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Conciselystated,ageneticalgorithm(orGAforshort)isaprogrammingtechniquethatmimicsbiologicalevolutionasaproblem-solvingstrategy.Givenaspecificproblemtosolve,theinputtotheGAisasetofpotentialsolutionstothatproblem,encodedinsomefashion,andametriccalledafitnessfunctionthatallowseachcandidatetobequantitativelyevaluated.Thesecandidatesmaybesolutionsalreadyknowntowork,withtheaimoftheGAbeingtoimprovethem,butmoreoftentheyaregeneratedatrandom.
TheGAthenevaluateseachcandidateaccordingtothefitnessfunction.Inapoolofrandomlygeneratedcandidates,ofcourse,mostwillnotworkatall,andthesewillbedeleted.However,purelybychance,afewmayholdpromise-theymayshowactivity,evenifonlyweakandimperfectactivity,towardsolvingtheproblem.
Thesepromisingcandidatesarekeptandallowedtoreproduce.Multiplecopiesaremadeofthem,butthecopiesarenotperfect;
randomchangesareintroducedduringthecopyingprocess.Thesedigitaloffspringthengoontothenextgeneration,forminganewpoolofcandidatesolutions,andaresubjectedtoasecondroundoffitnessevaluation.Thosecandidatesolutionswhichwereworsened,ormadenobetter,bythechangestotheircodeareagaindeleted;
butagain,purelybychance,therandomvariationsintroducedintothepopulationmayhaveimprovedsomeindividuals,makingthemintobetter,morecompleteormoreefficientsolutionstotheproblemathand.Againthesewinningindividualsareselectedandcopiedoverintothenextgenerationwithrandomchanges,andtheprocessrepeats.Theexpectationisthattheaveragefitnessofthepopulationwillincreaseeachround,andsobyrepeatingthisprocessforhundredsorthousandsofrounds,verygoodsolutionstotheproblemcanbediscovered.
Asastonishingandcounterintuitiveasitmayseemtosome,geneticalgorithmshaveproventobeanenormouslypowerfulandsuccessfulproblem-solvingstrategy,dramaticallydemonstratingthepowerofevolutionaryprinciples.Geneticalgorithmshavebeenusedinawidevarietyoffieldstoevolvesolutionstoproblemsasdifficultasormoredifficultthanthosefacedbyhumandesigners.Moreover,thesolutionstheycomeupwithareoftenmoreefficient,moreelegant,ormorecomplexthananythingcomparableahumanengineerwouldproduce.Insomecases,geneticalgorithmshavecomeupwithsolutionsthatbaffletheprogrammerswhowrotethealgorithmsinthefirstplace!
Methodsofrepresentation
Beforeageneticalgorithmcanbeputtoworkonanyproblem,amethodisneededtoencodepotentialsolutionstothatprobleminaformthatacomputercanprocess.Onecommonapproachistoencodesolutionsasbinarystrings:
sequencesof1'
sand0'
s,wherethedigitateachpositionrepresentsthevalueofsomeaspectofthesolution.Another,similarapproachistoencodesolutionsasarraysofintegersordecimalnumbers,witheachpositionagainrepresentingsomeparticularaspectofthesolution.Thisapproachallowsforgreaterprecisionandcomplexitythanthecomparativelyrestrictedmethodofusingbinarynumbersonlyandoften"
isintuitivelyclosertotheproblemspace"
(FlemingandPurshouse2002,p.1228).
Thistechniquewasused,forexample,intheworkofSteffenSchulze-Kremer,whowroteageneticalgorithmtopredictthethree-dimensionalstructureofaproteinbasedonthesequenceofaminoacidsthatgointoit(Mitchell1996,p.62).Schulze-Kremer'
sGAusedreal-valuednumberstorepresenttheso-called"
torsionangles"
betweenthepeptidebondsthatconnectaminoacids.(Aproteinismadeupofasequenceofbasicbuildingblockscalledaminoacids,whicharejoinedtogetherlikethelinksinachain.Oncealltheaminoacidsarelinked,theproteinfoldsupintoacomplexthree-dimensionalshapebasedonwhichaminoacidsattracteachotherandwhichonesrepeleachother.Theshapeofaproteindeterminesitsfunction.)Geneticalgorithmsfortrainingneuralnetworksoftenusethismethodofencodingalso.
AthirdapproachistorepresentindividualsinaGAasstringsofletters,whereeachletteragainstandsforaspecificaspectofthesolution.OneexampleofthistechniqueisHiroakiKitano'
s"
grammaticalencoding"
approach,whereaGAwasputtothetaskofevolvingasimplesetofrulescalledacontext-freegrammarthatwasinturnusedtogenerateneuralnetworksforavarietyofproblems(Mitchell1996,p.74).
Thevirtueofallthreeofthesemethodsisthattheymakeiteasytodefineoperatorsthatcausetherandomchangesintheselectedcandidates:
flipa0toa1orviceversa,addorsubtractfromthevalueofanumberbyarandomlychosenamount,orchangeonelettertoanother.(SeethesectiononMethodsofchangeformoredetailaboutthegeneticoperators.)Anotherstrategy,developedprincipallybyJohnKozaofStanfordUniversityandcalledgeneticprogramming,representsprogramsasbranchingdatastructurescalledtrees(Kozaetal.2003,p.35).Inthisapproach,randomchangescanbebroughtaboutbychangingtheoperatororalteringthevalueatagivennodeinthetree,orreplacingonesubtreewithanother.
Figure1:
Threesimpleprogramtreesofthekindnormallyusedingeneticprogramming.Themathematicalexpressionthateachonerepresentsisgivenunderneath.
Itisimportanttonotethatevolutionaryalgorithmsdonotneedtorepresentcandidatesolutionsasdatastringsoffixedlength.Somedorepresenttheminthisway,butothersdonot;
forexample,Kitano'
sgrammaticalencodingdiscussedabovecanbeefficientlyscaledtocreatelargeandcomplexneuralnetworks,andKoza'
sgeneticprogrammingtreescangrowarbitrarilylargeasnecessarytosolvewhateverproblemtheyareappliedto.
Methodsofselection
Therearemanydifferenttechniqueswhichageneticalgorithmcanusetoselecttheindividualstobecopiedoverintothenextgeneration,butlistedbelowaresomeofthemostcommonmethods.Someofthesemethodsaremutuallyexclusive,butotherscanbeandoftenareusedincombination.
Elitistselection:
Themostfitmembersofeachgenerationareguaranteedtobeselected.(MostGAsdonotusepureelitism,butinsteaduseamodifiedformwherethesinglebest,orafewofthebest,individualsfromeachgenerationarecopiedintothenextgenerationjustincasenothingbetterturnsup.)
Fitness-proportionateselection:
Morefitindividualsaremorelikely,butnotcertain,tobeselected.
Roulette-wheelselection:
Aformoffitness-proportionateselectioninwhichthechanceofanindividual'
sbeingselectedisproportionaltotheamountbywhichitsfitnessisgreaterorlessthanitscompetitors'
fitness.(Conceptually,thiscanberepresentedasagameofroulette-eachindividualgetsasliceofthewheel,butmorefitonesgetlargerslicesthanlessfitones.Thewheelisthenspun,andwhicheverindividual"
owns"
thesectiononwhichitlandseachtimeischosen.)
Scalingselection:
Astheaveragefitnessofthepopulationincreases,thestrengthoftheselectivepressurealsoincreasesandthefitnessfunctionbecomesmorediscriminating.Thismethodcanbehelpfulinmakingthebestselectionlateronwhenallindividualshaverelativelyhighfitnessandonlysmalldifferencesinfitnessdistinguishonefromanother.
Tournamentselection:
Subgroupsofindividualsarechosenfromthelargerpopulation,andmembersofeachsubgroupcompeteagainsteachother.Onlyoneindividualfromeachsubgroupischosentoreproduce.
Rankselection:
Eachindividualinthepopulationisassignedanumericalrankbasedonfitness,andselectionisbasedonthisrankingratherthanabsolutedifferencesinfitness.Theadvantageofthismethodisthatitcanpreventveryfitindividualsfromgainingdominanceearlyattheexpenseoflessfitones,whichwouldreducethepopulation'
sgeneticdiversityandmighthinderattemptstofindanacceptablesolution.
Generationalselection:
Theoffspringoftheindividualsselectedfromeachgenerationbecometheentirenextgeneration.Noindividualsareretainedbetweengenerations.
Steady-stateselection:
Theoffspringoftheindividualsselectedfromeachgenerationgobackintothepre-existinggenepool,replacingsomeofthelessfitmembersofthepreviousgeneration.Someindividualsareretainedbetweengenerations.
Hierarchicalselection:
Individualsgothroughmultipleroundsofselectioneachgeneration.Lower-levelevaluationsarefasterandlessdiscriminating,whilethosethatsurvivetohigherlevelsareevaluatedmorerigorously.Theadvantageofthismethodisthatitreducesoverallcomputationtimebyusingfaster,lessselectiveevaluationtoweedoutthemajorityofindividualsthatshowlittleornopromise,andonlysubjectingthosewhosurvivethisinitialtesttomorerigorousandmorecomputationallyexpensivefitnessevaluation.
Methodsofchange
Onceselectionhaschosenfitindividuals,theymustberandomlyalteredinhopesofimprovingtheirfitnessforthenextgeneration.Therearetwobasicstrategiestoaccomplishthis.Thefirstandsimplestiscalledmutation.Justasmutationinlivingthingschangesonegenetoanother,somutationinageneticalgorithmcausessmallalterationsatsinglepointsinanindividual'
scode.
Thesecondmethodiscalledcrossover,andentailschoosingtwoindividualstoswapsegmentsoftheircode,producingartificial"
offspring"
thatarecombinationsoftheirparents.Thisprocessisintendedtosimulatetheanalogousprocessofrecombinationthatoccurstochromosomesduringsexualreproduction.Commonformsofcrossoverinclud