CHALLENGES IN EVOLUTIONARY ALGORITHM TO FIND OPTIMAL PARAMETERS OF SVM: A REVIEW

Ashish Kumar Namdeo; Dileep Kumar Singh

doi:10.29121/shodhkosh.v5.i6.2024.1985

Authors

Ashish Kumar Namdeo School Of Engineering And Technology, Jagran Lakecity University, Bhopal (M.P.), India
Dr. Dileep Kumar Singh School Of Engineering And Technology, Jagran Lakecity University, Bhopal (M.P.) India

DOI:

https://doi.org/10.29121/shodhkosh.v5.i6.2024.1985

Keywords:

Particle Swarm Optimization, Genetic Algorithm, Firefly Algorithm, Fruitfly Optimization Algorithm, Cuckoo Search, Ski-Driver Algorithm, Support Vector Machines Introduction

Abstract [English]

In rapidly changing classification and predation environment, optimization techniques in determining the hyper parameter of Support Vector Machine has become crucial for the accuracy of result. It’s an important tool for improving output quality of classification and prediction which includes modeling parameters relationship and resolution of optimal hyper parameter. However, determination of regularization (C) and gamma (γ), through mathematical models have undergone substantial development and expansion. In this paper, optimization techniques are categorized under several criteria. We also included the benchmarks for measuring the performance of classifier after parameter tuning, and found there is still a scope of improvement.

References

V. N. Vapnik, Statistical learning theory, Wiley, NewYork, 1998.

B. Schölkopf, A.J. Smola, Learning with kernels:Support vector machines, regularization, optimization,and beyond, Cambridge, Mass: MIT Press, London,2002. DOI: https://doi.org/10.7551/mitpress/4175.001.0001

O. L. Mangasarian and D.R. Musicant, ``Successive overrelaxation for support vector machines," IEEETrans. on Neural Networks, vol. 10, no. 5, pp DOI: https://doi.org/10.1109/72.788643

Cortes, Corinna, and Vladimir Vapnik. "Support-vector networks." sMachine learning 20.3 (1995): 273-297. DOI: https://doi.org/10.1007/BF00994018

Drucker, Harris, Donghui Wu, and Vladimir N. Vapnik. "Support vector machines for spam categorization." IEEE Transactions on Neural networks 10.5 (1999): 1048-1054. DOI: https://doi.org/10.1109/72.788645

G.O.Young, “Syntheticstructureofindustrialplastics,”in Plastics, 2nd ed., vol. 3, J. Peters, Ed. New York: McGraw-Hill,1964,pp.15–64.

Mukkamala, Srinivas, Andrew H. Sung, and Ajith Abraham. "Intrusion detection using an ensemble of intelligent paradigms." Journal of network and computer applications 28.2 (2005): 167-182. DOI: https://doi.org/10.1016/j.jnca.2004.01.003

Duan K, Keerthi SS, Poo AN (2003) Evaluation of simple performance measures for tuning SVM hyperparameters. Neurocomputing 51:41–59 DOI: https://doi.org/10.1016/S0925-2312(02)00601-X

Eitrich T, Lang B (2006) Efficient optimization of Support Vector Machine learning parameters for unbalanced data sets. J ComputAppl Math 196(2):425–436 DOI: https://doi.org/10.1016/j.cam.2005.09.009

Friedrichs F, Igel C (2004) Evolutionary tuning of multiple SVM parameters. In: Trends in neurocomputing: 12th European symp on artificial neural networks 2004, vol 64, pp 107–117

Frohlich H, Zell A (2005) Efficient parameter selection for Support Vector Machines in classification and regression via model-based global optimization. In: Proc of IEEE int joint conf on neural networks (IJCNN ’05), 31 July–4 Aug 2005, vol 3, pp 1431–1436 DOI: https://doi.org/10.1109/IJCNN.2005.1556085

Gold C, Sollich P (2005) Fast Bayesian Support Vector Machine parameter tuning with the nystrom method. In: Proc. of the IEEE int joint conf on neural networks (IJCNN ’05), July 31–August 4, 2005, Montréal, Québec, Canada, vol 5, pp 2820–2825 DOI: https://doi.org/10.1109/IJCNN.2005.1556372

Imbault F, Lebart K (2004) A stochastic optimization approach for parameter tuning of support vector machines. In: Proc of the 17th intconf on pattern recognition (ICPR 2004), 23–26 August 2004, Cambridge, UK, vol 4, pp 597–600 DOI: https://doi.org/10.1109/ICPR.2004.1333843

Kulkarni A, Jayaraman VK, Kulkarni BD (2004) Support vector classification with parameter tuning assisted by agent-based technique. ComputChemEng 28(3):311–318 DOI: https://doi.org/10.1016/S0098-1354(03)00188-1

Kurasova O, Dzemyda G, Vainoras A (2007) Parameter system for human physiological data representation and analysis. In: Proc of 3rd Iberian conf on pattern recognition and image analysis, IbPRIA 2007, Girona, Spain, June 6–8, 2007. LNCS, vol 4477, pp 209–216 DOI: https://doi.org/10.1007/978-3-540-72847-4_28

Mattera D, Haykin S (1999) Support vector machines for dynamic reconstruction of a chaotic system. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in kernel methods: support vector learning, pp 209–241 DOI: https://doi.org/10.7551/mitpress/1130.003.0018

Chapelle O, Vapnik V, Bousquet O, Mukherjee S (2002) Choosing multiple parameters for support vector machines. Mach Learn 46(1–3):131–159 DOI: https://doi.org/10.1023/A:1012450327387

Smola AJ, Murata N, Schölkopf B, Miller KR (1998) Asymptotically optimal choice of ε-loss for support vector machines. In: Proc of 8th int conference on artificial neural networks, Berlin, Germany, pp 105–110 DOI: https://doi.org/10.1007/978-1-4471-1599-1_11

Cassabaum ML, Waagen DE, Rodriguez JJ, Schmitt HA (2004) Unsupervised optimization of Support Vector Machine parameters. In: Kadar I (ed) Automatic target recognition XIV. Proc of SPIE, vol 5426(1), SPIE Defense & Security Symposium, Orlando, FL, April 13–15, 2004, pp 316–325

Debnath R, Takahashi H (2004) An efficient method for tuning kernel parameter of the support vector machine. In: Proc of the IEEE intsymp on communications and information technology (ISCIT 2004), Sapporo, Japan, October 2004, vol 2, pp 1023–1028 DOI: https://doi.org/10.1109/ISCIT.2004.1413874

Lim H (2004). Support vector parameter selection using experimental design based generating set search (SVEG) with application to predictive software data modeling. PhD thesis, Syracuse University

Schittkowski K (2005) Optimal parameter selection in Support Vector Machines. J IndManagOptim 1(4):465–476 DOI: https://doi.org/10.3934/jimo.2005.1.465

Ancona N, Cicirelli G, Stella E, Distante A (2002) Object detection in images: Run-time complexity and parameter selection of Support Vector Machines. In: Proc of the 16th intconf on pattern recognition (ICPR’02), 11–15 August 2002, Quebec, Canada, vol 2, pp 426–429 DOI: https://doi.org/10.1109/ICPR.2002.1048330

Quan Y, Yang J (2003) An improved parameter tuning method for support vector machines. In: Proc of 9th intconf on rough sets, fuzzy sets, data mining, and granular computing (RSFDGrC 2003), Chongqing, China, May 26–29, 2003, pp 607–610 DOI: https://doi.org/10.1007/3-540-39205-X_99

Ali S, Smith KA (2003) Automatic parameter selection for polynomial kernel. In: Proc of the IEEE intconf on information reuse and integration (IRI 2003), October 27–29, 2003, Las Vegas, NV, USA, pp 243–249 DOI: https://doi.org/10.1109/IRI.2003.1251420

Zhuang L, Dai H (2006) Parameter optimization of kernel-based one-class classifier on imbalance learning. J Comput 1(7):32–40 DOI: https://doi.org/10.4304/jcp.1.7.32-40

Christmann A, Luebke K, Rüping S, Marin-Galianos M (2005) Determination of hyperparameters for kernel-based classification and regression. Technical report 38/05, SFB475, University of Dortmund, Germany

Boardman M, Trappenberg T (2006) A heuristic for free parameter optimization with Support Vector Machines. In: Proc of IEEE int joint conf on neural networks (IJCNN 2006), July 16–21, 2006, Vancouver, Canada, pp 1337–1344 DOI: https://doi.org/10.1109/IJCNN.2006.246739

Cherkassky V, Mulier F (1998) Learning from data: concepts, theory, and methods. Wiley, New York

Ayat NE, Cheriet M, Suen CY (2002) Empirical error based optimization of SVM kernels: Application to digit image recognition. In: Proc of the 8th int workshop on frontiers in handwriting recognition (IWFHR’02), August 6–8, 2002, p 292 DOI: https://doi.org/10.1109/IWFHR.2002.1030925

Fawcett, Tom. "ROC graphs: Notes and practical considerations for researchers." Machine learning 31.1 (2004): 1-38.

Hanley, James A., and Barbara J. McNeil. "The meaning and use of the area under a receiver operating characteristic (ROC) curve." Radiology 143.1 (1982): 29-36. DOI: https://doi.org/10.1148/radiology.143.1.7063747

Hajian-Tilaki, Karimollah. "Receiver operating characteristic (ROC) curve analysis for medical diagnostic test evaluation." Caspian journal of internal medicine 4.2 (2013): 627.

Lisowsky, Petro. "Seeking shelter: Empirically modeling tax shelters using financial statement information." The Accounting Review 85.5 (2010): 1693-1720. DOI: https://doi.org/10.2308/accr.2010.85.5.1693

Fawcett, Tom. "An introduction to ROC analysis." Pattern recognition letters 27.8 (2006): 861-874.

Fürnkranz, Johannes, and Peter A. Flach. "Roc ‘n’rule learning—towards a better understanding of covering algorithms." Machine Learning 58.1 (2005): 39-77. DOI: https://doi.org/10.1007/s10994-005-5011-x

Hand, David J., and Robert J. Till. "A simple generalisation of the area under the ROC curve for multiple class classification problems." Machine learning 45.2 (2001): 171-186. DOI: https://doi.org/10.1023/A:1010920819831

Zou, Kelly H. "Receiver operating characteristic (ROC) literature research." On-line bibliography available from:< http://splweb. bwh. harvard. edu 8000 (2002).

Fawcett, Tom. "An introduction to ROC analysis." Pattern recognition letters 27.8 (2006): 861-874. DOI: https://doi.org/10.1016/j.patrec.2005.10.010

W.-T. Pan, “A new fruit fly optimization algorithm: Taking the financial distress model as an example”, Knowledge-Based Systems, vol. 26, (2012), pp. 69-74. DOI: https://doi.org/10.1016/j.knosys.2011.07.001

Huang, Cheng-Lung, and Jian-Fan Dun. "A distributed PSO–SVM hybrid system with feature selection and parameter optimization." Applied Soft Computing 8.4 (2008): 1381-1391. DOI: https://doi.org/10.1016/j.asoc.2007.10.007

Provost, Foster J., and Tom Fawcett. "Analysis and visualization of classifier performance: Comparison under imprecise class and cost distributions." KDD. Vol. 97. 1997.

Huang, Cheng-Lung, and Chieh-Jen Wang. "A GA-based feature selection and parameters optimizationfor support vector machines." Expert Systems with applications 31.2 (2006): 231-240. DOI: https://doi.org/10.1016/j.eswa.2005.09.024

Shen, Liming, et al. "Fruit fly optimization algorithm based SVM classifier for efficient detection of Parkinson’s disease." International Conference in Swarm Intelligence. Springer International Publishing, 2015. DOI: https://doi.org/10.1007/978-3-319-20472-7_11

Chao, Chih-Feng, and Ming-HuwiHorng. "Theconstruction of support vector machine classifier using the firefly algorithm." Computational intelligence and neuroscience 2015 (2015). DOI: https://doi.org/10.1155/2015/212719

A. Asunicion , D. Newman, UCI Machine Learning Repository2013,http://www.ics.uci.edu/∼mlearn/MLRepository.html.

Chang, Chih-Chung, and Chih-Jen Lin. "LIBSVM: a library for support vector machines." ACM Transactions on Intelligent Systems and Technology (TIST)2.3 (2011): 27. DOI: https://doi.org/10.1145/1961189.1961199

Allah, Rizk M. Rizk. "Hybridization of Fruit Fly Optimization Algorithm and Firefly Algorithm for Solving Nonlinear Programming Problems." International Journal of Swarm Intelligence and Evolutionary Computation 5.2: 1000134.

Ye, Fei, Xin Yuan Lou, and Lin Fu Sun. "An improved chaotic fruit fly optimization based on a mutation strategy for simultaneous feature selection and parameter optimization for SVM and its applications." PloS one 12.4 (2017): e0173516.

Zhang, Qiantu, et al. "Parameters Optimization of SVM Based on Improved FOA and Its Application in Fault Diagnosis." JSW 10.11 (2015): 1301-1309

Jiang, Ai-hua, and Ni-xiao Liang. "Short-term load forecasting using support vector machine optimized by the improved fruit fly algorithm and the similar day method." Electricity Distribution (CICED), 2014 China International Conference on. IEEE, 2014. DOI: https://doi.org/10.1109/CICED.2014.6991949

Luo, Huixia, et al. "Mixed Fruit Fly Optimization Algorithm Based on Lozi's Chaotic Mapping." P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC), 2014 Ninth International Conference on. IEEE, 2014. DOI: https://doi.org/10.1109/3PGCIC.2014.54

Egan, James P. "Signal detection theory and {ROC} analysis." (1975).

Weston, Jason, and Chris Watkins. Multi-class support vector machines. Technical Report CSD-TR-98-04, Department of Computer Science, Royal Holloway, University of London, May, 1998.

Bredensteiner, Erin J., and Kristin P. Bennett. "Multicategory classification by support vector machines." Computational Optimization. Springer US, 1999. 53-79. DOI: https://doi.org/10.1007/978-1-4615-5197-3_5

Crammer, Koby, and Yoram Singer. "On the algorithmic implementation of multiclass kernel-based vector machines." Journal of machine learning research 2.Dec (2001): 265-292.

Lee, Yoonkyung, Yi Lin, and Grace Wahba. "Multicategory support vector machines: Theory and application to the classification of microarray data and satellite radiance data." Journal of the American Statistical Association 99.465 (2004): 67-81. DOI: https://doi.org/10.1198/016214504000000098

Shen, Liming, et al. "Evolving support vector machines using fruit fly optimization for medical data classification." Knowledge-Based Systems 96 (2016): 61-75. DOI: https://doi.org/10.1016/j.knosys.2016.01.002

D.H. Wolpert, W.G. Macready, No free lunch theorems for optimization, IEEE Transactions on Evolutionary Computation 1 (1997),pp.67–82.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA: Addison-Wesley, 1989

J. H. Holland, Adaptation in natural and artificial systems : an introductory analysis with applications to biology, control, and artificial intelligence. Cambridge, MA: MIT Press, 1994.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 2nd ed. Berlin: Springer, 1994. DOI: https://doi.org/10.1007/978-3-662-07418-3

H.-N. Nguyen, S.-Y. Ohn, and W.-J. Choi, “Combined kernel function for support vector machine and learning method based on evolutionary algorithm,” in Neural Information Processing: 11th International Conference - Proc. of ICONIP 2004, Calcutta, India, Nov 22-25, 2004. Heidelberg: Springer, 2004, pp.1273–1278, dOI 10.1007/b103766. DOI: https://doi.org/10.1007/978-3-540-30499-9_198

S.-Y. Ohn, H.-N. Nguyen, D. S. Kim, and J. S. Park, “Determining optimal decision model for support vector machine by genetic algorithm,” in Computational and Information Science: First International Symposium - Proc. of CIS 2004, Shanghai, China,Dec 16-18, 2004. Heidelberg: Springer, 2004, pp. 592–597, dOI 10.1007/b104566.

S.-Y. Ohn, H.-N. Nguyen, and S.-D. Chi, “Evolutionary parameter estimation algorithm for combined kernel function in support vector machine,” in Content Computing: Advanced Workshopon Content Computing – Proc. of AWCC 2004, ZhenJiang, JiangSu, China, Nov 15-17, 2004. Heidelberg: Springer, 2004, pp. 592–597, dOI 10.1007/b103383.

F. Friedrichs and C. Igel, “Evolutionary tuning of multiple svm parameters,” Neurocomputing (in press), 2005. DOI: https://doi.org/10.1016/j.neucom.2004.11.022

D. Eads, D. Hill, S. Davis, S. Perkins, J. Ma, R. Porter, and J. Theiler, “Genetic algorithms and support vector machines for time series classification,” in Proc. of Fifth Conf. on the Applications and Science of Neural Networks, Fuzzy Systems, and Evolutionary Computation. Symposium on Optical Science and Technology of the 2002 SPIE Annual Meeting, Seattle, WA, July 2002., 2002, pp. 74–85, lA-UR-02-6212. DOI: https://doi.org/10.1117/12.453526

Kennedy, J.; Eberhart, R.,“Particle Swarm Optimization”,Proceedings of IEEE International Conference on NeuralNetworks. IV. pp. 1942–1948, 1995. DOI: https://doi.org/10.1109/ICNN.1995.488968

J.H. Holland,"Genetic algorithms and the optimal allocationof trials, SIAM J. Comput. 2 (2), pp. 88–105, 1973. DOI: https://doi.org/10.1137/0202009

Yang, X. S.,"Nature-Inspired Metaheuristic Algorithms",Frome: Luniver Press, 2008.

Yang, Xin-She, Suash Deb, and Simon Fong. "Accelerated particle swarm optimization and support vector machine for business optimization and applications." Networked digital technologies (2011): 53-66. DOI: https://doi.org/10.1007/978-3-642-22185-9_6

Zhang, Qiantu, et al. "Parameters Optimization of SVM Based on Improved FOA and Its Application in Fault Diagnosis." JSW 10.11 (2015): 1301-1309. DOI: https://doi.org/10.17706//jsw.10.11.1301-1309

Mitić, Marko, et al. "Chaotic fruit fly optimization algorithm." Knowledge-Based Systems 89 (2015): 446-458.

Jiang, Minlan, et al. "A cuckoo search-support vector machine model for predicting dynamic measurement errors of sensors." IEEE Access 4 (2016): 5030-5037. DOI: https://doi.org/10.1109/ACCESS.2016.2605041

Yang X. Nature-inspired metaheuristic algorithms. Luniver Press; 2008.

Yang X-S, Deb S. Cuckoo search via levy flights. In: World congress on nature and biologically inspired computing; 2009. p. 210–4.

Blum, C. and Roli, A. (2003). Metaheuristics in combinatorial optimization: overview and conceptural comparision, ACM Comput. Surv., 35(2), 268–308. DOI: https://doi.org/10.1145/937503.937505

Yang X. S., (2010). Engineering Optimisation: An Introduction with Metaheuristic Applications, John Wiley and Sons. DOI: https://doi.org/10.1002/9780470640425

Wolpert D. H. andMacreadyW. G. No free lunch theorems for optimization, IEEE Transaction on Evolutionary Computation 1997; 1(1): 67–82 DOI: https://doi.org/10.1109/4235.585893

Mitić, Marko, et al. "Chaotic fruit fly optimization algorithm." Knowledge-Based Systems 89 (2015): 446-458. DOI: https://doi.org/10.1016/j.knosys.2015.08.010

Wolpert D. H. and Macready W. G. Coevolutonary free lunches, IEEE Trans. EvolutionaryComputation 2005; 9(6):,721–735. DOI: https://doi.org/10.1109/TEVC.2005.856205

Yang, X. S. and Deb, S., (2009). Cuckoo search via L´evy flights, Proceeings of World Congresson Nature & Biologically Inspired Computing (NaBIC 2009), IEEE Publications, USA, pp.210–214. DOI: https://doi.org/10.1109/NABIC.2009.5393690

Pavlyukevich I. (2007). L´evy flights, non-local search and simulated annealing, J. Computational Physics, 226, 1830–1844. DOI: https://doi.org/10.1016/j.jcp.2007.06.008

Yang X. S. and Deb S., (2010). Engineering optimization by cuckoo search, Int. J. Math.Modelling Num. Opt., 1 (4), 330–343 (2010). DOI: https://doi.org/10.1504/IJMMNO.2010.035430

Yang, X.S. and Deb, S. (2013). Multiobjective cuckoo search for design optimization, Computers and Operations Research, 40(6), 1616–1624 (2013). DOI: https://doi.org/10.1016/j.cor.2011.09.026

Walton, S., Hassan, O., Morgan, K., and Brown, M.R. (2011). Modified cuckoo search: a newgradient free optimization algorithm. Chaos, Solitons & Fractals, 44(9), 710-718. DOI: https://doi.org/10.1016/j.chaos.2011.06.004

Chandrasekaran, K., and Simon, S. P., (2012). Multi-objective scheduling problem: hybrid appraoch using fuzzy assisted cuckoo search algorithm, Swarm and Evolutionary Computation,5(1), pp. 1-16. DOI: https://doi.org/10.1016/j.swevo.2012.01.001

Dhivya, M., Sundarambal, M., Anand, L. N., (2011). Energy efficient computation of data fusion in wireless sensor networks using cuckoo based particle approach (CBPA), Int. J. of Communications, Network and System Sciences, 4, No. 4, pp. 249-255. DOI: https://doi.org/10.4236/ijcns.2011.44030

Dhivya, M. and Sundarambal, M., (2011). Cuckoo search for data gathering in wireless sensor networks, Int. J. Mobile Communications, 9, pp.642-656. DOI: https://doi.org/10.1504/IJMC.2011.042781

Durgun, I, Yildiz, A.R. (2012). Structural design optimization of vehicle components using cuckoo search algorithm, Materials Testing, 3, 185-188. DOI: https://doi.org/10.3139/120.110317

Layeb, A., (2011). A novel quantum-inspired cuckoo search for Knapsack problems, Int. J.Bio-inspired Computation, 3, No. 5, pp. 297-305. DOI: https://doi.org/10.1504/IJBIC.2011.042260

Moravej, Z., Akhlaghi, A., (2013). A novel approach based on cuckoo search for DG allocation in distribution network, Electrical Power and Energy Systems, 44, pp. 672-679. DOI: https://doi.org/10.1016/j.ijepes.2012.08.009

Noghrehabadi, A., Ghalambaz, M., and Vosough, A., (2011). A hybrid power series – Cuckoo search optimization algorithm to electrostatic deflection of micro fixed-fixed actuators, Int. J. Multidisciplinary Science and Engineering, 2, No. 4, pp. 22-26.

Srivastava, P. R., Chis, M., Deb, S., and Yang, X. S., (2012). An efficient optimization algorithm for structural software testing, Int. J. Artificial Intelligence, 9 (S12), pp. 68-77.

Valian, E., Mohanna, S., and Tavakoli, S., (2011). Improved cuckoo search algorithm for feedforward neural network training, Int. J. Articial Intelligence and Applications, 2, No. 3, 36-43(2011). DOI: https://doi.org/10.5121/ijaia.2011.2304

Yildiz, A. R., (2012). Cuckoo search algorithm for the selection of optimal machine parametersin milling operations, Int. J. Adv. Manuf. Technol., (2012). doi:10.1007/s00170-012-4013-7. DOI: https://doi.org/10.1007/s00170-012-4013-7

Fan Wang, Xing-Shi He, Yan Wang, and Song-Ming Yang, (2012). Markov model and convergence analysis based on cuckoo search algorithm. Jisuanji Gongcheng/ Computer Engineering, 38 (11), 181–185.

Yang X. S., (2009). Firefly algorithms for multimodal optimization, in: Stochastic Algorithms: Foundations and Applications, SAGA 2009, Lecture Notes in Computer Sciences, Vol. 5792, 169–178. DOI: https://doi.org/10.1007/978-3-642-04944-6_14

Yang X.-S., (2010). Firefly algorithm, stochastic test functions and design optimisation, Int. J. Bio-inspired Computation, 2(2), 78–84. DOI: https://doi.org/10.1504/IJBIC.2010.032124

Fister I., Fister Jr I., Yang X. S., Brest J., A comprehensive review of firefly algorithms, Swarm and Evolutionary Computation, (2013). http://dx.doi.org/10.1016/j.swevo.2013.06.001. DOI: https://doi.org/10.1016/j.swevo.2013.06.001

Yang X. S., (2008). Nature-Inspired Metaheuristic Algorithms, First Edition, Luniver Press, UK.

Sina K. Azad, Saeid K. Azad, Optimum Design of Structures Using an Improved FireflyAlgorithm, International Journal of Optimisation in Civil Engineering, 1(2), 327-340(2011).

[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). DOI: https://doi.org/10.1007/978-3-642-23857-4_38

Holland JH. Adaptation in natural and artificial systems. Michigan Press; 1975.

Ye, Fei, Xin Yuan Lou, and Lin Fu Sun. "An improved chaotic fruit fly optimization based on a mutation strategy for simultaneous feature selection and parameter optimization for SVM and its applications." PloS one 12.4 (2017): e0173516. DOI: https://doi.org/10.1371/journal.pone.0173516

Alcalá-Fdez, Jesús, et al. "Keel data-mining software tool: data set repository, integration of algorithms and experimental analysis framework." Journal of Multiple-Valued Logic & Soft Computing 17 (2011).

Tharwat, Alaa, and Thomas Gabel. "Parameters optimization of support vector machines for imbalanced data using social ski driver algorithm." Neural Computing and Applications (2019): 1-14 DOI: https://doi.org/10.1007/s00521-019-04159-z

Mirjalili S, Mirjalili SM, Lewis A "Grey wolf optimizer" Adv Eng Softw(2014) 69:46–61 DOI: https://doi.org/10.1016/j.advengsoft.2013.12.007

Tharwat A, Hassanien AE, Elnaghi "A ba-based algorithm for parameter optimization of support vector machine."BE Pattern Recognit Lett(2017) 93:13–22 DOI: https://doi.org/10.1016/j.patrec.2016.10.007