Abstract
Firefly algorithm (FA) is a new swarm intelligence optimization method, which has shown good search abilities on many optimization problems. However, the performance of FA highly depends on its control parameters. In this paper, we investigate the control parameters of FA, and propose a modified FA called FA with adaptive control parameters (ApFA). To verify the performance of ApFA, experiments are conducted on a set of well-known benchmark problems. Results show that the ApFA outperforms the standard FA and five other recently proposed FA variants.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Amiri B, Hossain L, Crawford JW, Wigand RT (2013) Community detection in complex networks: multi-objective enhanced firefly algorithm. Knowl-Based Syst 46:1–11
Baykasoğlu A, Ozsoydan FB (2015) Adaptive firefly algorithm with chaos for mechanical design optimization problems. Appl Soft Computi 36:152–164
Castiglione A, De Prisco R, De Santis A, Fiore U, Palmieri F (2014) A botnet-based command and control approach relying on swarm intelligence. J Netw Comput Appl 38:22–33
Chen J, Lin Q, Hu Q (2010) Application of novel clonal algorithm in multiobjective optimization. Int J Inf Technol Decis Mak 9(2):239–266
Chen J, Lin Q, Ji Z (2011) Chaos-based multi-objective immune algorithm with a fine-grained selection mechanism. Soft Comput 15(7):1273–1288
Chen B, Shu H, Coatrieux G, Chen G, Sun X, Coatrieux JL (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51(1):124–144
Cheung NJ, Ding X-M, Shen H-B (2014) Adaptive firefly algorithm: parameter analysis and its application. PLoS One 9(11):e112634. doi:10.1371/journal.pone.0112634
Chhikara RR, Singh L (2015) An improved discrete firefly and t-test based algorithm for blind image steganalysis. In: The 6th international conference on intelligent systems, modelling and simulation (ISMS). IEEE, pp 58–63
dos Santos Coelho L, Mariani VC (2013) Improved firefly algorithm approach applied to chiller loading for energy conservation. Energy Build 59:273–278
Duan H, Luo Q (2015) New progresses in swarm intelligence-based computation. Int J Bio-Inspired Comput 7(1):26–35
Farahani SM, Abshouri AA, Nasiri B, Meybodi MR (2011) A gaussian firefly algorithm. Int J Mach Learn Comput 1(5):448–453
Fister Jr I, Yang X-S, Fister I, Brest J (2012) Memetic firefly algorithm for combinatorial optimization. arXiv preprint arXiv:1204.5165
Fister I, Yang X-S, Brest J (2013a) A comprehensive review of firefly algorithms. Swarm Evolut Comput 13:34–46
Fister I, Yang X-S, Brest J (2013b) Modified firefly algorithm using quaternion representation. Expert Syst Appl 40(18):7220–7230
Fister I, Perc M, Kamal SM (2015a) A review of chaos-based firefly algorithms. Appl Math Comput 252:155–165
Fister I Jr, Yang X-S, Brest J, Fister D, Fister I (2015b) Analysis of randomisation methods in swarm intelligence. Int J Bio-Inspired Comput 7(1):36–49
Florence AP, Shanthi V (2014) A load balancing model using firefly algorithm in cloud computing. J Comput Sci 10(7):1156–1165
Fu Z, Sun X, Liu Q, Zhou L, Shu J (2015) Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing. IEICE Trans Commun E98–B(1):190–200
Gandomi AH, Yang X-S, Talatahari S, Alavi AH (2013) Firefly algorithm with chaos. Commun Nonlinear Sci Numer Simul 18(1):89–98
García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Inf Sci 180(10):2044–2064
Gopinadh V, Singh A (2015) Swarm intelligence approaches for cover scheduling problem in wireless sensor networks. Int J Bio-Inspired Comput 7(1):50–61
Gu B, Sheng VS, Tay KY, Romano W, Li S (2015a) Incremental support vector learning for ordinal regression. IEEE Trans Neural Netw Learn Syst 26(7):1403–1416
Gu B, Sheng VS, Wang Z, Ho D, Osman S, and Li S (2015b) Incremental learning for \(\nu \)-support vector regression. Neural Netw 67:140–150
Hassanzadeh T, Vojodi H, Moghadam AME (2011) An image segmentation approach based on maximum variance intra-cluster method and firefly algorithm. In: The seventh international conference on natural computation (ICNC). IEEE, pp 1817–1821
Kazem A, Sharifi E, Hussain FK, Saberi M, Hussain OK (2013) Support vector regression with chaos-based firefly algorithm for stock market price forecasting. Appl Soft Comput 13(2):947–958
Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE Int Conf Neural Netw 4:1942–1948
Kougianos E, Mohanty SP (2015) A nature-inspired firefly algorithm based approach for nanoscale leakage optimal rtl structure. Integr VLSI J 51:46–60
Li J, Kim K (2010) Hidden attribute-based signatures without anonymity revocation. Inf Sci 180(9):1681–1689
Li J, Chen X, Li M, Li J, Lee PPC, Lou W (2014) Secure deduplication with efficient and reliable convergent key management. Parallel Distrib Syst IEEE Trans 25(6):1615–1625
Li J, Li X, Yang B, Sun X (2015a) Segmentation-based image copy-move forgery detection scheme. IEEE Trans Inf Forensics Secur 10(3):507–518
Li J, Li J, Chen X, Jia C, Lou W (2015b) Identity-based encryption with outsourced revocation in cloud computing. IEEE Trans Comput 64(2):425–437
Liang Z, Sun J, Lin Q, Zhihua D, Chen J, Ming Z (2016) A novel multiple rule sets data classification algorithm based on ant colony algorithm. Appl Soft Comput 38:1000–1011
Lin Q, Chen J (2013) A novel micro-population immune multiobjective optimization algorithm. Comput Oper Res 40(6):1590–1601
Lin Q, Zhu Q, Huang P, Chen J, Ming Z, Yu J (2015) A novel hybrid multi-objective immune algorithm with adaptive differential evolution. Comput Oper Res 62:95–111
Long NC, Meesad P, Unger H (2015) A highly accurate firefly based algorithm for heart disease prediction. Expert Syst Appl 42(21):8221–8231
Ma T, Zhou J, Tang M, Tian Y, Al-dhelaan A, Al-rodhann M, Lee S (2015) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans Inf Syst E98–D(4):902–910
Marichelvam MK, Prabaharan T, Yang XS (2014) A discrete firefly algorithm for the multi-objective hybrid flowshop scheduling problems. IEEE Trans Evolut Comput 18(2):301–305
Palit S, Sinha SN, Molla MA, Khanra A, Kule M (2011) A cryptanalytic attack on the knapsack cryptosystem using binary firefly algorithm. In: 2011 2nd international conference on computer and communication technology (ICCCT). IEEE, pp 428–432
Poursalehi N, Zolfaghari A, Minuchehr A (2013) Multi-objective loading pattern enhancement of pwr based on the discrete firefly algorithm. Ann Nucl Energy 57:151–163
Rahmani A, MirHassani SA (2014) A hybrid firefly-genetic algorithm for the capacitated facility location problem. Inf Sci 283:70–78
Ren Y, Shen J, Wang J, Han J, Lee S (2015) Mutual verifiable provable data auditing in public cloud storage. J Internet Technol 16(2):317–323
Roy AG, Rakshit P, Konar A, Bhattacharya S, Kim E, Nagar AK (2013) Adaptive firefly algorithm for nonholonomic motion planning of car-like system. In: IEEE congress on evolutionary computation (CEC 2013). IEEE, pp 2162–2169
Saraç E, Özel SA (2013) Web page classification using firefly optimization. In: IEEE international symposium on innovations in intelligent systems and applications (INISTA). IEEE, pp 1–5
Sayadi MK, Hafezalkotob A, Naini SGJ (2013) Firefly-inspired algorithm for discrete optimization problems: an application to manufacturing cell formation. J Manuf Syst 32(1):78–84
Senthilnath J, Omkar SN, Mani V (2011) Clustering using firefly algorithm: performance study. Swarm Evolut Comput 1(3):164–171
Shen J, Tan H, Wang J, Wang J, Lee S (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178
Shomalnasab F, Sadeghzadeh M, Esmaeilpour M (2014) An optimal similarity measure for collaborative filtering using firefly algorithm. J Adv Comput Res 5(3):101–111
Srivatsava PS, Mallikarjun B, Yang X-S (2013) Optimal test sequence generation using firefly algorithm. Swarm Evolut Comput 8:44–53
Verma OP, Aggarwal D, Patodi T (2016) Opposition and dimensional based modified firefly algorithm. Expert Syst Appl 44:168–176
Wang H, Rahnamayan S, Sun H, Omran MGH (2013) Gaussian bare-bones differential evolution. IEEE Trans Cybern 43(2):634–647
Wang B, Li D-X, Jiang J-P, Liao Y-H (2014) A modified firefly algorithm based on light intensity difference. J Combin Optim 1–16. doi:10.1007/s10878-014-9809-y
Wang H, Wang WJ, Sun H, Rahnamayan S (2016) Firefly algorithm with random attraction. Int J Bio-Inspired Comput 8(1):33–41
Wen X, Shao L, Xue Y, Fang W (2015) A rapid learning algorithm for vehicle classification. Inf Sci 295:395–406
Xia Z, Wang X, Sun X, Liu Q, Xiong N (2014a) Steganalysis of LSB matching using differences between nonadjacent pixels. Multimedia Tools and Applications. doi:10.1007/s11042-014-2381-8
Xia Z, Wang X, Sun X, Wang B (2014b) Steganalysis of least significant bit matching using multi-order differences. Secur Commun Netw 7(8):1283–1291
Xia Z, Wang X, Sun X, Wang Q (2015) A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parallel Distributed Syst. doi:10.1109/TPDS.2015.2401003
Xie S, Wang Y (2014) Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wirel Pers Commun 78(1):231–246
Xu M, Liu G (2013) A multipopulation firefly algorithm for correlated data routing in underwater wireless sensor networks. Int J Distrib Sens Netw. doi:10.1155/2013/865154
Yang X-S (2008) Nature-inspired metaheuristic algorithms. Luniver Press, Beckington
Yang X-S (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, New York
Yang X-S, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl Soft Comput 12(3):1180–1186
Yu S, Su S, Lu Q, Huang L (2014) A novel wise step strategy for firefly algorithm. Int J Comput Math 91(12):2507–2513
Yu S, Zhu S, Ma Y, Mao D (2015) A variable step size firefly algorithm for numerical optimization. Appl Math Comput 263:214–220
Zheng Y, Jeon B, Xu D, Wu QM, Zhang H (2015) Image segmentation by generalized hierarchical fuzzy C-means algorithm. J Intell Fuzzy Syst 28(2):961–973
Acknowledgments
This work is supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Humanity and Social Science Foundation of Ministry of Education of China (No. 13YJCZH174), the National Natural Science Foundation of China (Nos. 61305150, 61261039, 61402294, and 61572328), Major Fundamental Research Project in the Science and Technology Plan of Shenzhen under Grants (Nos. JCYJ20140 828163633977, JCYJ20140418181958501, and JCYJ201 50630105452814), Open Research Fund of China-UK Visual Information Processing Lab, National Social Science Foundation of China (No. 15CGL040), the Foundation of State Key Laboratory of Software Engineering (No. SKLSE2014-10-04), and the Natural Science Foundation of Jiangxi Province (Nos. 20142BAB217020 and 20151BAB217007).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
N/A.
Additional information
Communicated by V. Loia.
Rights and permissions
About this article
Cite this article
Wang, H., Zhou, X., Sun, H. et al. Firefly algorithm with adaptive control parameters. Soft Comput 21, 5091–5102 (2017). https://doi.org/10.1007/s00500-016-2104-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-016-2104-3