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Most metaheuristic algorithms may have difficulty in dealing with stochastic test functions, and it seems that firefly algorithm can deal with stochastic test functions<ref>{{cite journal |last=Yang |first=X.-S. |title=Firefly algorithm, stochastic test functions and design optimisation |journal=Int. J. Bio-inspired Computation |volume=2 |issue=2 |pages=78–84 |year=2010 |arxiv=1003.1409 |doi=10.1504/ijbic.2010.032124}}</ref> very efficiently. In addition, FA is also better for dealing with noisy optimization problems with ease of implementation.<ref>{{cite journal |first=N. |last=Chai-ead |first2=P. |last2=Aungkulanon |first3=P. |last3=Luangpaiboon |title=Bees and firefly algorithms for noisy non-linear optimisation problems |work=Prof. Int. Multiconference of Engineers and Computer Scientists 2011 |year=2011 |volume=2 |pages=1449–1454 }}</ref><ref>{{cite journal |first=P. |last=Aungkulanon |first2=N. |last2=Chai-ead |first3=P. |last3=Luangpaiboon |title=Simulated manufacturing process improvement via particle swarm optimisation and firefly algorithms |work=Prof. Int. Multiconference of Engineers and Computer Scientists 2011 |volume=2 |pages=1123–1128 |year=2011 }}</ref>
Chatterjee et al.<ref>{{cite journal | last1 = Chatterjee | first1 = A. Chatterjee,| last2 = Mahanti | first2 = G. K. Mahanti,| andlast3 = Chatterjee | first3 = A. Chatterjee,| year = 2012 | title = Design of a fully digital controlled reconfigurable switched beam conconcentric ring array antenna using firefly and particle swarm optimization algorithm, | url = | journal = Progress in Elelectromagnetic Research B, Vol.| volume = 36, 113-131(2012)| issue = | pages = 113–131 }}</ref> showed that the firefly algorithm can be superior to particle swarm optimization in their applications, the effectiveness of the firefly algorithm was further tested in later studies. In addition, firefly algorithm can efficiently solve non-convex problems with complex nonlinear constraints.<ref>{{cite journal | last1 = Yang | first1 = X. S. Yang,| last2 = Hosseini | first2 = S. S. Hosseini,| last3 = Gandomi | first3 = A. H. Gandomi,| year = | title = "Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect, ''| url = | journal = Applied Soft Computing'', Vol.| volume = 12( | issue = 3),| 1180-1186(2012)pages = 1180–1186 }}</ref><ref>{{cite journal | last1 = Abdullah | first1 = A. Abdullah,| last2 = Deris | first2 = S. Deris,| last3 = Mohamad | first3 = M. S. Mohamad| andlast4 = Hashim | first4 = S. Z. M. Hashim,| year = 2012 | title = A new hybrid firefly algorithm for complex and nonlinear problem, in: Distributed Computing and Artificial Intelligence, | url = | journal = Advances in Intelligent and Soft Computing, 2012,| Volumevolume = 151/2012, 673-680,| issue = {{doi| pages = 673–680 | doi = 10.1007/978-3-642-28765-7_81 }}</ref>
Further improvement on the performance is also possible with promising results.<ref>{{cite journal | last1 = Farahani | first1 = S. M. Farahani,| last2 = Abshouri | first2 = A. A. Abshouri,| last3 = Nasiri | first3 = B. Nasiri,| last4 = Meybodi | first4 = M. R. Meybodi,| year = 2012 | title = "Some hybrid models to improve firefly algorithm performance, ''| url = | journal = Int. J. Artificial Intelligence'', Vol.| volume = 8 S(12),| 97-117issue (2012)= S12| pages = 97–117 }}</ref><ref>{{cite journal | last1 = Nasiri | first1 = B. Nasiri,| last2 = Meybodi | first2 = M. R. Meybodi,| year = 2012 | title = "Speciation-based firefly algorithm for optimization in dynamic environments, ''| url = | journal = Int. J. Artificial Intelligence'', Vol.| volume = 8 (| issue = S12),| 118-132pages (2012)= 118–132 }}</ref>
== Variants of Firefly Algorithm ==
=== Modified Firefly Algorithm ===
Many variants and modifications are done to increase its performance. A particular example will be modified firefly algorithm by Tilahun and Ong .,<ref>S. L. Tilahun, H. C. Ong, "Modified Firefly Algorithm, ''Journal of Applied Mathematics, Volume'' 2012 (2012), Article ID: 467631 .</ref> in which the updating process of the brightest firefly is modified to keep the best result throughout the iterations.
== Applications ==
=== Digital Image Compression and Image Processing ===
Very recently, an FF-LBG algorithm for vector quantization of digital image compression was based on the firefly algorithm, which proves to be faster than other algorithms such as [[Particle swarm optimization|PSO]]-LBG and HBMO-LBG (particle swarm optimization and honey-bee mating optimization; variations on the [[Linde–Buzo–Gray algorithm]]).<ref>Horng M.-H. and Jiang T. W., The codebook design of image vector quantization based on the firefly algorithm, in: Computational Collective Intelligence, Technologies and Applications, LNCS, Vol. 6423, pp. 438-447 (2010).</ref>
<ref>M.-H. Horng, 2011 vector quantization using the firefly algorithm for image compression, ''Expert Systems with Applications,'' Vol. 38, (article in press) 12 Aug. (2011).:</ref> For minimum cross entropy thresholding, firefly-based algorithm uses the least computation time<ref>M.-H. Horng and R.-J Liou, 2011 Multilevel minimum cross entropy threshold selection based on the firefly algorithm, ''Expert Systems with Applications'', Vol. 38, Issue 12, 14805-14811 (2011).</ref> Also, for gel electrophoresis images, FA-based method is very efficient.<ref>M. H. M. Noor, A. R. Ahmad, Z. Hussain, K. A. Ahmad, A. R. Ainihayati, Multilevel thresholding of gel electrophoresis images using firefly algorithm, in: Proceedings of Control System, Computing and Engineering (ICCSCE2011), pp. 18-21 (2011).</ref>
=== Eigenvalue optimization ===
=== Feature selection and fault detection ===
Feature selection can be also carried out successfully using firefly algorithm.<ref>H. Banati and M. Bajaj, 2011 Firefly based feature selection approach, ''Int. J. Computer Science Issues'', vol. 8, No. 2, 473-480 (2011).</ref> Real-time fault identification in large systems becomes viable, based on the recent work on fault identification with binary adaptive firefly optimization.<ref>R. Falcon, M. Almeida and A. Nayak, Fault identification with binary adaptive fireflies in parallel and distributed systems, IEEE Congress on Evolutionary Computation, (2011).</ref>
A hybrid filter-wrapper feature selection for load forecasting is proposed based on Firefly Algorithm.<ref>Hu, Z., Bao, Y., Xiong, T., & Chiong, R. (2015). Hybrid filter–wrapper feature selection for short-term load forecasting. ''Engineering Applications of Artificial Intelligence'', 40, 17-27.</ref>
===Antenna Design===
Firefly algorithms outperforms ABC for optimal design of linear array of isotropic sources <ref>B. Basu and G. K. Mahanti, 2011 "Firefly and artificial bees colony algorithm for synthesis of scanned and broadside linear array antenna, ''Progress in Electromagnetic Research B.'', Vol. 32, 169-190 (2011).</ref> and digital controllable array antenna.<ref>A. Chatterjee, G. K. Mahanti, and A. Chatterjee, Design of a fully digital controlled reconfigurable switched beam conconcentric ring array antenna using firefly and particle swarm optimization algorithm, Progress in Elelectromagnetic Research B, Vol. 36, 113-131(2012)</ref> It has found applications in synthesis of satellite footprint patterns as well.<ref>Anirban Chatterjee, Gautam Kumar Mahanti and Gourab Ghatak, Synthesis of satellite footprint patterns from rectangular planar array antenna by using swarm-based optimization algorithms, Int. J. Satell. Commun. Network. 2014; 32:25–47</ref>
===Structural Design===
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