外文翻译用蚁群算法在刀库索引位置的优化配置.docx
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外文翻译用蚁群算法在刀库索引位置的优化配置
Optimalallocationofindexpositionsontoolmagazinesusinganantcolonyalgorithm
AbstractGenerationofoptimalindexpositionsofcuttingtoolsisanimportanttasktoreducethenon-machiningtimeofCNCmachinesandforachievementofoptimalprocessplans.Thepresentworkproposesanapplicationofanantcolonyalgorithm,asaglobalsearchtechnique,foraquickidentificationofoptimalornearoptimalindexpositionsofcuttingtoolstobeusedonthetoolmagazinesofCNCmachinesforexecutingacertainsetofmanufacturingoperations.Minimisationoftotalindexingtimeistakenastheobjectivefunction.
KeywordsIndexingtime.Automatictoolchange.CNCmachine.Optimization.Antcolonyalgorithm
1Introduction
Intoday’smanufacturingenvironment,severalindustriesareadaptingflexiblemanufacturingsystems(FMS)tomeettheever-changingcompetitivemarketrequirements.CNCmachinesarewidelyusedinFMSduetotheirhighflexibilityinprocessingawiderangeofoperationsofvariouspartsandcompatibilitytobeoperatedunderacomputercontrolledsystem.TheoverallefficiencyofthesystemincreaseswhenCNCmachinesareutilizedtotheirmaximumextent.Sotoimprovetheutilization,thereisaneedtoallocatethepositionsofcuttingtoolsoptimallyonthetoolmagazines.
ThecuttingtoolsonCNCmachinescanbechangedorpositionedautomaticallywhenthecuttingtoolsarecalledwithinthepartprogram.TodothisturretsareusedinCNClathemachinesandautomatictoolchangers(ATC)inCNCmillingmachines.ThepresentmodelcanbeusedeitherfortheATCmagazinesorturretsonCNCmachines.
Theindexingtimeisdefinedasthetimeelapsedinwhichaturretmagazine/ATCmovesbetweenthetwoneighbouringtoolstationsorpockets.Bi-directionalindexingofthetoolmagazineisalwayspreferredoveruni-directionalindexingtoreducethenon-machiningtimeofthemachine.Inthisthemagazinerotatesinbothdirectionstoselectautomaticallythenearerpathbetweenthecurrentstationandtargetstation.Thepresentworkconsidersbi-directionalmovementofthemagazine.Inbidirectionalindexing,thedifferencebetweentheindexnumbersofcurrentstationandtargetstationiscalculatedinsuchawaythatitsvalueissmallerthanorequaltohalfofthemagazinecapacity.
Derelietal.[1]formulatedthepresentproblemasa“travelingsalesmanproblem”(TSP),whichisNPcomplete.Theyappliedgeneticalgorithms(GA)tosolvetheproblem.Dorigoetal.[2,3]introducedtheantcolonyalgorithm(ACA)forsolvingtheNP-completeproblems.ACAcanfindthesuperiorsolutiontoothermethodssuchasgeneticalgorithms,simulatedannealingandevolutionaryprogrammingforlarge-sizedNP-completeproblemswithminimumcomputationaltime.So,ACAhasbeenextendedtosolvethepresentproblem.
2Methodology
Determinationoftheoptimalsequenceofmanufacturingoperationsisaprerequisiteforthepresentproblem.Thissequenceisusuallydeterminedbasedonminimumtotalset-upcost.Theauthors[4]suggestedanapplicationofACAtofindtheoptimalsequenceofoperations.Oncethesequenceofoperationsisdetermined,thefollowingapproachcanbeusedtogettheoptimalarrangementofthetoolsonthemagazine.
Step1Initiallyasetofcuttingtoolsrequiredtoexecutethefixed(optimal)sequenceofthemanufacturingoperationsisassigned.Eachoperationisassignedasinglecuttingtool.Eachtoolischaracterizedbyacertainnumber.Forexample,letthesequenceofmanufacturingoperations{M1-M4-M3-M2-M6-M8-M9-M5-M7-M10}beassignedtothesetofcuttingtools{T8-T1-T6-T4-T3-T7-T8-T2-T6-T5}.Thesetoftoolscanbedecodedas{8-1-6-4-3-7-8-2-6-5}.HerethemanufacturingoperationM1requirescuttingtool8,M4requires1andsoon.Intotalthereareeightdifferenttoolsandthuseightfactorialwaysoftoolsequencespossibleonthetoolmagazine.
Step2ACAisappliedastheoptimizationtooltofindthebesttoolsequencethatcorrespondstotheminimumtotalindexingtime.Foreverysequencethatisgeneratedbythealgorithmthesamesequenceofindexpositions(numbers)isassigned.Forexample,letthesequenceoftools{4-6-7-8-2-5-3-1}begeneratedandhenceassignedtotheindexingpositions{1-2-3-4-5-6-7-8}inthesequentialorder,i.e.tool4isassignedtothe1stposition,tool6tothe2ndpositionandsoon.
Step3Thedifferencesbetweentheindexnumbersofsubsequentcuttingtoolsarecalculatedandthentotaledtodeterminethetotalnumberofunitrotationsforeachsequenceofcuttingtools.Absolutedifferencesaretobetakenwhilecalculatingthenumberofunitrotationsrequiredfromcurrenttooltotargettool.Thisfollowingsectiondescribesanexampleindetail.
ThefirsttwooperationsM1andM4inthepre-assumedfixedsequenceofoperationsrequirethecuttingtools8and1,respectively.Thetoolsequencegeneratedbythealgorithmis{4-6-7-8-2-5-3-1}.Inthissequencetools8and1areplacedinthe4thand8thindexingpositionsoftheturret/ATC.Hencethetotalnumberofunitrotationsrequiredtoreachfromcurrenttool8totargettool1is|4-8|=4.Similarlythetotalnumberofunitrotationsrequiredfortheentiresequenceis|4-8|+|8-2|+|2-1|+|1-7|+|7-3|+|3-4|+|4-5|+|5-2|+|2-6|=30.
Step4Minimizationoftotalindexingtimeistakenastheobjectivefunction.Thevalueoftheobjectivefunctioniscalculatedbymultiplyingthetotalnumberofunitrotationswiththecataloguevalueofturret/ATCindextime.Ifanindextimeof4sisassumedthenthetotalindextimerequiredforthetoolsequencebecomes120s.
Step5AsthenumberofiterationsincreasesACAconvergestotheoptimalsolution.
3Allocationpolicy
Thefollowingarethethreecaseswherethetotalnumberofavailablepositionscanberelatedwiththetotalnumberofcuttingtoolsemployed.
Case1Thenumberofindexpositionsisequaltothenumberofcuttingtools
Case2Thenumberofindexpositionsisgreaterthanthenumberofcuttingtools(a)withoutduplicationoftools,(b)withduplicationtools
Case3Thenumberofindexpositionsissmallerthanthenumberofcuttingtools
Iftheproblemfallsintocase1,duplicationofcuttingtoolsinthetoolingsetisnotrequiredasthesecondset-upalwaysincreasesthenon-machiningtimeofthemachine.
Table1Listoffeaturesandtheirabbreviations
Incase2,theeffectofduplicationofcuttingtoolsshouldbetestedcarefully.Mostofthetimestheduplicationoftoolingistooexpensive.Case3leadstofindingthecuttingtoolstobeusedinthesecondset-up.However,othersubphasesarepossibleincases2(b)and3.TheduplicatedtoolsmaybeusedinsuchawaythatnounloadedindexisleftonATCorsomeindexingpositionsareleftunloaded.
Table2Operationsassignedtothefeatures
4Antcolonyalgorithm
Theantcolonyalgorithm(ACA)isapopulation-basedoptimizationapproachthathasbeenappliedsuccessfullytosolvedifferentcombinatorialproblemsliketravelingsalesmanproblems[2,3],quadraticassignmentproblems[5,6],andjobshopschedulingproblems[7].Thisalgorithmisinspiredbytheforagingbehaviourofreallifeantcoloniesinwhichindividualantsdepositasubstancecalledpheromoneonthepathwhilemovingfromonepointtoanother.Thepathswithhigherpheromonewouldbemorelikelytobeselectedbytheotherantsresultinginfurtheramplificationofcurrentpheromonetrails.Becauseofthisnature,aftersometimeantswillselecttheshortestpath.Thealgorithmasapplicabletothepresentproblemisdescribedinthefollowingsection.
Itisassumedthatthereis‘k’numberofantsandeachantcorrespondstoaparticularnode.Thenumberofantsistakenasequaltothenumberofnodesrequiredtoexecutethefixedsetofmanufacturingoperations.Thetaskofeachantistogenerateafeasiblesolutionbyaddinganewcutting\toolatatimetothecurrentone,tillalloperationsarecompleted.Anant‘k’situatedinstate‘r’movestostate‘s’usingthefollowingstatetransitionrule:
Table3Cuttingtoolsassignedtooptimalsequenceofoperations
Whereτ(r,s)iscalledapheromonelevel.τ(r,s)’sarechangedatruntimeandareintendedtoindicatehowusefulitistomakemove‘s’wheninstate‘r’.η(r,s)isaheuristicfunction,whichevaluatestheutility
ofmove‘s’whenat‘r’.Inthepresentwork,itistheinverseofthenumberofunitrotationsrequiredtomovefrom‘r’to‘s’.
Parameter‘β’weighstherelativeimportanceoftheheuristicfunction.‘q’isavaluechosenrandomlywithuniformprobabilityin[0,1],and‘q0’e0q01Tisaparameter.Thesmallerthe‘q0’,thehighertheprobabilitytomakearandomchoice.Inshort‘q0’determinestherelativeimportanceofexploitationversusexplorationinEq.1.
Jk(r)representsthenumberofstatesstilltobevisitedbythe‘k’antwhenat‘r’.Sisarandomvariableselectedaccordingtothedistribution
givenbyEq.2,whichgivestheprobabilitywithwhichanantinoperation‘r’chooses‘s’tomoveto.
Thisstatetransitionrulewillfavourtransitionstowardsnodesconnectedbyshortedgeswithhighamountoftrail.
4.1Localupdatingrule
Whilebuildingasolution,antschangetheirtrailsbyapplyingthefollowinglocalupdatingrule:
Whereτ0representstheinitialpheromonevalue.
4.2Globalupdatingrule
Globaltrailupdatingprovidesahigheramountoftrailtoshortersolutions.Inasensethisissimilartoareinforcementlearningschemeinwhichbettersolutionsgetahigherreinforcement.
Onceallantshavecompletedtheirsolutions,edges(r,s)belongingtotheshortestsolutionmadebyananthavetheirtrailchangedbyapplyingthefo