iglesias A, Galvez A, Del Ser J et al (2019) Novelty search for global optimization. Appl Math Comput 347:865–881

    MathSciNet  Google Scholar 

  135. Deep K, Thakur M (2007) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193:211–230

    MathSciNet  Google Scholar 

  136. Gupta S, Deep K (2019) A novel random walk grey wolf optimizer. Swarm Evol Comput 44:101–112

    Article  Google Scholar 

  137. Friedman M (1940) A comparison of alternative tests of significance for the problem of m rankings. Ann Math Stat 11:86–92

    Article  MathSciNet  Google Scholar 

  138. García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inform Sci 180:2044–2064

    Article  Google Scholar 

  139. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15:617–644

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Hoda Zamani & Mohammad H. Nadimi-Shahraki

  2. Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Hoda Zamani & Mohammad H. Nadimi-Shahraki

  3. Centre for Artificial Intelligence Research and Optimisation, Torrens University, Torrens, Australia

    Mohammad H. Nadimi-Shahraki & Seyedali Mirjalili

  4. Yonsei Frontier Lab, Yonsei University, Seoul, South Korea

    Seyedali Mirjalili

  5. Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran

    Farhad Soleimanian Gharehchopogh

  6. Depto. de Ingeniería Electro-Fotónica, Universidad de Guadalajara, CUCEI, Guadalajara, Jal, Mexico

    Diego Oliva

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  1. Hoda Zamani
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  2. Mohammad H. Nadimi-Shahraki
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Correspondence to Hoda Zamani or Mohammad H. Nadimi-Shahraki.

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Zamani, H., Nadimi-Shahraki, M.H., Mirjalili, S. et al. A Critical Review of Moth-Flame Optimization Algorithm and Its Variants: Structural Reviewing, Performance Evaluation, and Statistical Analysis. Arch Computat Methods Eng 31, 2177–2225 (2024). https://doi.org/10.1007/s11831-023-10037-8

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