CombiningMachineLearningwithEvolutionaryComputation: RecentResultsonLEM GuidoCervone RyszardS.Michalski* KennethK.Kaufman LiviuA.Panait MachineLearningandInferenceLaboratory GeorgeMasonUniversity Fairfax,VA,22030 *AlsowiththeInstituteofComputerScience,PolishAcademyofSciences,Warsaw,Poland Abstract TheLearnableEvolutionModel(LEM),firstpresentedattheFourthInternationalWorkshopon MultistrategyLearning,employsmachinelearingtoguideevolutionarycomputation .Specifically, LEMintegratestwomodesofoperation:MachineLearningmode,whichemploysamachine learningalgorithm,andDarwinianEvolutionmode,whichemploysaconventionalevolutionary algorithm.ThecentralnewideaofLEMisthatinmachinelear ningmode,newindividualsare “geneticallyengineered”byarepeatedprocessofhypothesisformationandinstantiation,rather thancreatedbyrandomoperatorsofmutationand/orrecombination,asinDarwinian -type evolutionaryalgorithms.Ateachstageo fevoluation,hypothesesareinducedbyamachine learningsystemfromexamplesofhighandlowperformanceindividuals.Newindividualsare createdbyinstantiatingthehypothesesindifferentways.Inrecentexperimentsconcernedwith complexfunctionop timizationproblems,LEMhassignif icantlyoutperformedselected evolutionarycomputationa lgorithms,sometimesachievingspeed -upsoftheevolutionaryprocess bytwoormoreordersofmagnitude(intermsofthenumberofgenerations).Inanotherrecent applicationinvolvingaproblemofoptimizingheatexchangers,LEMproduceddesignsequalor superiortobestexpertdesigns.TherecentresultshaveconfirmedearlierfindingsthatLEMisable tosignificantlyspeed-upevolutionaryprocesses(intermsofthenumberofgenerations)forcertain problems.FurtherresearchisneededtodetermineclassesofproblemsforwhichLEMismost advantagious. 1Introduction Theideathatmachinelearningcanbeusedtodirectlyguideevolutionarycomputationwasfirstpresentedat theFourthInternationalWorkshoponMultistrategyLearning(Michalski,1998).Thispresentation describedtheLearnableEvolutionModel(LEM),whichintegratesamachinelearningalgorithmwitha conventionalevolutionaryalgorithm,andrepo rtedinitialresultsfromLEM'sapplicationtoselected functionoptimizationproblems.Presentedresultswereverypromisingbuttentative.Theywereobtained usingLEM1,arudimentaryimplementationoftheproposedmethod,andtheexperimentswereperfor med onlyonafewproblems. 1 Subsequently,amoreadvancedimplementation,LEM2,wasdeveloped,andmanymoreexperimentswere performedwithit(Cervone,1999).Theoriginalmethodologywasalsosubstantiallyextendedandimproved (Michalski,2000).One oftheimportantimprovementsisthedevelopmentoftheadaptiveanchoring discretizationmethod,ANCHOR,forhandlingcontinuousvariables(MichalskiandCervone,2000).This paperpresentsrecentresultsfromtheapplicationofLEM2toarangeoffunctio noptimizationproblems andtoaproblemofdesigningoptimalheatexchangers.Toprovidethereaderwithasufficientbackground information,thenextsectionbrieflyreviewsthecurrentversionoftheLearnableEvolutionModel. 2ABriefOverviewoftheLearnableEvolutionModel TheLearnableEvolutionModel(LEM)representsafundamentallydifferentapproachtoevolutionary processesthanDarwinian -typeevolutionaryalgorithms.InDarwinian -typeevolutionaryalgorithms,new individualsaregeneratedb yprocessesofmutationand/orrecombination.Thesearesemi -blindoperators thattakeintoconsiderationneithertheexperienceofindividualsinagivenpopulation(likeinLamarckian typeofevolution),northepasthistoryofevolution.InLEM,theevo lutionisguidedbyhypothesesderived fromthecurrentand,optionallyalsopastgenerationsofindividuals.Thesehypothesesidentifytheareasof thesearchspace(landscape)thatmostlikelycontaintheglobaloptimum(oroptima).Themachinelearning programisusedinLEMeitherasthesoleengineofevolutionarychange(theuniLEMversion),orin combinationwiththeDarwinian-typeofevolutionprocess(theduoLEMversion). TheduoLEMversionintegratestwomodesofoperation:MachineLearningmode andDarwinianEvolution mode.TheDarwinianEvolutionmodeimplementsaconventionalevolutionaryalgorithm,whichemploys mutationand/orrecombinationoperatorstogeneratenewindividuals.TheMachineLearningmode generatesnewindividualsbyaprocessofhypothesisgenerationandinstantiation.Specifically,ateachstep ofevolution,itselectstwogroupsofindividualsfromthecurrentpopulation:High -performingindividuals (H-group),whichscorehighonthefitnessfunction,andLow -performanceindividuals(L-group),which scorelowonthefitnessfunction.Thesegroupsareselectedfromthecurrentpopulationorfromsome combinationofthecurrrentandpastpopulations.Thesetwogroupsarethensuppliedtoalearningprogram thatgenerateshypot hesesdistinguishingbetweentheH -groupandtheL -group.Newindividualsare generatedbyinstantiatingthehypothesesinvariousways.Thesenewindividualscompetewiththeexisting individualsfortheinclusioninthenewpopulation. IntheduoLEMvers ion,LEMalternatesbetweenthetwomodesofoperation,switchingtoanothermode whenamodeterminationcondition ismet(e.g.,whenthereisaninsufficientimprovementofthefitness functionafteracertainnumberofpopulations).IntheuniLEMversio n,theevolutionprocessisguided solelybythemachinelearningprogram.Whenthemodeterminationconditionismet,a StartOver operationisperformed.Insuchanoperation,systemgeneratesanewpopulationrandomly,oraccordingto certainrules(Michalski,2000). 2 Figure1presentsaflowchartofuniLEMandduoLEMversionofLEM.Foracomprehensivedescriptionof theLEMmethodologyreferto(Michalski,1998,Cervone,1999,Michalski,2000). uniLEMversion duoLEMversion Startover Startover Switchmode SelectHandL groups SelectHandL SelectParents groups Generatenewindividuals viahypothesescreation andinstantiation Generatenewindividuals Generatenewindividuals viahypothesescreation viamutationand/or andinstantiation crossover Evaluateindividuals Evaluateindividuals Generatenewpopulation Generatenewpopulation Adjustparameters Adjustparameters Figure1.AflowchartoftheuniLEMandduoLEMversions. Belowisabriefdescriptionoftheindividualsteps,withanindicationofhowtheyareimplementedinthe LEM2system. StartOver:Thisoperatorgeneratesanewpopulationrandomlyoraccordingtocetainrules.InLEM2,a newpopulationisgeneratedrandomly,withaprovisothatanumberofthebestperformingindividualsfrom thepastpopulationsareaddedtothenewlygeneratedpopulation(elitism). SelectH -groupandL -group:ThisselectioncanbedoneinLEM2usingoneoftw omethods:Fitness - BasedSelection(FBS),orPopulation -BasedSelection(PBS).InFBS,theH -group(L-group)consistsof individualswhosefitnessisabovetheHFT%fromthetopvalue(belowtheLFT%fromthelowestvalue). InPBS,theH -group(L-group)consistsofHPT%highest -fitness(LPT%lowest -fitness)individualsinthe population.Figure2illustratesthesetwoselectionmethodsandtheparametersHFT(highfitness threshold),LFT(lowfitnessthreshold),HPT(highpopulationthreshold),LPT(lowpopulationthreshold). 3 Figure2.Anexampleofthefitnessprofilefunction,andanillustrationof parametersHFT,LFT,HPT,LPTwouldselecttheHandLgroups. Selectparents: TheselectionoftheparentsisrelatedtotheDarwinianmode.Itsele ctsrepresentative individuals(parents)fromthecurrentpopulationthatwillbemutatedand/orrecombined.LEM2 implementstwotypesofmutation:deterministicanduniform.Inthefirsteveryindividualinthepopulation isselected,whileinthelatte r,everyindividualhasthesamechanceofbeingselected,independentlyfrom itsfitness. Generatenewindividualsviahypothesiscreationandinstantiation :TheLEMmethodologyisnot constrainedtoanyparticularlearningalgorithm,butcanbeused,in principle,withanyconceptlearning method.LEM2employsAQ18rulelearningprogramthatishighlysuitableforLEMduetoitsvarious characteristics,suchastheabilitytolearnruleswithdifferentlevelsofgenerality,theuseofinternal disjunctionoperator,andapowerfulknowledgerepresentation. Figures3and4showanexampleoftheinputandoutputfromAQ18,respectively(aftersmallediting). ¡ ¢ ¡ £ ¤ ¥ ¤ ¢ ¦ ¢ § ¨ ¡ £ © ¥ ¢ £ £ ¤ £ ¡ ¦ ¥ ¡ ¢ ¨ ¦ ¤ ¤ £ ¥ ¦ ¤ ¨ ( ) * + , + - + ( . * / 0 / - , 1 2 + 3 4 , ( 5 ) 6 7 ' ¡ ¢ ¡ © ¤ ¦ 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ ¥ ¤ ¦ ¤ ¦ ¥ ¨ ¡ £ ¤ ¨ _ ` a b c d e f g a g h i f j k d b b l b d m n ¨ o p b q d r q a r d n s t s b d k j g m b ¨ ¨ b d f q a r d n s t s b d k j g m b u ¢ § ¤ ¤ ¨ ¥ ¦ ¤ ! ¥ Note:Thevaluesintheconditionsoftherule " " " # $ $ " % " abovearesymbolsrepresentingrangesoforiginal $ " # " " valuesofthesevariables,nottheoriginalvalues. $ $ " # Theserangeshasbeendeteminedin theprocess $ " $ # of adaptiveanchoringquantization (Michalski ¢ § ¤ ¤ ¨ ¥ ¦ & andCervone,2000). ¤ ! ¥ $ $ # " # $ v " " " Figure4.AQ18input. w Figure5.AQ18output. AQ18takesasintputtheH -groupandL -group,aspecificationofthetypesand domainsofthevariables, plus,optionally,controlparameters[see(KaufmanandMichalski,2000)foradetailedexplanation],and producesasetofattributionalruleswithannotationscharacterizingtherules.Eachlearnedruleisa 4 conjunctionofcondi tionsthatspecifyrangesofvaluesanattributemaytake(inthecasewhenAQ18runs withoutinvokingconstructiveinduction).Aruleisinstantiatedbyselectingvaluessatisfyingrule conditions.Thelearnedrulesareusedtogeneratenewindividuals byrandomizingvariableswithinthe rangesofvaluesdefinedbytheruleconditions.Ifaruledoesnotincludesomevariable,itmeansthatthis variablewasfoundirrelevantfordistinguishingbetweentheH -groupandtheL -group.Variablesthatare noti ncludedintheruleareinstantiatedbyrandomlychoosingavaluefromtheirdomain,orchoosinga valuethatispresentinarandomlyselectedindividualfromthecurrentpopulation. Generatenewindividualsviamutationand/orcrossover :Individualsin theparentpopulationaremutated and/orrecombined.ResearchonDarwinian -typeevolutionaryalgorithmshasinvestigatedmanydifferent