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ResearchofImprovedAntColonyHybridAlgorithmLiShijun1,a,HanYu1,b,GuHongjun1,c,GongHe1,d,LiJian1,el1CollegeofInformation&Technology,JilinAgriculturalUniversity,Changchun130118,China.
a452835889@qq.
com,b372600730@qq.
com,c330837495@qq.
comd29878671@qq.
com,e2312852319@qq.
comKeywords:antcolonyalgorithm,immunealgorithm,artificialfishswarmalgorithm,hybridalgorithm.
Abstract.
Inordertoextendtheapplicationofantcolonyalgorithm(ACA),manyscholarscombinedtheantcolonyalgorithmwithimmunealgorithm(IA)orotheralgorithmstosolvetheproblemofslowconvergence.
Tofullysolvethetoolongsearchtime,easilyfallingintolocaloptimization,slowconvergenceandsomeotherdefects,theimmunealgorithmandartificialfishswarmalgorithm(AFSA)combinewiththeantcolonyalgorithm,andtheantcolonyhybridalgorithmisproposed.
Thenbysolvingthetravelingsalesmanproblem(TSP),thenewalgorithmissimulated,andtheresultsshowthatimprovingalgorithmiseffectiveandfeasible.
IntroductionTheantcolonyalgorithm(ACA)wasfirstproposedbyItalyscholarDorigoM.
andothersin1991,anovelsimulatedevolutionaryalgorithm,antssearchforapaththroughthesecretionofpheromonescatteredonitspath.
Thentheantsrandomlychoosearoadthatdidn'tpass,releasepheromoneaboutthelengthofthispath.
Buttheamountofinformationreleasedisinverselyproportionaltothelengthofthepath,whichlikelytochoosethepathofalargeramountofinformation,it'sapositivefeedbackmechanism.
Thebestpathistheamountofinformationthatisgettingbiggerandbigger,theamountofinformationontheotherpathisgraduallyreduced,antseventuallyfindoptimalpath.
Bysimulatingants'behaviorsuchasforaging,assignmentandbuildingthegraveyard,weputforwardACA.
It'seasytocombinewithotheralgorithms,andithasastrongrobustnessandexcellentdistributedcomputersystem,andit'seasytocombinewithotheralgorithms.
Thisalgorithmachievedgoodeffectintheacademicfield,theproblemssuchasfunctionoptimization,combinationoptimization,datamining,networkrouting,etc.
ACAbecameahotspotformanyscholarstoanalyzetheoptimizationalgorithm,ithasuniqueandwidelyabilitytosolveproblems.
Improvedthealgorithmitself,andcombinedwithotheralgorithms,appliedtomanyoftheactualfieldofwhich.
Basicprinciplesofantcolonyalgorithm)(tijtFirst,solvingtheTSPproblemasanexample,thespecificimplementationstepsofthebasicACAareasfollows.
Givingncitiesandtwoofthedistancebetweenthetwocities,therequirementstodetermineapassedthrougheachcityonlyonceintheshortestpath.
Inordertosimulatethebehaviorofrealants,weintroducedthefollowingnotation;misthenumberofants.
ijd(i,j=1,2,.
.
.
,n)representsthedistancebetweeniandjinthecity,representstheamountofinformationremainingonthepathbetweeniandjinthetcity,it'susedtosimulatethepheromoneconcentrationkallowedktabu)(tpkijoftheactualants.
.
Wheninitialized,mantswereplacedrandomlyondifferentcities,givingthe)0(ijτamountofinformationwasoneachside.
Eachantkofthatthefirstelementwasassignedtothecitywhereitwaslocated.
indicatethattheantkwastransferredfromcityitocityjprobabilitytime,usingformula(1).
indicatesthatantkallowstochosethecityinthenextstep;αasinformationheuristicfactor,indicatesrelativelocusimportance.
Itreflectsthatantsaccumulatedinformationinthemovementtoplaytherolefortheantmovement;βasexpectationheuristicfactor,indicatesrelativevisibilityimportance,itreflectstheimportancedegreeofheuristicinformationwhenantschosethepathinthemovement.
(1)0j,)()()()()(∈=∑∈elseallowediftttttpkallowedsisisijijkijk,ββηtηtAfternmoments,antkwalkedthroughallthecities,completedacycle.
Thenupdatedtheamountofinformationoneachpathbytheformula(2).
ijτ)2()()()1()(ttntijijijttρt+=+Among,calculatedbytheformula(3),itrepresentstheamountofinformationonthekantinthepath(i,j)intheloop.
Thecalculationmethodisbasedonthecalculationmodel,inthemostcommonlyusedAnt-Cyclemodel,usingformula(4),Qrepresentsthepheromoneintensity,itaffectstheconvergencerateofthealgorithmtosomeextent.
kLrepresentsthetotallengthofthepathofthekantinthiscycle.
(3))()(1∑==mkkijijtttt)4(otherwise,0),i(throughcycleinthisantsonlyKtheIf,)(=jLQtkkijtCombinationofantcolonyalgorithmandimmunealgorithm.
Thebasicideaofthecombinationofantcolonyalgorithmandimmunealgorithm.
CombingIAwithACA,usedACAtosolvetheproblemasantigen,andtheextractionofthevaccinetopheromoneinitialization,ACAproducedantibodiestoassignavaluetoaparameter,appliedtothesolutionofspecificproblems,theobtainedresultsasthecurrentantibodyfitnessvaluebyinoculationofvaccineIA,crossover,mutation,affinityselection,retainedtoadaptgoodantibody,eliminatedadaptationofantibody,theiterative,gottheantibodyinfinally,theparameterACAcombinationwasobtainedforthespecificproblem.
Algorithmbyupdatingbasedonaffinity,thuseffectivelypreventsthe'premature'problem,ledthesearchprocesstotheglobaloptimum.
Theinitialvalueofpheromonewasextractedbytheextractionmechanismofvaccine,avoidedtherandomnessoftheinitialsolution.
Byusingthevaccinationmechanism,crossoverandmutationtoacceleratetheconvergencespeed.
ACAandIAiscalledimmuneantcolonyalgorithm(IAACA).
Thebasicstepsoftheimmuneantcolonyalgorithm.
ImmuneantcolonyalgorithmflowchartisshowninFig.
1.
Fig.
1ImmunealgorithmflowchartCombinationofartificialfishswarmalgorithmandimmuneantcolonyalgorithmThebasicideaofthehybridalgorithm(AFSA-IAACA)basedonartificialfishswarmalgorithmandantcolonyimmunealgorithm.
AFSAhastheadvantagesoffastconvergencespeed,wewilladdedtoeveryiterativeprocessofimmuneantcolonyalgorithmtoacceleratetheconvergencespeedofantcolonyalgorithm,anddependingontheforagingbehaviorofAFSAtohelpimproveIAACAtojumpoutoflocaloptimum.
AFSA-IAACAfortheTSPproblemofadetailedimprovementstrategyandalgorithmdetailedsteps:Step1Attheinitialt=0,mantswererandomlyplacedinthencities,eachpathinitialpheromoneconcentrationis.
)0(constij=tStep2Antscalculatedtransferprobabilitybytheformula(1),selectedtoprojecttransitionpath.
Thencalculatedthepathcongestionatthattimeijqbytheformula(5).
If)(tqijδindicatedthatpathisnottoocrowded,antschosethepathtotransferfrompositionitopositionj.
Otherwise,thepathwastoocrowded,theantselectedapathoftransferinthefeasibleneighborhoodtorandomly.
Amongthem,)(tδiscongestionthresholdinttime,updatedtypebytheformula(6).
Amongthem,cisthethresholdcoefficientofvariation.
(5))()(2∑≠=jiijijijttqtt(6)1)(ctet=δStep3Afternmoment,thekantwentallCitiestocompleteacycle.
Thenupdatedtheinformationoneachpathbytheformula(2).
Step4Repeatedformula(1)and(2),untilthemantschosethesamepathorreachthespecifiedmaximum.
SimulationResultsandAnalysisTable1Comparisonofexperimentalresultsnumberofcities(ACA)(IAACA)(AFSA-IAACA)averageiterationnumberOptimumsolutionaverageiterationnumberOptimumsolutionaverageiterationnumberOptimumsolution101032.
708617982.
708617912.
70861730728423.
631000596423.
631000547423.
631000501465429.
543000962427.
865000715427.
653.
000752103569.
7830001421551.
649000892541.
443000TheresultsshowthattheAFSA-IAACAalgorithmproveditsfeasibility,effectivenessandconvergencebyapplicationandsimulationexperimentintheTSPproblem.
ThealgorithmwillAFSAaddedtoeachiterativeprocessofIAACA,takingadvantageofAFSAwithfastconvergencewhichacceleratetheconvergencespeedofACAandforagingbehaviorofAFSAcouldhelpimprovedtheabilityofACAtojumpoutoflocaloptimum.
Bydoingthis,wecanreducenotonlythenumberofinvalidsearch,butalsothealgorithmintothelocaloptimalsolution,improvetheabilityandconvergencespeedofthealgorithm.
ConclusionsACAhassomeproblems,suchasprematureconvergence,slowconvergence,thecombinationofACAandIAisaneffectivemethodtosolvethesedefects.
ThencombinetheIAACAandAFSAtosolvethesedefectsthatlongsearchtimeandeasilyfallintolocaloptimization,andtoimprovetheabilitytojumpextreme,andsignificantlyimprovetheaccuracyofthealgorithm.
ThesimulationexperimentwascarriedoutbysolvingtheTSPproblem,andresultsshowthattheimprovedalgorithmiseffectiveandfeasible.
AcknowledgmentsTheauthorswishtoexpresstheirgratitudetotheprojects:JilinProvinceEconomicStructuralAdjustmentLeadingFundSpecialProject(No.
2014Y108)andChangchunCityScienceandTechnologyPlanProject(No.
14nk029),KeyTacklingItemofJilinProvinceScience&TechnologyDepartment(No.
20140204045NY),DesignofStandardizedBreedingSystemforRabbitsBasedonInternetofThingsfromEducationDepartmentofJilinProvince,ChangchunCityScienceandTechnologyPlanProject(No.
13KG71),fortheirgeneroussupportofthiswork.
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