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/NAdaFa/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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=== Adaptive Firefly Algorithm (AdaFa) ===
An adaptive variant of firefly algorithm, termed AdaFa,<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>. In AdaFa, the parameter selection and adaptation strategies are investigated. There are three strategies in AdaFa including (1) a distance-based light absorption coefficient; (2) a gray coefficient enhancing fireflies to share difference information from attractive ones efficiently; and (3) five different dynamic strategies for the randomization parameter. Promising selections of parameters in the strategies are analyzed to guarantee the efficient performance of AdaFa.
