萤火虫算法

J.Senthilnathetal./SwarmandEvolutionaryComputation1(2011)164–171167

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Agent movementCluster center

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Fig.2.Optimalclustercenters.

andupdatethemovementphaseofeachagentbyevaluatingnewsolutionsandupdatelightintensityusingEq.(1).Thisprocedureiscontinuedtillitconvergestotheoptimalclustercenteri.e.ximin,asshowninFig.2.Theclustercentersgeneratedare

(x,y)={(7.2233,7.6659);(16.0580,16.3230)}.

Theclassificationresultusingthetestingdatasetofeachclasscentersfoundbythefireflyalgorithmhaszeroclassificationerrorpercentage.Fortheentiredataset,theperformanceofindividual,averageandoverallefficiencyis100%.5.Resultsanddiscussion

Inthiswork,wepresenttheresultsobtainedusingtheFireflyAlgorithm(FA)on13typicalbenchmarkdatasetswhicharewellknownintheliterature(UCIdatabaserepository[25]).First,wedescribethecharacteristicsofthestandardclassificationdataset.NextwepresenttheresultsobtainedfromtheFAfor13benchmarkdatasetproblems.FinallywepresentthecomparisonoftheFAwithothertwonatureinspiredtechniques—ArtificialBeeColony(ABC)andParticleSwarmOptimization(PSO)andother9methodsusedintheliterature[9,14]andanalyzetheirperformance.5.1.Datasetdescription

The13classificationdatasetisawell-knownandwell-usedbenchmarkdatasetbythemachinelearningcommunity.Thenumberofdatasets,thenumberofinputfeaturesandthenumberofclassesarepresentedinTable1.These13benchmarkproblemsarechosenexactlythesameasin[9,14],tomakeareliablecomparison.Theentiredatasetissegregatedintotwoparts,the75%ofdataisusedfortrainingpurposeandtheremaining25%ofdataisusedastestingsamples.ThenumberofthetrainingandtestsetscanbefoundinTable1.Aftertraining,weobtaintheclustercenters(extractedknowledge)thatcanbeusedforclassifyingthetestdataset.Theproblemsconsideredinthisworkcanbedescribedbrieflyasfollows.

Dataset1:TheBalancedatasetisbasedonbalancescaleweightanddistance.Itcontains625patternswhicharesplitinto429fortrainingand156fortesting.Theirare4integervaluedattributesand3classes.

Dataset2and3:TheCancerandCancer-Intdatasetisbasedonthediagnosisof‘‘breastcancerWisconsin—Diagnostic’’and‘‘breastcancerWisconsin—Original’’datasetsrespectively.Itcontains2classeswithatumoraseitherbenignormalignant.Acancerdata

Table1

setcontains569patternswith30attributesandtheCancer-Intcontains699patterns,9attributes.

Dataset4:TheCreditdatasetisbasedontheAustraliancreditcardtoassessapplicationsforcreditcards.Thereare690patterns(numberofapplicants),15inputfeaturesandtheoutputhas2classes.

Dataset5:TheDermatologydatasetisbasedondifferentialdiagnosisoferythemato-squamousdiseases.Thereare6classes,366samples,and34attributes.

Dataset6:ThePima—Diabetesdatasethas768instancesof8attributesandtwoclasseswhicharetodetermineifthedetectionofdiabetesispositive(classA)ornegative(classB).

Dataset7:TheEscherichiacolidatasetisbasedonthecellularlocalizationsitesofproteins.Heretheoriginaldatasethas336patternsformedof8classes,but3classesarerepresentedwithonly2,2and5numberofpatterns.Therefore,these9examplesareomittedbyconsidering327patterns,5classesand7attributes.Dataset8:TheGlassdatasetisdefinedintermsoftheiroxidecontentasglasstype.Nineinputsarebasedon9chemicalmeasurementswithoneof6typesofglass.Thedatasetcontains214patternswhicharesplitinto161fortrainingand53fortesting.Dataset9:TheHeartdatasetisbasedonthediagnosisofheartdisease.Itcontains76attributesforeachpattern,35ofwhichareusedasinputfeatures.ThedataisbasedonClevelandHeartdatafromtherepositorywith303patternsand2classes.

Dataset10:TheHorsedatasetisusedtopredictthefortuneofahorsewithacolicandtoclassifywhetherthehorsewilldie,willsurvive,orwillbeeuthanized.Thedatasetcontains364patterns,eachofwhichhas58inputsfrom27attributesand3classes.

Dataset11:TheIrisdatasetconsistsofthreevarietiesofflowers—setosa,virginicaandversicolor.Thereare150instancesand4attributesthatmakeupthe3classes.

Dataset12:TheThyroiddatasetisbasedonthediagnosisofthyroidwhetheritishyperorhypofunction.Thedatasetcontains215patterns,5attributesand3classes.

Dataset13:TheWinedataobtainedfromthechemicalanalysisofwineswerederivedfromthreedifferentcultivators.Thedatasetcontains3typesofwines,with178patternsand13attributes.5.2.Resultsobtainedusingfireflyalgorithm

Inthissection,wediscusstheresultsobtainedusingtheFireflyAlgorithm(FA)on13benchmarkdatasetproblemsandcomparetheFAwithother11methodsusedintheliteraturebasedontheperformancemeasures.

5.2.1.FAclusteringandparametersetting

Thefirefliesareinitializedrandomlyinthesearchspace.Theparametervaluesusedinouralgorithmare