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Further, classical variants of the algorithm have unexpected parameter settings and limited update laws, notably the homogeneous rule needs to be improved in order to do more search on different fitness landscape. Ref. analyzes the trajectory of a single firefly in the traditional algorithm and an adaptive variant, respectively. These analyses lead to a general model of the algorithms including a set of the boundary conditions for the parameters guaranteeing the convergence tendencies of the two algorithms.<ref>{{cite journal |first=Ngaam J. |last=Cheung |first2=X.-M.|last2=Ding |first3=H.-B. |last3=Shen |title=A Non-Homogeneous Firefly Algorithm and Its Convergence Analysis |journal=Journal of Optimization Theory and Applications |volume= |issue= |pages= |year=2016 |url=http://godzilla.uchicago.edu/pages/ngaam/NAdaFa/index.html |doi=10.1007/s10957-016-0875-4}}</ref>
== Variants of Firefly Algorithm ==
A recent, comprehensive review showed that the firefly algorithm and its variants have been used in almost all areas of science<ref>{{cite journal | last1 = Fister | first1 = I. | last2 = Fister | first2 = Jr. | last3 = Yang | first3 = X. S. | last4 = Brest | first4 = J. | year = 2013 | title = A comprehensive review of firefly algorithms | url = | journal = Swarm and Evolutionary Computation | volume = 13 | issue = 1| pages = 34–46 | doi=10.1016/j.swevo.2013.06.001}}</ref> There are more than twenty variants:
=== 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.
=== Discrete Firefly Algorithm (DFA) ===
A discrete version of Firefly Algorithm, namely, Discrete Firefly Algorithm (DFA) proposed recently by M. K. Sayadi, R. Ramezanian and N. Ghaffari-Nasab can efficiently solve NP-hard scheduling problems.<ref>{{cite journal |first=M. K. |last=Sayadi |first2=R. |last2=Ramezanian |first3=N. |last3=Ghaffari-Nasab |title=A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems |journal=Int. J. of Industrial Engineering Computations |volume=1 |issue= |pages=1–10 |year=2010 |url=http://growingscience.com/ijiec/VOL1/IJIEC_2010_7.pdf |doi=10.5267/j.ijiec.2010.01.001}}</ref> DFA outperforms existing algorithms such as the ant colony algorithm.
For image segmentation, the FA-based method is far more efficient to Otsu's method and recursive Otsu.<ref>T. Hassanzadeh, H. Vojodi and A. M. E. Moghadam, An image segmentation approach based on maximum variance intra-cluster method and firefly algorithm, in: Proc. of 7th Int. Conf. on Natural Computation (ICNC), pp. 1817-1821 (2011).</ref> Meanwhile, a good implementation of a discrete firefly algorithm for QAP problems has been carried out by Durkota.<ref>K. Durkota,
Implementation of a discrete firefly algorithm for the QAP problem within the sage framework, BSc thesis, Czech Technical University, (2011).
http://cyber.felk.cvut.cz/research/theses/papers/189.pdf</ref>
=== Multiobjective FA ===
An important study of FA was carried out by Apostolopoulos and Vlachos,<ref>{{cite journal |first=T. |last=Apostolopoulos |first2=A. |last2=Vlachos |title=Application of the Firefly Algorithm for Solving the Economic Emissions Load Dispatch Problem |journal=International Journal of Combinatorics |volume=2011 |year=2011 |page=Article ID 523806 |url=http://www.hindawi.com/journals/ijct/2011/523806.html }}</ref> which provides a detailed background and analysis over a wide range of test problems including multobjective load dispatch problem.
=== Lagrangian FA ===
An interesting, Lagrangian firefly algorithm is proposed to solve power system optimization unit commitment problems.<ref>Rampriya B., Mahadevan K. and Kannan S., Unit commitment in deregulated power system using Lagrangian firefly algorithm, Proc. of IEEE Int. Conf. on Communication Control and Computing Technologies (ICCCCT), pp. 389-393 (2010).</ref>
=== Chaotic FA ===
A chaotic firefly algorithm (CFA) was developed and found to outperform the previously best-known solutions available.<ref>L. dos Santos Coelho, D. L. de Andrade Bernert, V. C. Mariani, a chaotic firefly algorithm applied to reliability-redundancy optimization, in: 2011 IEEE Congress on Evolutionary Computation (CEC'11), pp. 517-521 (2011).</ref>
=== Hybrid Algorithms ===
A [[hybrid algorithm|hybrid]] intelligent scheme has been developed by combining the firefly algorithm with the ant colony optimization.<ref>{{cite journal | last1 = Giannakouris | first1 = G. | last2 = Vassiliadis | first2 = V. | last3 = Dounias | first3 = G. | year = 2010 | title = Experimental study on a hybrid nature-inspired algorithm for financial portfolio optimization | url = | journal = SETN | volume = 6040 | issue = | pages = 101–111 | doi=10.1007/978-3-642-12842-4_14}}</ref>
=== Firefly Algorithm Based Memetic Algorithm===
A firefly algorithm (FA) based memetic algorithm (FA-MA) is proposed to appropriately determine the parameters of SVR forecasting model for electricity load forecasting. In the proposed FA-MA algorithm, the FA algorithm is applied to explore the solution space, and the pattern search is used to conduct individual learning and thus enhance the exploitation of FA.<ref>Zhongyi Hu, Yukun Bao, and Tao Xiong, Electricity Load Forecasting using Support Vector Regression with Memetic Algorithms, The Scientific World Journal, 2014, http://www.hindawi.com/journals/tswj/aip/292575/</ref>
=== Parallel Firefly Algorithm with Predation (pFAP) ===
An implementation for shared memory environments with the addition of a predation mechanism that helps the method to escape local optimum.<ref>E. F. P. Luz, H. F. Campos Velho, J. C. Becceneri, Firefly Algorithm with Predation: A parallel implementation applied to inverse heat conduction problem, in: Proc. of 10th World Congress on Computational Mechanics (WCCM 2012), (2012).</ref>
=== 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>{{cite journal | last1 = Tilahun | first1 = S. L. | last2 = Ong | first2 = H. C. | year = | title = Modified Firefly Algorithm | url = | journal = Journal of Applied Mathematics | volume = 2012 | issue = | page = 467631 }}</ref> in which the updating process of the brightest firefly is modified to keep the best result throughout the iterations. Another example is a modified firefly algorithm to solve univariate nonlinear equations having real as well as complex roots.<ref>{{Cite journal|last = Ariyaratne|first = M. K. A.|last2 = Fernando|first2 = T. G. I.|last3 = Weerakoon|first3 = S.|date = 2015-08-01|title = A modified firefly algorithm to solve univariate nonlinear equations with complex roots|url = http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7377683|journal = 2015 Fifteenth International Conference on Advances in ICT for Emerging Regions (ICTer)|pages = 160–167|doi = 10.1109/ICTER.2015.7377683}}</ref>
==See also==
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