Genetic algorithm

Introduction

Theoriginofgeneticalgorithmscanbetracedbacktotheearly1960s.In1967,Bagley,astudentofProfessorJ.HollandattheUniversityofMichiganintheUnitedStates,firstproposedthetermgeneticalgorithminhisdoctoralthesisanddiscussedtheapplicationofgeneticalgorithmingames.Thedevelopmentofcomputingtools.In1975,J.Hollandetal.proposedamodeltheorythatisextremelyimportantforthetheoreticalresearchofgeneticalgorithms.Thedevelopmentofgeneticalgorithms.Afterthe1980s,geneticalgorithmsenteredaperiodofprosperousdevelopmentandwerewidelyusedinresearchfieldssuchasautomaticcontrol,productionplanning,imageprocessing,androbotics.

Basicframework

Coding

Becausegeneticalgorithmscannotdirectlydealwiththeparametersoftheproblemspace,theproblemtobesolvedmustbeexpressedasachromosomeinthegeneticspacethroughcodingOrindividual.Thisconversionoperationiscalledencoding,anditcanalsobecalled(problem)representation.

Thefollowing3criteriaareoftenusedtoevaluatecodingstrategies:

a)Completeness:allpoints(candidatesolutions)intheproblemspacecanbeusedaspointsintheGAspace(Chromosome)performance.

b)Soundness:ThechromosomesintheGAspacecancorrespondtoallcandidatesolutionsintheproblemspace.

c)Nonredundancy(nonredundancy):Thechromosomecorrespondstothecandidatesolutiononetoone.

Fitnessfunction

Thefitnessinthetheoryofevolutionmeanstheabilityofanindividualtoadapttotheenvironmentandtheabilityoftheindividualtoreproduceoffspring.Thefitnessfunctionofthegeneticalgorithmisalsocalledtheevaluationfunction.Itisanindexusedtojudgetheprosandconsoftheindividualsinthegroup.Itisevaluatedaccordingtotheobjectivefunctionoftheproblem.

Geneticalgorithmsgenerallydonotneedotherexternalinformationinthesearchandevolutionprocess,andonlyuseevaluationfunctionstoevaluatetheprosandconsofindividualsorsolutions,andserveasthebasisforfuturegeneticoperations.Inthegeneticalgorithm,thefitnessfunctionneedstobecomparedandrankedandtheselectionprobabilityiscalculatedonthisbasis,sothevalueofthefitnessfunctionmusttakeapositivevalue.Itcanbeseenthat,inmanycases,itisnecessarytomaptheobjectivefunctionintoafitnessfunctionwithamaximumvalueandanon-negativefunctionvalue.

Thedesignofthefitnessfunctionmainlymeetsthefollowingconditions:

a)Singlevalue,continuous,non-negative,maximized

b)Reasonableandconsistent

c)Smallamountofcalculation

d)Strongversatility.

Inspecificapplications,thedesignofthefitnessfunctionshouldbecombinedwiththerequirementsofsolvingtheproblemitself.Thedesignoffitnessfunctiondirectlyaffectstheperformanceofgeneticalgorithm.

Initialpopulationselection

Inthegeneticalgorithm,theindividualsintheinitialpopulationarerandomlygenerated.Generallyspeaking,thesettingoftheinitialgroupcanadoptthefollowingstrategies:

a)Accordingtotheinherentknowledgeoftheproblem,trytograspthedistributionrangeofthespaceoccupiedbytheoptimalsolutionintheentireproblemspace,andthen,hereSettheinitialpopulationwithinthedistributionrange.

b)Firstrandomlygenerateacertainnumberofindividuals,andthenselectthebestindividualsfromthemandaddthemtotheinitialpopulation.Thisprocesscontinuestoiterateuntilthenumberofindividualsintheinitialpopulationreachesapredeterminedscale.

Operationprocess

Thebasicoperationprocessofgeneticalgorithmisasfollows:

(1)Initialization:Settheevolutionalgebracountert=0,setthemaximumevolutionalgebraT,RandomlygenerateMindividualsastheinitialpopulationP(0).

(2)Individualevaluation:CalculatethefitnessofeachindividualinthegroupP(t).

(3)Selectionoperation:Theselectionoperatorisappliedtothegroup.Thepurposeofselectionistoinherittheoptimizedindividualsdirectlytothenextgenerationortogeneratenewindividualsthroughpairingandcrossoverandtheninheritthemtothenextgeneration.Theselectionoperationisbasedontheassessmentofthefitnessoftheindividualsinthegroup.

(4)Crossoveroperation:Thecrossoveroperatorisappliedtothegroup.Thekeyroleinthegeneticalgorithmisthecrossoveroperator.

(5)Mutationoperation:Themutationoperatorisappliedtothepopulation.Thatistochangethegenevalueofsomelociintheclusterofindividualsinthepopulation.ThepopulationP(t)isselected,crossed,andmutatedtoobtainthenextgenerationpopulationP(t+1).

(6)Judgmentofterminationconditions:Ift=T,theindividualwiththemaximumfitnessobtainedintheevolutionprocessisusedastheoptimalsolutionoutput,andthecalculationisterminated.

Geneticoperationsincludethefollowingthreebasicgeneticoperators:selection;crossover;mutation.

Selection

Theoperationofselectingsuperiorindividualsfromthegroupandeliminatinginferiorindividualsiscalledselection.Selectionoperatorsaresometimescalledreproductionoperators.Thepurposeofselectionistoinherittheoptimizedindividual(orsolution)directlytothenextgenerationortogenerateanewindividualthroughpairingandcrossoverandtheninheritittothenextgeneration.Theselectionoperationisbasedonthefitnessevaluationofindividualsinthegroup.Thecommonlyusedselectionoperatorsareasfollows:fitnessratiomethod,randomtraversalsamplingmethod,andlocalselectionmethod.

Crossover

Thereorganization(plusmutation)ofbiologicalgeneticgenesplaysacentralroleintheevolutionofnaturalorganisms.Similarly,thekeyroleingeneticalgorithmsisthecrossoveroperatorofgeneticoperations.Theso-calledcrossoverreferstotheoperationofreplacingandrecombiningthepartialstructuresoftwoparentindividualstogeneratenewindividuals.Throughcrossover,thesearchabilityofgeneticalgorithmcanbegreatlyimproved.

Mutation

Thebasiccontentofthemutationoperatoristochangethegenevalueatsomelocioftheindividualstringsinthepopulation.Accordingtothedifferentrepresentationmethodsofindividualcodes,thefollowingalgorithmscanbeused:

a)Real-valuedmutation.

b)Binarymutation.

Generallyspeaking,thebasicstepsofthemutationoperatoroperationareasfollows:

a)Determinewhethertoperformmutationbasedonthepresetmutationprobabilityforallindividualsinthegroup

b)Randomlyselectthemutatedpositionforthemutatedindividualtomutate.

Geneticalgorithmintroducesmutationfortwopurposes:oneistomakegeneticalgorithmhavelocalrandomsearchability.Whenthegeneticalgorithmisclosetotheoptimalsolutionneighborhoodthroughthecrossoveroperator,thelocalrandomsearchabilityofthemutationoperatorcanacceleratetheconvergencetotheoptimalsolution.Obviously,theprobabilityofmutationinthiscaseshouldbeasmallvalue,otherwisethebuildingblocksclosetotheoptimalsolutionwillbedestroyedduetomutation.Thesecondistoenablegeneticalgorithmstomaintaingroupdiversitytopreventimmatureconvergence.Atthistime,theconvergenceprobabilityshouldtakealargervalue.

Terminationcondition

Whenthefitnessoftheoptimalindividualreachesagiventhreshold,orthefitnessoftheoptimalindividualandtheWhenthealgebraisset,thealgorithmterminates.Thepresetnumberofgenerationsisgenerallysetto100-500generations.

Features

Geneticalgorithmisageneralalgorithmforsolvingsearchproblems,whichcanbeusedforvariousgeneralproblems.Thecommonfeaturesofsearchalgorithmsare:

(1)Firstformasetofcandidatesolutions

(2)Measurethefitnessofthesecandidatesolutionsaccordingtocertainadaptabilityconditions

(3)Retainsomecandidatesolutionsbasedonfitnessanddiscardothercandidatesolutions

(4)Performcertainoperationsontheretainedcandidatesolutionstogeneratenewcandidatesolutions.

Ingeneticalgorithms,theabove-mentionedfeaturesarecombinedinaspecialway:parallelsearchbasedonchromosomegroups,selectionoperationswithguessingproperties,exchangeoperations,andmutationoperations.Thisspecialcombinationmethoddistinguishesgeneticalgorithmfromothersearchalgorithms.

Geneticalgorithmalsohasthefollowingcharacteristics:

(1)Thealgorithmstartsfromthesetofproblemsolutions,ratherthanfromasinglesolution.Thisisagreatdifferencebetweengeneticalgorithmandtraditionaloptimizationalgorithm.Traditionaloptimizationalgorithmsiterativelyfindtheoptimalsolutionfromasingleinitialvalue;itiseasytostrayintothelocaloptimalsolution.Thegeneticalgorithmstartsthesearchfromthestringset,andhasalargecoveragearea,whichisconducivetoglobalselection.

(2)Geneticalgorithmprocessesmultipleindividualsinthegroupatthesametime,thatis,evaluatesmultiplesolutionsinthesearchspace,reducingtheriskoffallingintolocaloptimalsolutions,andthealgorithmitselfiseasytoparallelize.

(3)Geneticalgorithmsbasicallydonotusesearchspaceknowledgeorotherauxiliaryinformation,butonlyusefitnessfunctionvalues​​toevaluateindividuals,andperformgeneticoperationsonthisbasis.Thefitnessfunctionisnotonlynotrestrictedbycontinuousdifferentiability,butitsdomaincanbesetarbitrarily.Thisfeaturegreatlyexpandstheapplicationrangeofgeneticalgorithms.

(4)Thegeneticalgorithmdoesnotusedeterministicrules,butusesprobabilistictransitionrulestoguideitssearchdirection.

(5)Self-organization,self-adaptationandself-learning.Whenthegeneticalgorithmusestheinformationobtainedintheevolutionprocesstoorganizethesearchbyitself,individualswithgreaterfitnesshaveahighersurvivalprobabilityandobtainageneticstructurethatismoreadaptedtotheenvironment.

(6)Inaddition,thealgorithmitselfcanalsousedynamicadaptivetechnologytoautomaticallyadjustalgorithmcontrolparametersandcodingaccuracyduringtheevolutionprocess,suchasusingfuzzyadaptivemethod.

Disadvantages

(1)Thecodingisnotstandardizedandthecodingisnotaccurate.

(2)Asinglegeneticalgorithmcodecannotfullyexpresstheconstraintsoftheoptimizationproblem.Onewaytoconsiderconstraintsistousethresholdsforinfeasiblesolutions.Inthisway,thecalculationtimewillinevitablyincrease.

(3)Theefficiencyofgeneticalgorithmisgenerallylowerthanthatofothertraditionaloptimizationmethods.

(4)Geneticalgorithmstendtoconvergeprematurely.

(5)Geneticalgorithmhasnoeffectivequantitativeanalysismethodfortheaccuracy,feasibility,andcomputationalcomplexityofthealgorithm.

Application

Becausetheoverallsearchstrategyandoptimizedsearchmethodofgeneticalgorithmdonotdependongradientinformationorotherauxiliaryknowledgeincalculation,onlytheobjectivefunctionandcorrespondingThefitnessfunctionofthegeneticalgorithm,sogeneticalgorithmprovidesageneralframeworkforsolvingcomplexsystemproblems.Itdoesnotdependonthespecificfieldoftheproblem,andhasstrongrobustnesstothetypeofproblem,soitiswidelyusedinmanysciences.BelowweSomemainapplicationareasofgeneticalgorithmwillbeintroduced:

Functionoptimization

Functionoptimizationisaclassicapplicationfieldofgeneticalgorithm,anditisalsoacommonexampleofgeneticalgorithmforperformanceevaluation.ManypeopleconstructTherearevariouscomplexformsoftestfunctions:continuousfunctionanddiscretefunction,convexfunctionandconcavefunction,low-dimensionalfunctionandhigh-dimensionalfunction,unimodalfunctionandmultimodalfunction,etc.Forsomenon-linear,multi-model,multi-objectivefunctionoptimizationproblems,otheroptimizationmethodsaremoredifficulttosolve,andgeneticalgorithmscaneasilygetbetterresults.

Combinatorialoptimization

Astheproblemsizeincreases,thesearchspaceofcombinatorialoptimizationproblemsalsoincreasessharply,andsometimesitisdifficulttofindtheoptimalsolutionusingenumerationincalculations..Forsuchcomplexproblems,peoplehaverealizedthatthemainenergyshouldbefocusedonseekingsatisfactorysolutions,andgeneticalgorithmisoneofthebesttoolsforseekingsuchsatisfactorysolutions.PracticehasprovedthatgeneticalgorithmisveryeffectiveforNPproblemsincombinatorialoptimization.Forexample,geneticalgorithmhasbeensuccessfullyappliedinsolvingtravelingsalesmanproblem,knapsackproblem,packingproblem,graphpartitionproblemandsoon.

Inaddition,GAhasalsobeenwidelyusedinproductionschedulingproblems,automaticcontrol,robotics,imageprocessing,artificiallife,geneticcoding,andmachinelearning.

Workshopscheduling

TheproblemofworkshopschedulingisatypicalNP-Hardproblem.Asaclassicintelligentalgorithm,geneticalgorithmiswidelyusedinworkshopscheduling.ManyscholarsarecommittedtousingThegeneticalgorithmsolvestheproblemofworkshopschedulingandhasachievedveryfruitfulresultstoday.Fromtheoriginaltraditionaljobshopscheduling(JSP)problemtotheflexiblejobshopschedulingproblem(FJSP),geneticalgorithmshaveexcellentperformanceandhaveobtainedoptimalornear-optimalsolutionsinmanyexamples.