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Chatterjee et al.<ref>{{cite journal | last1 = Chatterjee | first1 = A. | last2 = Mahanti | first2 = G. K. | last3 = Chatterjee | first3 = A. | 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 | volume = 36 | issue = | pages = 113–131 | doi=10.2528/pierb11083005}}</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. | last2 = Hosseini | first2 = S. S. | last3 = Gandomi | first3 = A. H. | year = | title = Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect | url = | journal = Applied Soft Computing | volume = 12 | issue = 3| pages = 1180–1186 | doi=10.1016/j.asoc.2011.09.017}}</ref><ref>{{cite journal | last1 = Abdullah | first1 = A. | last2 = Deris | first2 = S. | last3 = Mohamad | first3 = M. S. | last4 = Hashim | first4 = S. Z. M. | 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 | volume = 151 | issue = | 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. | last2 = Abshouri | first2 = A. A. | last3 = Nasiri | first3 = B. | last4 = Meybodi | first4 = M. R. | year = 2012 | title = Some hybrid models to improve firefly algorithm performance | url = | journal = Int. J. Artificial Intelligence | volume = 8 | issue = S12| pages = 97–117 }}</ref><ref>{{cite journal | last1 = Nasiri | first1 = B. | last2 = Meybodi | first2 = M. R. | year = 2012 | title = Speciation-based firefly algorithm for optimization in dynamic environments | url = | journal = Int. J. Artificial Intelligence | volume = 8 | issue = S12| pages = 118–132 }}</ref>
== Theoretical Analysis ==
Although much progress has been achieved FA-based algorithms since 2008, significant efforts are required to further improve the performance of FA <ref>http://godzilla.uchicago.edu/pages/ngaam/AdaFa/index.html</ref>:
* Theoretical analysis for convergence trajectory;
* Deriving the sufficient and necessary conditions for the selections of control coefficients;
* Efficient strategies or mechanisms for the selections of the control parameters;
* Non-homogeneous update rules for enhancing the search ability <ref>http://godzilla.uchicago.edu/pages/ngaam/AdaFa/index.html</ref>, was proposed in ref. <ref>{{cite journal |first=Ngaam J. |last=Cheung |first2=X.-M.|last2=Ding |first3=H.-B. |last3=Shen |title=Adaptive Firefly Algorithm: Parameter Analysis and its Application |journal=PLOS One |volume=9 |issue=11 |pages= e112634 |year=2014 |url=http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0112634 |doi=10.1371/journal.pone.0112634}}</ref>.
== Variants of Firefly Algorithm ==
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