ClusteringusingfireflyalgorithmPerformancestudy萤火虫算法SwarmandEvolutionaryComputation1(2021)164–171ContentslistsavailableatSciVerseScienceDirectSwarmandEvolutionaryComputationjournalhomepage:/locate/swevoRegularpaperClusteringusingfireflyalgorithm:PerformancestudyJ.Senthilnath,S.N.Omkar,V.ManiDepartmentofAerospaceEngineering,IndianInstituteofScience,Bangalore,IndiaarticleinfoabstractAFireflyAlgorithm(FA)isarecentnatureinspiredoptimizationalgorithm,thatsimulatestheflashpatternandcharacteristicsoffireflies.Clusteringisapopulardataanalysistechniquetoidentifyhomogeneousgroupsofobjectsbasedonthevaluesoftheirattributes.Inthispaper,theFAisusedforclusteringonbenchmarkproblemsandtheperformanceoftheFAiscomparedwithothertwonatureinspiredtechniques—ArtificialBeeColony(ABC),ParticleSwarmOptimization(PSO),andotherninemethodsusedintheliterature.ThirteentypicalbenchmarkdatasetsfromtheUCImachinelearningrepositoryareusedtodemonstratetheresultsofthetechniques.Fromtheresultsobtained,wecomparetheperformanceoftheFAalgorithmandconcludethattheFAcanbeefficientlyusedforclustering.CrownCopyright2021PublishedbyElsevierLtd.Allrightsreserved.Articlehistory:Received10February2021Receivedinrevisedform5May2021Accepted2June2021Availableonline30June2021Keywords:ClusteringClassificationFireflyalgorithm1.IntroductionClusteringisanimportantunsupervisedclassificationtech-nique,whereasetofpatterns,usuallyvectorsinamulti-dimensionalspace,aregroupedintoclusters(orgroups)basedonsomesimilaritymetric[1–4].Clusteringisoftenusedforavari-etyofapplicationsinstatisticaldataanalysis,imageanalysis,dataminingandotherfieldsofscienceandengineering.Clusteringalgorithmscanbeclassifiedintotwocategories:hierarchicalclusteringandpartitionalclustering[5,6].Hierarchicalclusteringconstructsahierarchyofclustersbysplittingalargeclusterintosmalleronesandmergingsmallerclusterintotheirnearestcentroid[7].Inthis,therearetwomainapproaches:(i)thedivisiveapproach,whichsplitsalargerclusterintotwoormoresmallerones;(ii)theagglomerativeapproach,whichbuildsalargerclusterbymergingtwoormoresmallerclusters.Ontheotherhandpartitionalclustering[8,9]attemptstodividethedatasetintoasetofdisjointclusterswithoutthehierarchicalstructure.Themostwidelyusedpartitionalclusteringalgorithmsaretheprototype-basedclusteringalgorithmswhereeachclusterisrepresentedbyitscenter.Theobjectivefunction(asquareerrorfunction)isthesumofthedistancefromthepatterntothecenter[6].Inthispaperweareconcernedwithpartitionalclusteringforgeneratingclustercentersandfurtherusingtheseclustercenterstoclassifythedataset.Apopularpartitionalclusteringalgorithm—k-meansclustering,isessentiallyafunctionminimizationtechnique,wheretheobjectivefunctionisthesquarederror.However,themainCorrespondingauthor.E-mailaddress:omkar@aero.iisc.ernet.in(S.N.Omkar).drawbackofk-meansalgorithmisthatitconvergestoalocalminimafromthestartingpositionofthesearch[10].Inordertoovercomelocaloptimaproblems,manynatureinspiredalgorithmssuchas,geneticalgorithm[11],antcolonyoptimization[12],artificialimmunesystem[13],artificialbeecolony[9],andparticleswarmoptimization[14]havebeenused.Recently,efficienthybridevolutionaryoptimizationalgorithmsbasedoncombiningevolutionarymethodsandk-meanstoovercomelocaloptimaproblemsinclusteringareused[15–17].TheFireflyAlgorithm(FA)isarecentnatureinspiredtech-nique[18],thathasbeenusedforsolv...