Artificial Intelligence Review

, Volume 51, Issue 3, pp 445–492 | Cite as

Continuous versions of firefly algorithm: a review

  • Surafel Luleseged TilahunEmail author
  • Jean Medard T. Ngnotchouye
  • Nawaf N. Hamadneh


Firefly algorithm is a swarm based metaheuristic algorithm designed for continuous optimization problems. It works by following better solutions and also with a random search mechanism. It has been successfully used in different problems arising in different disciplines and also modified for discrete problems. Unlike its easiness to understand and to implement; its effectiveness is highly affected by the parameter values. In addition modifying the search mechanism may give better performance. Hence different modified versions are introduced to overcome its limitations and increase its performance. In this paper, the modifications done on firefly algorithm for continuous optimization problems will be reviewed with a critical analysis. A detailed discussion on the modifications with possible future works will also be presented. In addition a comparative study will be conducted using forty benchmark problems with different dimensions based on ten base functions. The result shows that some of the modified versions produce superior results with a tradeoff of high computational time. Hence, this result will help practitioners to decide which modified version to apply based on the computational resource available and the sensitivity of the problem.


Firefly algorithm Optimization Bio-inspired algorithm Swarm intelligence 


  1. Abdelaziz AY, Mekhamer SF, Badr MAL, Algabalawy MA (2015) The firefly meta-heuristic algorithms: developments and applications. Int Electr Eng J (IEEJ) 6(7):1945–1952Google Scholar
  2. Abdel-Raouf O, Abdel-Baset M, El-henawy I (2014) Chaotic firefly algorithm for solving definite integral, I.J. information technology and computer. Science 06:19–24Google Scholar
  3. Abshouri AA, Meybodi MR, Bakhtiary A (2011) New firefly algorithm based on multi swarm & learning Automata in dynamic environments. In: Third international conference on signal processing systems (ICSPS2011), August 27Ű28, Yantai, China, 73–77, IEEEGoogle Scholar
  4. Ali N, Othman MA, Husain MN, Misran MH (2014) A review of firefly algorithm. ARPN J Eng Appl Sci 9(10):1732–1736Google Scholar
  5. Al-Wagih K (2015) Improved firefly algorithm for unconstrained optimization problems. Int J Comput Appl Technol Res 4(1):77–81Google Scholar
  6. Alweshah M (2014) Firefly algorithm with artificial neural network for time series problems. Res J Appl Sci Eng Technol 7(19):3978–3982Google Scholar
  7. Amaya I, Cruz J, Correa R (2014) A modified firefly-inspired algorithm for global computatiional optimization. DYNA 81(187):85–90Google Scholar
  8. Amiri B, Hossain L, Crawford JW, Wigand RT (2013) Community detection in complex networks: multi-objective enhanced firefly algorithm. Knowl Based Syst 46:1–11Google Scholar
  9. Ariyaratne MKA, Pemarathne WPJ (2015) A review of recent advancements of firefly algorithm: a modern nature inspired algorithm. In: Proceedings of the 8th international research conference, 61–66, KDU, Published November 2015Google Scholar
  10. Arora S, Singh S (2014a) Performance research on firefly optimization algorithm with mutation. In: International conference on communication, computing & systems (ICCCS2014), 168–172Google Scholar
  11. Arora S, Singh S, Singh S, Sharma B (2014b) Mutated fireïňĆy algorithm. In: International conference on parallel, distributed and grid computing, IEEE, 33–38Google Scholar
  12. Azad SK (2011) Optimum design of structures using an improved firefly algorithm. Int J Opt Civil Eng 2:327–340Google Scholar
  13. Baghlani A, Makiabadi MH, Rahnema H (2013) A new accelarated firefly algorithm for size optimization of truss structures. Scientia Iranica Trans A Civil Eng 20(6):1612–1625Google Scholar
  14. Banati H, Bajaj M (2011) Fire fly based feature selection approach. IJCSI Int J Comput Sci Issues 8(4):473–480Google Scholar
  15. Bidar M, Kanan HR (2013) Jumper firefly algorithm. In: Proceeding of international conference on computer and knowledge engineering (ICCKE 2013), Oct. 31–Nov. 01, 2013, Ferdowsi University of Mashhad, 278–282Google Scholar
  16. Bingham D (2016) Virtual library of simulation experiments: test functions and datasets, 2015. Accessed Feb 2016
  17. Brajevic I, Ignjatovic J (2015) An enhanced firefly algorithm for mixed variable structural optimization problems. Ser Math Inf 30(4):401–417MathSciNetzbMATHGoogle Scholar
  18. Cheung NJ, Ding X-M, Shen H-B (2014) Adaptive firefly algorithm: parameter analysis and its application. PLoS ONE 9(11):1–12Google Scholar
  19. Coelho LdS, Mariani VC (2012) Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning. Comput Math Appl 64:2371–2382MathSciNetzbMATHGoogle Scholar
  20. Coelho LdS, Mariani VC (2013) Improved firefly algorithm approach applied to chiller loading for energy conservation. Energy Build 59:273–278Google Scholar
  21. Coelho LdS, de A Bernert DL, Mariani VC (2011) A chaotic firefly algorithm applied to reliability-redundancy optimization. In: 2011 IEEE congress on evolutionary computation (CEC11), 517–521Google Scholar
  22. de Paula LCM, Soares AS, Soares TWL, Delbem ACB, Coelho CJ, Filho ARG (2014) Parallelization of a modified firefly algorithm using GPU for variable selection in a multivariate calibration problem. Int J Nat Comput Res 4(1):31–42Google Scholar
  23. Dhal KG, Quraishi MdI, Das S (2015a) A chaotic levy flight approach in bat and firefly algorithm for gray level image enhancement. I.J. Image Gr Signal Process 7:69–76Google Scholar
  24. Dhal KG, Quraishi MdI, Das S (2015b) Development of firefly algorithm via chaotic sequence and population diversity to enhance the image contrast. Nat Comput. doi: 10.1007/s11047-015-9496-3
  25. Dieterich J, Hartke B (2012) Empirical review of standard benchmark functions using evolutionary global optimization. Appl Math 3:1552–1564Google Scholar
  26. Dugonik J, Fister I (2014) Multi-population firefly algorithm. In: Proceedings of the 2014, 1st student computer science research conference, Ljubljana, Slovenia, 7 October 19–23Google Scholar
  27. Farahani ShM, Abshouri AA, Nasiri B, Meybodi MR (2011a) An improved firefly algorithm with directed movement. In: Proceedings of 4th IEEE international conference on computer science and information technology, Chengdu, 248–251Google Scholar
  28. Farahani ShM, Abshouri AA, Nasiri B, Meybodi MR (2011b) A Gaussian firefly algorithm. Int J Mach Learn Comput 1(5):448–453Google Scholar
  29. Farahani SM, Nasiri B, Meybodi MR (2011c) A multiswarm basedfirefly algorithm in dynamic environments. In Third international conference on signal processing systems (ICSPS2011), August 27–28, Yantai, China, 68–72, IEEEGoogle Scholar
  30. Fateen S-EK, Bonilla-Petriciolet A (2014) Intelligent firefly algorithm for global optimization. In: Yang X-S (ed) Cuckoo search and firefly algorithm, studies in computational intelligence 516, 315–330Google Scholar
  31. Fister I, Yang X-S, Brest J, Fister I Jr (2013a) Modified firefly algorithm using quaternion representation. Expert Syst Appl 40:7220–7230Google Scholar
  32. Fister I, Fister Jr I, Yang XS, Brest J (2013b) A comprehensive review of firefly algorithms, swarm and evolutionary computation. doi: 10.1016/j.swevo.2013.06.001
  33. Fister I, Yang X-S, Brest J, Fister Jr I (2014) On the randomized FireïňĆy Algorithm. In: Yang X-S (ed) Cuckoo search and FireïňĆy algorithm, studies in computational intelligence 516, 27–48Google Scholar
  34. Fu Q, Liu Z, Tong N, Wang M, Zhao Y (2015) A novel firefly algorithm based on improved learning mechanism. In: International conference on logistics engineering, management and computer science (LEMCS 2015), 1343–1351Google Scholar
  35. Gandomi AH, Yang X-S, Talatahari S, Alavi AH (2013) FireïňĆy algorithm with chaos. Commun Nonlinear Sci Numer Simulat 18:89–98zbMATHGoogle Scholar
  36. Gavana A (2013) Global optimization benchmarks and AMPGO. Accessed Feb 2016
  37. Goel S, Panchal VK (2014) Performance evaluation of a new modified firefly algorithm. In: 3rd International conference reliability, infocom technologies and optimization (ICRITO) (Trends and Future Directions), IEEEGoogle Scholar
  38. Grachten M, Arcos JL, de Mantaras RL (2014) Evolutionary optimization of music performance annotation. In: CMMR, 1–12Google Scholar
  39. Hamadneh N, Sathasivam S, Tilahun SL, Choon OH (2012) Learning logic programming in radial basis function network via genetic algorithm. J Appl Sci (Faisalabad) 12(9):840–847zbMATHGoogle Scholar
  40. Hassanzadeh T, Kanan HR (2014) Fuzzy FA: a modified firefly algorithm. Appl Artif Intell 28:47–65Google Scholar
  41. Hernandez S, Fontan A (2014) Cost optimization in bridge construction: application to launched bridges. Struct Congr 2014:2801–2812Google Scholar
  42. Hongwei Z, Liwei T, Dongzheng W (2015) Research on improved firefly optimization algorithm based on cooperative for clustering. Int J Smart Home 9(3):205–214Google Scholar
  43. Husselmann AV, Hawick KA (2011) Parallel parametric optimisation with firefly algorithms on graphical processing units, Technical Report CSTN-141Google Scholar
  44. Jamil M, Yang X-S (2013) A literature survey of benchmark functions for global optimization problems. Int J Math Model Numer Optim 4(2):150–194zbMATHGoogle Scholar
  45. Jansi S, Subashini P (2015) A novel fuzzy clustering based modified firefly algorithm with chaotic map for mri brain tissue segmentation. MAGNT Res Rep 3(1):52–58Google Scholar
  46. Kanimozhi T, Latha K (2013) An adaptive approach for content based image retrieval using Gaussian firefly algorithm. In: Huang DS et al. (eds) ICIC 2013, CCIS 375, pp 213–218Google Scholar
  47. Kavousi-Fard A, Samet H, Marzbani F (2014) A new hybrid modified firefly algorithm and support vector regression model for accurate short term load forecasting. Expert Syst Appl 41:6047–6056Google Scholar
  48. Kazemzadeh-Parsi MJ (2014) A modified firefly algorithm for engineering design optimization problems. IJST Trans Mech Eng 38(M2):403–421Google Scholar
  49. Kazemzadeh-Parsi MJ (2015) Optimal shape design for heat conduction using smoothed fixed grid finite element method and modified firefly algorithm. IJST Trans Mech Eng 39(M2):367–387Google Scholar
  50. Kazemzadeh-Parsi MJ, Daneshmand F, Ahmadfard MA, Adamowski J (2015) Optimal Remediation Design of Unconfined Contaminated Aquifers Based on the Finite Element Method and a Modified Firefly Algorithm. Water Resour Manage. doi: 10.1007/s11269-015-0976-0
  51. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks IV, Nov 27–Dec 1, Perth, Australia, IEEE, 4, 1942–1948Google Scholar
  52. Khan WA, Hamadneh NN, Tilahun SL, Ngnotchouye JMT (2016) A review and comparative study of firefly algorithm and its modified versions. In: Chapter 13 of optimization algorithms- methods and applications, associate Prof. Ozgur Baskan (Ed.), InTech, doi: 10.5772/62472
  53. Kwiecien J, Filipowicz B (2012) Firefly algorithm in optimization of queueing systems. Bull Pol Acad Sci Tech Sci 60(2):363–368Google Scholar
  54. Lin X, Zhong Y, Zhang H (2013) An enhanced firefly algorithm for function optimisation problems. Int J Modell Identif Control 18(2):166–173Google Scholar
  55. Liu C, Zhao Y, Gao F, Liu L (2015) Three-dimensional path planning method for autonomous underwater vehicle based on modified firefly algorithm. Math Probl Eng 2015, Article ID 561394, 10 pagesGoogle Scholar
  56. Long NC, Meesad P, Unger H (2015) A highly accurate firefly based algorithm for heart disease prediction. Expert Syst Appl 42:8221–8231Google Scholar
  57. Lucia A, Xu J (1990) Chemical process optimization using Newton-like methods. Comput Chrm Eng 14(2):119–138Google Scholar
  58. Lukasik S, Zak S (2009) Firefly algorithm for continuous constrained optimization task, ICCCI 2009. In: Ngugen NT, Kowalczyk R, Chen SM (eds) Lecture notes in artificial intelligence, 5796, 97–100Google Scholar
  59. Maidl G, Schwerz de Lucena D, dos S Coelho L (2013) Economic dispatch optimization of thermal units based on a modified firefly algorithm. In: 22nd International congress of mechanical engineering (COBEM 2013), November. ABCM, RibeirÃčo Preto, SP, Brazil, pp 3–7Google Scholar
  60. Manoharan GV, Shanmugalakshmi R (2015) Multi-objective firefly algorithm for multi-class gene selection. Ind J Sci Technol 8(1):27–34Google Scholar
  61. Meena S, Chitra K (2015) Modified approach of firefly algorithm for non-minimum phase systems. Indian J Sci Technol 8(23):1–8Google Scholar
  62. Mohammadi S, Mozafari B, Solimani S, Niknam T (2013) An adaptive modified firefly optimisation algorithm based on Hong’s point estimate method to optimal operation management in a microgrid with consideration of uncertainties. Energy 51:339–348Google Scholar
  63. Negnevitsky M (2005) Artifcial intelligence: a guide to intelligent system. Henry Ling Limited, HarlowGoogle Scholar
  64. Olamaei J, Moradi M, Kaboodi T (2013) A new adaptive modified firefly algorithm to solve optimal capacitor placement problem. In: 18th Electric power disteibution network conference, art. No. 6565962Google Scholar
  65. Ondrisek B (2009) E-voting system security optimization. In: Proceedings of the 42nd Hawaii international conference on system sciences, Jan. 2009, 1–8Google Scholar
  66. Othman MM, Hegazy YG, Abdelaziz AY (2015) A modified firefly algorithm for optimal sizing and siting of voltage controlled distributed generators in distribution networks. Period Polytech Electr Eng Comput Sci 59(3):104–109Google Scholar
  67. Pan F, Ye C, Wang K, Jiangbo Cao (2013) Research on the vehicle routing problem with time windows using firefly algorithm. J Comput 8(9):2256–2261Google Scholar
  68. Pike J, Bogich T, Elwood S, Finnoff DC, Daszak P (2014) Economic optimization of a global strategy to address the pandemic threat. Proc Natl Acad Sci 111(52):18519–18523Google Scholar
  69. Poursalehi N, Zolfaghari A, Minuchehr A, Moghaddam HK (2013) Continuous firefly algorithm applied to PWR core pattern enhancement. Nucl Eng Des 258:107–115Google Scholar
  70. Reddy PDP, Sekhar JNC (2014) Application of firefly algorithm for combined economic load and emission dispatch. Int J Rec Innov Trends Comput Commun 2(8):2448–2452Google Scholar
  71. Ropponen A, Ritala R, Pistikopoulos EN (2010) Broke management optimization in design of paper production systems. In: Computer aided chemical engineering (20th European symposium on computer aided process engineering), 28, 865–870Google Scholar
  72. Sahoo A, Chandra S (2013) Levy-flight firefly algorithm based active contour model for medical image segmentation, Contemporary Computing (IC3). In: Sixth international conference, IEEE, 159–162Google Scholar
  73. Selvarasu R, Kalavathi MS (2015) TCSC placement for loss minimization using self adaptive firefly algorithm. J Eng Sci Technol 10(3):291–306Google Scholar
  74. Selvarasu R, Kalavathi MS, Rajan CCA (2013) SVC placement for voltage constrained loss minimization using self-adaptive Firefly algorithm. Arch Electr Eng 62(4):649–661Google Scholar
  75. Shafaati M, Mojallali H (2012) Modified firefly optimization for IIR system identification. Control Eng Appl Inf 14(4):59–69Google Scholar
  76. Shakarami MR, Sedaghati R (2014) A new approach for network reconfiguration problem in order to deviation bus voltage minimization with regard to probabilistic load model and DGs. Int J Electr Comput Energ Electr Commun Eng 8(2):430–435Google Scholar
  77. Subotic M, Tuba M, Stanarevic N (2012) Parallelization of the firefly algorithm for unconstrained optimization problems. Latest Adv Inf Sci Appl 264–269, ISBN: 978-1-61804-092-3Google Scholar
  78. Subramanian R, Thanushkodi K (2013) An efficient firefly algorithm to solve economic dispatch problems. Int J Soft Comput Eng (IJSCE) 2(1):52–55Google Scholar
  79. Sulaiman MH, Daniyal H, Mustafa MW (2012) Modified firefly algorithm in solving economic dispatch problems with practical constraints. In: IEEE international conference on power and energy (PECon), 2–5 December 2012, Kota Kinabalu Sabah, MalaysiaGoogle Scholar
  80. Sweitzer BJ (2008) Preoperative screening, evaluation, and optimization of the patient’s medical status before outpatient surgery. Curr Opin Anaesthesiol 21(6):711–718Google Scholar
  81. Tian Y, Gao W, Yan S (2012) An improved inertia weight firefly optimization algorithm and application. In: 2012 International conference on control engineering and communication technology. IEEE 64–68Google Scholar
  82. Tilahun SL, Asfaw A (2012) Modeling the expansion of Prosopis Juliflora and determining its optimum utilization rate to control its invasion in afar regional state of ethiopia. Int J Appl Math Res 1(4):726–743Google Scholar
  83. Tilahun SL, Ngnotchouye JMT (2016) Prey predator algorithm with adaptive step length. Int J Bio-Inspir Comput 8(4):195–204Google Scholar
  84. Tilahun SL, Ngnotchouye JMT (2017) Firefly algorithm for discrete optimization problems: a survey. KSCE J Civil Eng 21(2):535–545Google Scholar
  85. Tilahun SL, Ong HC (2012a) Bus timetabling as a fuzzy multiobjective optimization problem using preference based genetic algorithm. PROMET—traffic & transportation 24(3):183–191Google Scholar
  86. Tilahun SL, Ong HC (2012b) Fuzzy preference of multiple decision makers in solving multiobjective optimization problems using genetic algorithm. Maejo Int J Sci Technol 6(02):224–237Google Scholar
  87. Tilahun SL, Ong HC (2012c) Modified firefly algorithm. J Appl Math, Article ID 467631, 12 pagesGoogle Scholar
  88. Tilahun SL, Ong HC (2013) Vector optimisation using fuzzy preference in evolutionary strategy based firefly algorithm. Int J Op Res 16(1):81–95MathSciNetzbMATHGoogle Scholar
  89. Tilahun SL, Ong HC (2014) Prey-predator algorithm: a new metaheuristic optimization algorithm. Int J Inf Technol Decis Mak 13:1–22Google Scholar
  90. Tilahun SL, Kassa SM, Ong HC (2012) A new algorithm for multilevel optimization problems using evolutionary strategy, inspired by natural adaptation. In: Anthony A, Ishizuka M, Lukose D (eds) PRICAI 2012, LNAI 7458. Springer, Berlin, pp 577–588Google Scholar
  91. Tilahun SL, Hamadneh NN, Sathasivam S, Ong HC (2013) Prey-predator algorithm as a new optimization technique using in radial basis function neural networks. Res J Appl Sci 8(7):383–387Google Scholar
  92. Tilahun SL, Ong HC, Ngnotchouye JM (2016) Extended prey predator algorithm with a group hunting scenario. Advances in Operations Research. doi: 10.1155/2015/587103
  93. Tilahun SL (2017) Prey predator hyperheuristic. Appl. Soft Comput 59:104–114Google Scholar
  94. Verma OP, Aggarwal D, Patodi T (2016) Opposition and dimensional based modiïňĄed firefly algorithm. Expert Syst Appl 44:168–176Google Scholar
  95. Villegas JG (2016) Using nonparametric test to compare the performance of metaheuristics. Retrieved Feb 2016
  96. Volpato G, Maria E, Michielin Z, Ferreira SRS, Petrus JCC (2008) Optimization of the chicken breast cooking process. J Food Eng 84(4):576–581Google Scholar
  97. Wadhwa Y, Kaur P, Kaur B (2014) Golomb Ruler sequence generation and optimization using modified firefly algorithm. SSRG Int J Electr Commun Eng (SSRG-IJECE) 1(5):1–8Google Scholar
  98. Wang G, Guo L, Duan H, Liu L, Wang H (2012) A modified firefly algorithm for UCAV path planning. Int J Hybrid Inf Technol 5(3):123–144Google Scholar
  99. Wang G-G, Guo L, Duan H, Wang H (2014a) A new improved FireïňĆy algorithm for global numerical optimization. J Comput Theor Nanosci 11:477–485Google Scholar
  100. Wang B, Li D-X, Jiang J-P, Liao Y-H (2014b) A modified firefly algorithm based on light intensity difference. J Comb Optim. 31:1045–1060. doi: 10.1007/s10878-014-9809-y
  101. Yan X, Zhu Y, Wu J, Chen H (2012) An improved FireïňĆy algorithm with adaptive strategies. Adv Sci Lett 16:249–254Google Scholar
  102. Yang X-S (2008) Nature-inspired metaheuristic algorithm, 2nd edn. Luniver Press, EnglandGoogle Scholar
  103. Yang XS (2010) Firefly algorithm, levy flights and global optimization. In: Bramer M, Ellis R, Petridis M (eds) Research and development in intelligent systems XXVI. Springer, London, pp 209–218Google Scholar
  104. Yang X-S (2011) Review of metaheuristics and generalized evolutionary walk algorithm. Int J Bio-Inspir Comput 3(2):77–84Google Scholar
  105. Yang X-S (2013) Multiobjective ïňĄreïňĆy algorithm for continuous optimization. Eng Comput 29:175–184Google Scholar
  106. Yu S, Yang S, Su S (2013) Self-adaptive step firefly algorithm. J Appl Math 832718:8MathSciNetzbMATHGoogle Scholar
  107. Yu S, Zhu S, Ma Y, Mao D (2015a) A variable step size ïňĄreïňĆy algorithm for numerical optimization. Appl Math Comput 263:214–220Google Scholar
  108. Yu S, Mao D, Zhu S, Ma Y (2015b) Enhancing firefly algorithm using generalized opposition-based learning. Computing 97:741–754Google Scholar
  109. Yu S, Su S, Huang L (2015) A simple diversity guided firefly algorithm. Kybernetes 44(1):43–56Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Surafel Luleseged Tilahun
    • 1
    Email author
  • Jean Medard T. Ngnotchouye
    • 2
  • Nawaf N. Hamadneh
    • 3
  1. 1.Department of Mathematical SciencesUniversity of ZululandKwaDlangezwaSouth Africa
  2. 2.School of Mathematics, Statistics and Computer ScienceUniversity of KwaZulu-NatalScottsvilleSouth Africa
  3. 3.Department of Basic Sciences, College of Science and Theoretical StudiesSaudi Electronic UniversityRiyadhSaudi Arabia

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