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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>
== 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>{{cite journal | last1 = Horng | first1 = M.-H. | last2 = Jiang | first2 = T. W. | year = 2010 | title = The codebook design of image vector quantization based on the firefly algorithm | url = | journal = Computational Collective Intelligence, Technologies and Applications, LNCS | volume = 6423 | issue = | pages = 438–447 | doi=10.1007/978-3-642-16696-9_47}}</ref>
<ref>{{cite journal | last1 = Horng | first1 = M.-H. | year = 2011 | title = vector quantization using the firefly algorithm for image compression | url = | journal = Expert Systems with Applications | volume = 38 | issue = | page = }}</ref> For minimum cross entropy thresholding, firefly-based algorithm uses the least computation time<ref>{{cite journal | last1 = Horng | first1 = M.-H. | last2 = Liou | first2 = R.-J | year = 2011 | title = Multilevel minimum cross entropy threshold selection based on the firefly algorithm | url = | journal = Expert Systems with Applications | volume = 38 | issue = 12| pages = 14805–14811 | doi=10.1016/j.eswa.2011.05.069}}</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 ===
Eigenvalue optimization of isospectral systems has solved by FA and multiple optimum points have been found efficiently.<ref>{{cite journal | last1 = Dutta | first1 = R. | last2 = Ganguli | first2 = R. | last3 = Mani | first3 = V. | year = 2011 | title = Exploring isospectral spring-mass systems with firefly algorithm | url = http://rspa.royalsocietypublishing.org/content/early/2011/06/16/rspa.2011.0119.abstract | journal = Proc. Roy. Soc. A. | volume = 467 | issue = | page = }}</ref>
=== Nanoelectronic Integrated Circuit and System Design ===
The multiobjective firefly algorithm (MOFA) has been used for the design optimization of a 90 nm CMOS based operational amplifier (OP-AMP) which could perform simultaneous power minimization and slew rate maximization within 500 iterations.<ref>G. Zheng, S. P. Mohanty, E. Kougianos, and O. Okobiah, "[http://www.cse.unt.edu/~smohanty/Publications_Conferences/2013/Mohanty_ASAP2013_iVAMS-OPAMP.pdf iVAMS: Intelligent Metamodel-Integrated Verilog-AMS for Circuit-Accurate System-Level Mixed-Signal Design Exploration]", in Proceedings of the 24th IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP), 2013, pp. 75--78.</ref>
=== Feature selection and fault detection ===
Feature selection can be also carried out successfully using firefly algorithm.<ref>{{cite journal | last1 = Banati | first1 = H. | last2 = Bajaj | first2 = M. | year = 2011 | title = Firefly based feature selection approach | url = | journal = Int. J. Computer Science Issues | volume = 8 | issue = 2| pages = 473–480 }}</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>{{cite journal | last1 = Hu | first1 = Z. | last2 = Bao | first2 = Y. | last3 = Xiong | first3 = T. | last4 = Chiong | first4 = R. | year = 2015 | title = Hybrid filter–wrapper feature selection for short-term load forecasting | url = | journal = Engineering Applications of Artificial Intelligence | volume = 40 | issue = | pages = 17–27 | doi=10.1016/j.engappai.2014.12.014}}</ref>
===Antenna Design===
Firefly algorithms outperforms ABC for optimal design of linear array of isotropic sources <ref>{{cite journal | last1 = Basu | first1 = B. | last2 = Mahanti | first2 = G. K. | year = 2011 | title = Firefly and artificial bees colony algorithm for synthesis of scanned and broadside linear array antenna | url = | journal = Progress in Electromagnetic Research B. | volume = 32 | issue = | pages = 169–190 | doi=10.2528/pierb11053108}}</ref> and digital controllable array antenna.<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> It has found applications in synthesis of satellite footprint patterns as well.<ref>{{cite journal | last1 = Chatterjee | first1 = Anirban | last2 = Kumar Mahanti | first2 = Gautam | last3 = Ghatak | first3 = Gourab | year = 2014 | title = Synthesis of satellite footprint patterns from rectangular planar array antenna by using swarm-based optimization algorithms | url = | journal = Int. J. Satell. Commun. Network | volume = 32 | issue = | pages = 25–47 | doi=10.1002/sat.1055}}</ref>
===Structural Design===
For mixed-variable problems, many optimization algorithms may struggle. However, firefly algorithm can efficiently solve optimization problems with mixed variables.<ref>{{cite journal | last1 = Gandomi | first1 = A. H. | last2 = Yang | first2 = X. S. | last3 = Alavi | first3 = A. H. | year = 2011 | title = Mixed variable structural optimization using firefly algorithm | url = | journal = Computers and Structures | volume = 89 | issue = 23-24| pages = 2325–2336 | doi = 10.1016/j.compstruc.2011.08.002 }}</ref>
=== Scheduling and TSP ===
Firefly-based algorithms for scheduling task graphs and job shop scheduling requires less computing than all other metaheuristics.<ref>U. Hönig, A firefly algorithm-based approach for scheduling task graphs in homogeneous systems, Proceeding Informatics, {{doi|10.2316/P.2010.724-033}}, 724 (2010).</ref><ref>A. Khadwilard, S. Chansombat, T. Thepphakorn, P. Thapatsuwan, W. Chainat, P. Pongcharoen,
Application of firefly algorithm and its parameter setting for job shop scheduling, First Symposius on
Hands-On Research and Development, (2011).</ref>
A binary firefly algorithm has been developed to tackle the knapsack
cryptosystem efficiently<ref>S. Palit, S. Sinha, M. Molla, A. Khanra, M. Kule,
A cryptanalytic attack on the knapsack cryptosystem using binary Firefly algorithm,
in: 2nd Int. Conference on Computer and Communication Technology (ICCCT), 15-17 Sept 2011,India, pp. 428-432 (2011).</ref> Recently, an evolutionary discrete FA has been developed for solving [[travelling salesman problem]]s<ref>G. K. Jati and S. Suyanto, Evolutionary discrete firefly algorithm for travelling salesman problem, ICAIS2011, Lecture Notes in Artificial Intelligence (LNAI 6943), pp.393-403 (2011).</ref> Further improvement in performance can be obtained by using preferential directions in firefly movements.
===Semantic Web Composition===
A hybrid FA has been developed by Pop et al. for selecting optimal solution in semantic web service composition.<ref>C. B. Pop, V. R. Chifu, I. Salomie,R. B. Baico, M. Dinsoreanu, G. Copil, A hybrid firefly-inspired approach for optimal semantic web service composition, in: Proc. of 2nd Workshop on Software Services: Cloud Computing and Applications, June, 2011.</ref>
=== Chemical Phase equilibrium ===
For phase equilibrium calculations and stability analysis, FA was found to be the most reliable compared with other techniques.<ref>{{cite journal | last1 = Fateen | first1 = S. E. | last2 = Bonilla-Petrociolet | first2 = A. | last3 = Rangaiah | first3 = G. P. | year = 2012 | title = Evaluation of covariance matrix adaptation evolution strategy, shuffled complex evolution and firefly algorithms for phase stability, phase equilibrium and chemical equilibrium problems | url = | journal = Chemical Engineering Research and Design | volume = 90| issue = | pages = 2051–2071| doi = 10.1016/j.cherd.2012.04.011 }}</ref>
=== Clustering ===
Performance study for clustering also suggested that firefly algorithm is very efficient.<ref>J. Senthilnath, S. N. Omkar and V. Mani, Clustering using firefly algorithm: Performance study, Swarm and Evolutionary Computation, June (2011). {{doi|10.1016/j.swevo.2011.06.003}}</ref>
===Dynamic Problems===
Firefly algorithm can solve optimization problems in dynamic environments very efficiently.
<ref>S. M. Farahani, B. Nasiri and M. R. Meybodi, A multiswarm based firefly algorithm in dynamic environments, Third Int. Conference on Signal Processing Systems (ICSPS2011), Aug 27-28, Yantai, China, pp. 68-72 (2011)</ref><ref>A. A. Abshouri, M. R. Meybodi and A. Bakhtiary, New firefly algorithm based on multiswarm and learning automata in dynamic environments, Third Int. Conference on Signal Processing Systems (ICSPS2011), Aug 27-28, Yantai, China, pp. 73-77 (2011).</ref>
===Rigid Image Registration Problems===
Firefly algorithm can solve the rigid image registration problems more efficient than genetic algorithm, particle swarm optimization, and artificial bee colony <ref>Yudong Zhang and Lenan Wu, A Novel Method for Rigid Image Registration based on Firefly Algorithm, International Journal of Research and Reviews in Soft and Intelligent Computing, vol.2, no.2, pp. 141-146 (2012).</ref>
=== Protein Structure Prediction ===
Prediction of protein structures is NP-hard, and a recent study by Maher et al.<ref>{{cite journal | last1 = Maher | first1 = B. | last2 = Albrecht | first2 = A. | last3 = Loomes | first3 = M. | last4 = Yang | first4 = X. S. | last5 = Steinhofel | first5 = K. | year = 2014 | title = A firefly-inspired method for protein structure prediction in lattice models | url = | journal = Biomolucules | volume = 4 | issue = 1| pages = 56–75 | doi=10.3390/biom4010056}}</ref> shows that firefly-based methods can speed up the predictions.
Firefly algorithm can solve two dimensional HP model. In their experiment, they took 14 sequences of different chain lengths from 18 to 100 as the dataset and compared the FA with standard genetic algorithm and immune genetic algorithm. The averaged energy convergence results show that FA achieves the lowest values.<ref>{{cite journal|last1=Yudong|first1=Zhang|last2=Lenan|first2=Wu|last3=Shuihua|first3=Wang|title=Solving Two-Dimensional HP model by Firefly Algorithm and Simplified Energy Function|journal=Mathematical Problems in Engineering|date=2013|volume=2013|doi=10.1155/2013/398141|url=http://www.hindawi.com/journals/mpe/2013/398141/|pages=1–9}}</ref>
=== Parameter Optimization of SVM ===
Firefly algorithm (FA)is applied to determine the paraemters of MSVR (Multiple-output support vector regression) in interval-valued stock price index forecasting.<ref>{{cite journal | last1 = Xiong | first1 = Tao | last2 = Bao | first2 = Yukun | last3 = Hu | first3 = Zhongyi | year = 2014 | title = Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting | url = http://www.sciencedirect.com/science/article/pii/S0950705113003237 | journal = Knowl.-Based Syst. | volume = 55 | issue = | pages = 87–100 | doi=10.1016/j.knosys.2013.10.012}}</ref>
Meanwhile, 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>
=== IK-FA, Solving Inverse Kinematics using FA ===
FA, heuristic is used as inverse kinematics solver. The proposal is called IK-FA, for inverse Kinematics using Firefly Algorithm. Inverse kinematic consists in finding a valuable joints solution allowing achieving a specific end segment position. The proposed method used a forward kinematics model, the FA heuristic, a fitness function and a set of motions constraints, to solve inverse kinematics.<ref>Rokbani, Nizar, et al. "IK-FA, Inverse Kinematics Using Firefly Algorithm with Application to Biped Gait Generation, International Conference on Control, Engineering & Information Technology (CEIT’14), Tunisia, 2014</ref>
==See also==
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