Abstract
Firefly Algorithm (FA) is one of the popular algorithm of Swarm Intelligence domain that can be used in most of the areas of optimization. FA and its variants are simple to implement and easily understood. These can be used to successfully solve the problems of different areas. Modification in original FA or hybrid FA algorithms are required to solve diverse range of engineering problems. In this paper, a comprehensive review of firefly algorithm is presented and various characteristics are discussed. The various variant of FA such as binary, multi-objective and hybrid with other meta-heuristics are discussed. The applications and performance evolution metric are presented. This paper provides the possible future research direction of FA.
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References
Blum C, Li X (2008) Swarm intelligence in optimization. Springer, Berlin, pp 43–85
Chakraborty A, Kar AK (2017) Swarm intelligence: a review of algorithms. Springer, Cham, pp 475–494
Beekman M, Sword GA, Simpson SJ (2008) Biological foundations of swarm intelligence. Springer, Berlin, pp 3–41
Yang X-S (2008) Nature-inspired metaheuristic algorithms. Luniver press, London
Črepinšek M, Mernik M, Liu S-H (2011) Analysis of exploration and exploitation in evolutionary algorithms by ancestry trees. Int J Innov Comput Appl 3(1):11–19
Fister I, Fister I, Yang X-S, Brest J (2013) A comprehensive review of firefly algorithms. Swarm Evol Comput 13:34–46
Lee SA (2010) k-phase oscillator synchronization for graph coloring. Math Comput Sci 3(1):61–72
Yang X-S (2009) Firefly algorithms for multimodal optimization. In: International symposium on stochastic algorithms. Springer, pp 169–178
Yang X-S (2010). Firefly algorithm, stochastic test functions and design optimisation. arXiv:1003.1409
Yang X-S (2011) Review of metaheuristics and generalized evolutionary walk algorithm. arXiv:1105.3668
Parpinelli RS, Lopes HS (2011) New inspirations in swarm intelligence: a survey. Int J Bio-Inspired Comput 3(1):1–16
Zang H, Zhang S, Hapeshi K (2010) A review of nature-inspired algorithms. J Bionic Eng 7(4):S232–S237
Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3:124–141
Eiben AE, Smith JE et al (2003) Introduction to evolutionary computing, vol 53. Springer, Berlin
Tilahun S, Ong HC (2012) Modified firefly algorithm. J Appl Math 467631:11
Palit S, Sinha SN, Molla MA, Khanra A, Kule M (2011) A cryptanalytic attack on the knapsack cryptosystem using binary firefly algorithm. In: 2011 2nd international conference on computer and communication technology (ICCCT-2011), pp 428–432
Falcon R, Almeida M, Nayak A (2011) Fault identification with binary adaptive fireflies in parallel and distributed systems. In: 2011 IEEE congress of evolutionary computation (CEC), pp 1359–1366
Yang H, Elhadef M, Nayak A, Yang X (2008) Network fault diagnosis:aAn artificial immune system approach. In: 2008 14th IEEE international conference on parallel and distributed systems, pp 463–469
Falcon R, Almeida M, Nayak A (2010) A binary particle swarm optimization approach to fault diagnosis in parallel and distributed systems. In: IEEE congress on evolutionary computation, pp 1–8
Chandrasekaran K, Simon SP (2012) Network and reliability constrained unit commitment problem using binary real coded firefly algorithm. Int J Electr Power Energy Syst 43(1):921–932
Farahani SM, Abshouri A, Nasiri B, Meybodi M (2011) A gaussian firefly algorithm. Int J Mach Learn Comput 1(5):448
Yang X-S (2011) Metaheuristic optimization: algorithm analysis and open problems. In: Pardalos PM, Rebennack S (eds) Experimental algorithms. Berlin, Heidelberg, pp 21–32
Yang X-S (2010) Firefly algorithm, lévy flights and global optimization. In: Bramer M, Ellis R, Petridis M (eds) Research and development in intelligent systems XXVI. Springer, London, pp 209–218
Yang X-S (2012) Efficiency analysis of swarm intelligence and randomization techniques. J Comput Theor Nanosci 9(2):189–198
dos Santos Coelho L, de Andrade Bernert DL, Mariani VC (2011) A chaotic firefly algorithm applied to reliability-redundancy optimization. In: 2011 IEEE congress of evolutionary computation (CEC), pp 517–521
Gandomi A, Yang X-S, Talatahari S, Alavi A (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98
Subutic M, Tuba M, Stanarevic N (2012) Parallelization of the firefly algorithm for unconstrained optimization problems. Latest Adv Inf Sci Appl 22(3):264–269
Husselmann AV, Hawick K (2012) Parallel parametric optimisation with firefly algorithms on graphical processing units. In: Proceedings of the international conference on genetic and evolutionary methods (GEM12). Number CSTN-141, Las Vegas, USA, CSREA (16–19 July 2012), pp 77–83
Yang X-S, Deb S (2010) Eagle strategy using Lévy Walk and firefly algorithms for stochastic optimization. Springer, Berlin, pp 101–111
Luthra J, Pal SK (2011) A hybrid firefly algorithm using genetic operators for the cryptanalysis of a monoalphabetic substitution cipher. In: 2011 world congress on information and communication technologies, pp 202–206
Abdullah A, deris SB, Mohamad M, Hashim SM (2012) A new hybrid firefly algorithm for complex and nonlinear problem, 03
Fister I, Mernik M, Filipič B (2013) Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm. Comput Optim Appl 54(3):741–770
Hassanzadeh T, Faez K, Seyfi G (2012) A speech recognition system based on structure equivalent fuzzy neural network trained by firefly algorithm. In: 2012 international conference on biomedical engineering (ICoBE), pp 63–67
Nandy S, Sarkar PP, Das A (2012) Analysis of a nature inspired firefly algorithm based back-propagation neural network training. arXiv:1206.5360
Hassanzadeh T, Meybodi MR (2012) A new hybrid algorithm based on firefly algorithm and cellular learning automata. In: 20th Iranian conference on electrical engineering (ICEE2012), pp 628–633
Farahani S, Abshouri A, Nasiri B, Meybodi M (2012) Some hybrid models to improve firefly algorithm performance. Int J Artif Intell 8:97–117
Rajini A, David VK (2011) A comparative performance study on hybrid swarm model for microarray data. Int J Comput Appl 975:8887
Yang X-S (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, Hoboken
Shafaati M, Mojallali H (2012) Modified firefly optimization for IIR system identification. Control Eng Appl Inform 14:59–69
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 Eng 8(2):430–435
Olamaei J, Moradi M, Kaboodi T (2013) A new adaptive modified firefly algorithm to solve optimal capacitor placement problem. In: 18th Electric power distribution conference, pp 1–6
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(13):6047–6056
Yu S, Yang S, Su S (2013) Self-adaptive step firefly algorithm. J Appl Math 2013
Yang X-S (2012) Multiobjective firefly algorithm for continuous optimization. Eng Comput 29:175–184
Yu S, Su S, Lu Q, Huang L (2014) A novel wise step strategy for firefly algorithm. Int J Comput Math 91(12):2507–2513
Lin X, Zhong Y, Zhang H (2013) An enhanced firefly algorithm for function optimisation problems. Int J Model Ident Control 18(2):166–173
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):52–58
Long NC, Meesad P, Unger H (2015) A highly accurate firefly based algorithm for heart disease prediction. Expert Syst Appl 42(21):8221–8231
Abdel-Basset M (2020) Chaotic firefly algorithm for solving definite integral. Int J Inf Technol Comput Sci 6:19–24
Khalil A (2014) Improved firefly algorithm for unconstrained optimization problems. Int J Comput Appl Technol Res 4(1):77–81
Selvarasu R, Kalavathi MS, Rajan CCA (2013) Svc placement for voltage constrained loss minimization using self-adaptive firefly algorithm. Arch Electr Eng 62(4):649–661
Meena S, Chitra K (2015) Modified approach of firefly algorithm for non-minimum phase systems. Indian J Sci Technol 8(23):1
Yan X, Zhu Y, Wu J, Chen H (2012) An improved firefly algorithm with adaptive strategies. Adv Sci Lett 16(1):249–254
Sulaiman MH, Daniyal H, Mustafa MW (2012) Modified firefly algorithm in solving economic dispatch problems with practical constraints. In: 2012 IEEE international conference on power and energy (PECon), pp 157–161
Wang B, Li D-X, Jiang J-P, Liao Y-H (2016) A modified firefly algorithm based on light intensity difference. J Comb Optim 31(3):1045–1060
Othman MM, Hegazy YG, Abdelaziz AY (2015) A modified firefly algorithm for optimal sizing and siting of voltage controlled distributed generators in distribution networks. Periodica Polytech Electr Eng Comput Sci 59(3):104–109
Subramanian R, Thanushkodi K (2013) An efficient firefly algorithm to solve economic dispatch problems. Int J Soft Comput Eng 2(1):52–55
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
Fister I, Yang X-S, Brest J, Fister IJ (2013) 4-memetic self-adaptive firefly algorithm. In: Yang X-S, Cui Z, Xiao R, Gandomi AH, Karamanoglu M (eds) Swarm intelligence and bio-inspired computation. Elsevier, Oxford, pp 73–102
Fu Q, Liu Z, Tong N, Wang M, Zhao Y (2015/07) A novel firefly algorithm based on improved learning mechanism. In: International conference on logistics engineering, management and computer science (LEMCS 2015). Atlantis Press
dos Santos Coelho L, Mariani VC (2013) Improved firefly algorithm approach applied to chiller loading for energy conservation. Energy Build 59:273–278
dos Santos Coelho L, Mariani VC (2012) Firefly algorithm approach based on chaotic tinkerbell map applied to multivariable pid controller tuning. Comput Math Appl 64(8):2371–2382
Łukasik S, Żak S (2009) Firefly algorithm for continuous constrained optimization tasks. In: International conference on computational collective intelligence. Springer, pp 97–106
Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336
Gomes HM (2012) A firefly metaheuristic structural size and shape optimisation with natural frequency constraints. Int J Metaheuristics 2(1):38–55
Durkota K (2011) Implementation of a discrete firefly algorithm for the QAP problem within the sage framework. Bachelor thesis, Czech Technical University
Sayadi M, Ramezanian R, Ghaffari-Nasab N (2010) A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems. Int J Ind Eng Comput 1(1):1–10
Yousif A, Abdullah AH, Nor SM, Abdelaziz AA (2011) Scheduling jobs on grid computing using firefly algorithm. J Theor Appl Inf Technol 33(2):155–164
Hönig U (2010) A firefly algorithm-based approach for scheduling task graphs in homogeneous systems. Proc Inform 724
Jati GK Suyanto (2011) Evolutionary discrete firefly algorithm for travelling salesman problem. I: Bouchachia A (ed) Adaptive and intelligent systems. Springer, Berlin, pp 393–403
Khadwilard A, Chansombat S, Thepphakorn T, Chainate W, Pongcharoen P (2012) Application of firefly algorithm and its parameter setting for job shop scheduling. J Ind Technol 8(1):49–58
Liu C, Gao Z, Zhao W (2012) A new path planning method based on firefly algorithm. In: 2012 fifth international joint conference on computational sciences and optimization, pp 775–778
Wang G, Guo L, Duan H, Liu L, Wang H et al (2012) A modified firefly algorithm for ucav path planning. Int J Hybrid Inf Technol 5(3):123–144
Kwiecień J, Filipowicz B (2012) Firefly algorithm in optimization of queueing systems. Bull Pol Acad Sci Tech Sci 60(2):363–368
Abshouri AA, Meybodi MR, Bakhtiary A (2011) New firefly algorithm based on multi swarm & learning automata in dynamic environments. IEEE Proc 13:989–993
Chai-Ead N, Aungkulanon P, Luangpaiboon P (2010) Bees and firefly algorithms for noisy non-linear optimisation problems. In: World congress on engineering 2012, July 4–6, 2012. London, UK., vol. 2189. International Association of Engineers, pp 1449–1454
Farahani SM, Nasiri B, Meybodi MR (2011) A multiswarm based firefly algorithm in dynamic environments. In: Third international conference on signal processing systems (ICSPS2011), Citeseer, vol 3, pp 68–72
Nasiri B, Meybodi M (2012) Speciation based firefly algorithm for optimization in dynamic environments. Int J Artif Intell 8(S12):118–132
Sulaiman MH, Mustafa MW, Azmi A, Aliman O, Rahim S R Abdul (2012) Optimal allocation and sizing of distributed generation in distribution system via firefly algorithm. In: 2012 IEEE international power engineering and optimization conference Melaka, Malaysia, pp 84–89
Yang X-S (2013) Multiobjective firefly algorithm for continuous optimization. Eng Comput 29(2):175–184
Abedinia O, Amjady N, Naderi MS (2012) Multi-objective environmental/economic dispatch using firefly technique. In: 2012 11th international conference on environment and electrical engineering, pp 461–466
Niknam T, Azizipanah-Abarghooee R, Roosta A, Amiri B (2012) A new multi-objective reserve constrained combined heat and power dynamic economic emission dispatch. Energy 42(1):530–545
Zhang Y-D, Wu L (2012) A novel method for rigid image registration based on firefly algorithm. In: International journal of research and reviews in soft and intelligent computing (IJRRSIC), vol 2, 01
Horng M-H, Jiang T-W (2010) The codebook design of image vector quantization based on the firefly algorithm. In: Pan J-S, Chen S-M, Nguyen N-T (eds) Computational collective intelligence technologies and applications. Springer, Berlin, pp 438–447
Horng M-H (2012) Vector quantization using the firefly algorithm for image compression. Expert Syst Appl 39:1078–1091
Hassanzadeh T, Vojodi H, Mahmoudi F (2011) Non-linear grayscale image enhancement based on firefly algorithm. In: Proceedings of the second international conference on swarm, evolutionary, and memetic computing—volume part II, SEMCCO’11. Springer, Berlin, pp 174–181
Hassanzadeh T, Vojodi H, Moghadam AME (2011) An image segmentation approach based on maximum variance intra-cluster method and firefly algorithm. In: 2011 seventh international conference on natural computation, vol 3, pp 1817–1821
Noor MH Mohd, Ahmad AR, Hussain Z, Ahmad KA, Ainihayati AR (2011) Multilevel thresholding of gel electrophoresis images using firefly algorithm. In: 2011 IEEE international conference on control system, computing and engineering, pp 18–21
Horng M, Jiang T (2010) Multilevel image thresholding selection based on the firefly algorithm. In: 2010 7th international conference on ubiquitous intelligence computing and 7th international conference on autonomic trusted computing, pp 58–63
Horng M-H, Liou R-J (2011) Multilevel minimum cross entropy threshold selection based on the firefly algorithm. Expert Syst Appl 38:14805–14811
Basu B, Mahanti G (2011) Fire fly and artificial bees colony algorithm for synthesis of scanned and broadside linear array antenna. Prog Electromagn Res B 32:169–190
Basu B, Mahanti G (2012) Thinning of concentric two-ring circular array antenna using fire fly algorithm. Sci Iran 19(6):1802–1809
Zaman MA, Matin M Abdul (2012) Nonuniformly spaced linear antenna array design using firefly algorithm. Int J Microw Sci Technol 2012
Chatterjee A, Mahanti GK (2013) Minimization in variations of different parameters in different \(\varphi\) planes of a small-size concentric ring array antenna using firefly algorithm. Annal Telecommun 68(5–6):299–306
Jakimovski B, Meyer B, Maehle E (2010) Firefly flashing synchronization as inspiration for self-synchronization of walking robot gait patterns using a decentralized robot control architecture. In: Müller-Schloer C, Karl W, Yehia S (eds) Architecture of computing systems (ARCS 2010). Springer, Berlin, pp 61–72
Severin S, Rossmann J (2012) A comparison of different metaheuristic algorithms for optimizing blended ptp movements for industrial robots. In: Su C-Y, Rakheja S, Liu H (eds) Intelligent robotics and applications. Springer, Berlin, pp 321–330
Pop CB, Chifu VR, Salomie I, Baico RB, Dinsoreanu M, Copil G (2011) A hybrid firefly-inspired approach for optimal semantic web service composition. Scalable Comput Pract Exp 12(3):363–370
Breza M, McCann JA (2008) Lessons in implementing bio-inspired algorithms on wireless sensor networks. In: 08 NASA/ESA conference on adaptive hardware and systems, pp 271–276
Yang X-S, Deb S, Fong S (2011) Accelerated particle swarm optimization and support vector machine for business optimization and applications. In: Fong S (ed) Networked digital technologies. Springer, Berlin, pp 53–66
Giannakouris G, Vassiliadis V, Dounias G (2010) Experimental study on a hybrid nature-inspired algorithm for financial portfolio optimization. In: Konstantopoulos S, Perantonis S, Karkaletsis V, Spyropoulos CD, Vouros G (eds) Artificial intelligence: theories, models and applications. Springer, Berlin, pp 101–111
Fateen S-EK, Bonilla-Petriciolet A, Rangaiah GP (2012) Evaluation of covariance matrix adaptation evolution strategy, shuffled complex evolution and firefly algorithms for phase stability, phase equilibrium and chemical equilibrium problems. Chem Eng Res Des 90(12):2051–2071
Talatahari S, Gandomi AH, Yun GJ (2014) Optimum design of tower structures using firefly algorithm. Struct Des Tall Spec Build 23(5):350–361
Kazemzadeh AS (2011) Optimum design of structures using an improved firefly algorithm. Int J Optim Civ Eng 1(2):327–340
Gholizadeh S, Barati H (2012) A comprative study of three metaheuristics for optimum design of trusses
dos Santos AF, de Campos Velho HF, Luz EF, Freitas SR, Grell G, Gan MA (2013) Firefly optimization to determine the precipitation field on south america. Inverse Probl Sci Eng 21(3):451–466
Apostolopoulos T, Vlachos A (2010) Application of the firefly algorithm for solving the economic emissions load dispatch problem. Int J Comb 2011
Yang X-S, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl Soft Comput 12(3):1180–1186
Jeklene O (2011) Optimization of the quality of continuously cast steel slabs using the firefly algorithm. Mater Tehnol 45(4):347–350
Chatterjee A, Mahanti GK, Chatterjee A (2012) Design of a fully digital controlled reconfigurable switched beam concentric ring array antenna using firefly and particle swarm optimization algorithm. Prog Electromagn Res 36:113–131
Aungkulanon P, Chai-ead N, Luangpaiboon P (2011) Simulated manufacturing process improvement via particle swarm optimisation and firefly algorithms. Lect Not Eng Comput Sci 2:03
Rampriya B, Mahadevan K, Kannan SS (2010) Unit commitment in deregulated power system using lagrangian firefly algorithm. In: 2010 international conference on communication control and computing technologies, pp 389–393
Chandrasekaran SSK (2011) Demand response scheduling in scuc problem for solar integrated thermal system using firefly algorithm. IET Conf Proc 44–44(1)
Hu H (2012) Fa-based optimal strategy of train’s energy saving with energy materials. Adv Mater Res 485:93–96
Dekhici L, Borne P, Khaled B (2012) Firefly algorithm for economic power dispatching with pollutants emission. Inform Econ 16(2):45–57
Roeva O, Slavov T (2012) Firefly algorithm tuning of pid controller for glucose concentration control during e. coli fed-batch cultivation process. In: FedCSIS, pp 455–462
Roeva O (2012) Optimization of e. coli cultivation model parameters using firefly algorithm. Int J Bioautom 16(1):23–32
Abedinia O, Amjady N, Kiani K, Shayanfar H (2012) Fuzzy PID based on firefly algorithm: load frequency control in deregulated environment. In: Proceedings on the international conference on artificial intelligence (ICAI), p 1. The Steering Committee of The World Congress in Computer Science, Computer
Dutta R, Ganguli R, Mani V (2011) Exploring isospectral spring-mass systems with firefly algorithm. Proc R Soc A: Math Phys Eng Sci 467(2135):3222–3240
Banati H, Bajaj M (2011) Fire fly based feature selection approach. Int J Comput Sci Issues (IJCSI) 8(4):473
Horng M-H, Lee Y-X, Lee M-C, Liou R-J (2012) Firefly metaheuristic algorithm for training the radial basis function network for data classification and disease diagnosis. Theory New Appl Swarm Intell 4(7):115–132
Senthilnath J, Omkar S, Mani V (2011) Clustering using firefly algorithm: performance study. Swarm Evol Comput 1(3):164–171
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Kumar, V., Kumar, D. A Systematic Review on Firefly Algorithm: Past, Present, and Future. Arch Computat Methods Eng 28, 3269–3291 (2021). https://doi.org/10.1007/s11831-020-09498-y
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DOI: https://doi.org/10.1007/s11831-020-09498-y