夏水流萤182A.Cardonetal./RoboticsandAutonomousSystems33(2000)179–190
willuseasdistributionforthenumberofmutationbygeneration,acurveofparameters(α,β)
f:x→β
withβ∈R+andα∈R+ .
(1)Thus,byusingthistypeofdistribution,weintroducealotofmutationsatthebeginningofthesimulationandfewattheendinordertoavoiddisruptingtheprocessofevolutionbydeeplymodifyingcharacteristicsofchromosomes,andthereforeofindividuals.Toomanymutationsinthesystemswouldinexorablysowtheseedsofchaos.Wehavepreviouslyseenapossibledistribution.Nevertheless,byusingaGaussiandistri-butiontodeterminetheprobabilityofmutation,wekeeptheswitchboardofthegeneticalgorithm[39].4.Thecrossoveroperator
Fromanhistoricalpointofview,geneticalgorithms[27]correspondtoarandomphenomenon,butthemaindifferencecomparedtoaclassicrandommethodisthathere,weconverge,stepbysteptoanoptimum(localorglobal)inthespaceofsolutions[3].Thus,wearenotsubjecttochanceasweareintheformer,totallyrandommethod.A rstcrossingapproachwouldbetoconsideranagentasa“piechart”whereeachslicecorrespondstoacharacter.Byrandomlychoosingtwocutpointsinouragentcomparedtoareferential,wewouldexchangetwopartstoformnewindividuals.However,aproblemarises,astohowdowesetourreferential?Wecannotsetapermanentreferential,be-causeinthiscase,itsupposestoconsideranadjustableindividual.So,anagentisanentitythathasnofacets.Anagentiscomparabletoanindividualpartofanor-ganization.Nevertheless,itisnotpossibletodescribeitasaphysicalindividual(aman).Thereforethis rstapproachisinterestingbutdoesnotgivesatisfaction.Knowingthatnotallagentshavethesamegeneticpatrimony,thatistosaythattheyhavenoequalchro-mosomelengths,andknowingthatanagenthasnofacets,wecanrepresentitasatoroïdalchainofbits: Thisrepresentationdoesnotsupposetheinterven-tionofthenotionoffacetsofanagent.
Wecancrossindividualsofdifferentlengths[20].Itisalwaysnecessarytode neastartingpointforourchromosomeinordertocorrectlyexchangephe-notypes.Whichonedowechoose?Inoursystem,anagentiscomposedoffunctionsofaction,knowledge
andbehavior,thatmakeacertainnumberofpossi-blereferentials.Therefore,thechoiceofareferentialwouldbeaproblem,exceptbyrandomlychoosingit.Amongpossiblefunctions,whatdistributionwemustuse?Intheory,nodistributionisideal,nevertheless,tocontinuewiththiscirclescheme,wewilluseacir-cledistributionorGaussianmethodaccordingtotheprobability.Thus,itispossibletosetareferentialforthecrossing.However,theuseofasimplecrossingdoesnotalwaysgivegoodresults.Consequently,theuseofmultiplecrossingsallowsustomakeabiggermix.Wewillusetheuniformcrossovertoalwayshaveviableindividualsforourrepresentation.However,itisalwayspossibletousethecrossoversde nedbyGoldberg[20]suchastheCX,OXandthePMX[38],thatalwaysgiveviableindividuals.5.The tnessfunction
Inourcase,itisnecessaryforustooptimizeaGanttdiagram[43].Therefore,thelastoperationtoundertakewillhavetocorrespondtotheduedatemi-nuscompletiontime.Itisnecessary,thereforetomin-imizethedelayandtheadvanceofthesetofjobs.Theobjectivewithanadvanceandanulldelayisnearlyimpossible.Inageneralmanner,weallowacertaindelayoradvance.Whenwecalculatethe tnessofanagent,wedetermineitsimpactontheGantt[46].Ofcourseforthesetofjobs,wecanhaveadelayoraweakadvance.Consequently,wenolongerhaveasin-gle tnessfunctionbutmany.Wehaveasmanyobjec-tivesaswehavejobs.Consequently,wehaveacaseof“multi-objectivegeneticalgorithms”[44,45].Forthistypeofproblem,wewillusethebasicconceptsofthemulti-objectiveoptimizationproblem(MOP)[42].5.1.Basicconceptsandde nitions
Thefundamentaldifferencebetweenanoptimiza-tionhavingsimpleormultipleobjectivesisintheideaofthede nitionofanoptimalsolution.Theideaofoptimalityinthemulti-objectivecaseisanaturalex-tensionofwhatwehaveduringanoptimizationforauniqueobjective.
AnMOPcanbede nedasfollows:MOP:minx∈X
f(x),
wheref(x)=(f1(x),...,fn(x))(2)
