ֻ16जֻ3௹۽ြ۽ӱ 2013୍6ᄅJune2013IndustrialEngineeringJournaldoi: ໓ངѓᆽ:A ໓ᅣщݼ:1007-7375(2013)03-0131-07ResearchonProcessPlanningandDecisionProblemBasedonHybridGeneticAlgorithm1,21,2LiuQi-you,LiTie-ke(,UniversityofScienceandTechnologyBeijing,Beijing100083,China;&SteelProduction,MinistryofEducation,Beijing100083,China)Abstract:Inpartprocessing,duetovariousprocessingfeatures,differentprocesses,andprocess-con-strainedprocessingsequencingrules,,,,,,:processconstraint;multi-objectiveoptimization;geneticalgorithm ෛሢग़ླ֥ರ۱ྟ߄,؟ᇕ、ഒਈളႭູᇗေ。ಖطᄝളӁൌ࠽ᇏ,ႮႿ1)ࡆ۽۽ၜ࿊Ӂၘᇯ҄Ӯູ֒ࣂᇅᄯఒြ֥ᇶေളӁٚൔᆭ၂。ᄴ:၂ӁหᆘऎႵ҂֥ࡆ۽۽ၜ;2)ࡆ۽ࠏఖၹՎ,ೂޅਲࠃֹཙႋ൧ӆ֥۱ྟ߄、؟ဢ߄ླ,࿊ᄴ:၂۽ॖၛ࿊ᄴ҂֥ࡆ۽ഡС;3)ࡆ۽۽ֹࡼग़ླሇ߄ӮളӁᆷ,ིۚੱ֮ӮЧஆ:ളӁࡆ۽֥ӁऎႵ҂֥ࡆ۽หᆘ,ᆃֹུᇅᄯԛग़ડၩ֥רֆӁ,۽ၜܿ߃ߌࢫཁ֤ࡆ۽หᆘ֥ࡆ۽ඨෙಖ൳֞၂ק֥۽ၜჿඏ,൬۠ರ௹:2012-09-13ࠎࣁཛଢ:࢝ტ҆Ѱൖ࿐॓ׄህཛ॓ࠎࣁ(20100006110006);ᇏနۚࠎЧ॓ြༀٮህཛሧࣁሧᇹ(FRF-AS-09-007B)ቔᆀࡥࢺ:ਾᠱႰ(1983-),ଳ,ࡾ༆സದ,Ѱൖ࣮ള,ᇶေ࣮ٚཟູ༵ࣉᇅᄯܵ、ᇆି࠹ෘ.
۽ ြ ۽ ӱֻ16ज 132ѩ٤෮Ⴕหᆘᆭࡗթᄝ֥༵۬ުՑܱ༢。ႮORष֞JOINࢲඏ,іൕॖၛ࿊ఃᇏ၂่ਫ਼ཌ,Ⴟၛഈ಼ྟၹ֥թᄝ,֤໙ีऎႵNPหྟ,ೂݔ҂൞ႮOR෮৵ࢤ,ࣼсྶေປӮՎਫ਼ཌ෮Ⴕ֒໙ีղ֞၂קܿଆ۽。2൞ၛ۽1ູൕ২ؓࡆ۽۽֥བྷ༥૭,Ⴈࣚಒෘمᄝކൡൈࡗଽၛᅳ֞ડၩࢳ。ၹՎ,Ч໓ࡼᇗׄંඍ০Ⴈջჿඏඍൕ২,ٚॿଽ൞ؓ۽֥བྷ༥ᅚष,ٳљ૭ඍਔ۽ݼ、۽ॖ࿊ࠏఖࠣ۽ᄝཌྷႋॖ࿊ࠏఖഈࡆטᆜ֥؟ଢѓ၌Ԯෘمটࢳھ໙ี。۽ൈࡗ。ఃऎุଽಸೂі1෮ൕ。ᆌؓھ໙ี֥࣮,໓ང[1]Ⴈ܋ളစ߄ෘمࢠݺֹࢳथਔ಼ྟᇅᄯ༢֥؟ଢѓ۽ၜܿ߃აथҦ໙ี,໓ᇏࡼࡆ۽ٚم、ॖ࿊ࠏఖၛࠢӮٚൔࣉྛщ。ھщٚൔ֥Ⴊׄ൞ၞႿіղ、ᆰܴބࢳٚൔࡥֆ,ႮႿ၂۱ࠎၹЇݣ֥ྐ༏ݖ؟,ᄯӮ၌ԮҠቔࢠູگᄖ,Ֆط႕ཙෘم൬৻؇。໓ང[2]བྷ1 ਬࡱࡆ۽؟۽ၜਫ਼ཌຩሑ༥૭ඍਔGAᄝਬ҆ࡱളӁࡆ۽ᇏ۽ၜਫ਼ཌथҦٚ Partsprocessingmulti-routenetwork૫֥ႋႨ。໓ᅣؓԚᇕಕളӮၛࠣࢌҭ、эၳݖӱᇏӁള֥ິّ۽ၜჿඏ֥ಙุࣉྛࡥֆ֥วԩ。ھٚمҠቔࡥֆ,ᄝࢳݖӱᇏॖି߶שാࢠݺ֥၌Ԯࠎၹ。ᄝԩ؟ଢѓ၌Ԯෘمᄝ۽ၜਫ਼ཌႪ߄ა࿊ᄴٚ૫֥ႋႨൈ,໓ང[3]ࡼ۲ଢѓݦ2 ۽བྷ༥ൕ২ඔၛܥק֥ಃᇗ༢ඔཌྷࡆުሇ߄Ӯֆଢѓ,ھٚم Detailedprocessexample֥Ⴊׄ൞Ϝࢳथ؟ଢѓႪ߄֥گᄖ໙ีሇ߄ູࢠࡥ Ⴎഈॖᆩ,҂֥ࡆ۽หᆘஆၛࠣ҂֥۽ֆ֥ֆଢѓႪ߄໙ี,ಃᇗ֥࿊ᄴაٳ༅ᆀႵૡၜބࠏఖ࿊ᄴ,ႮႿఃࡆ۽ൈࡗބӮЧ҂,߶ቆކ్ཌྷܱ,ط҂ିޓݺֹෆ෬֞Paretoభခ。Ӯሸކ۽ၜି৯҂֥۽ၜਫ਼ࣥ。[4]Ч໓ᄝၘႵ࣮֥ࠎԤഈ,๙ݖؓॖ࿊۽ູਔьႿ໙ี֥૭ඍބࡹଆ,൮༵ؓ໙ีࣉྛބࠏఖࣉྛٳ؍щটࢳथ؟۽ބࠏఖ࿊ᄴ໙ೂ༯֥ࡌഡބژݼקၬ。ࡌഡ1)ૄࠏఖ၂ൈี;ѩႨჿඏטᆜෘمԩԚᇕಕބэၳݖӱᇏख़ᆺିࡆ۽၂֡۽,၂Ӂ֥҂۽,҂ିӁള֥ິّ۽ၜჿඏ֥ஆ໙ี。ᆌؓൌ࠽ളӁᇏൈࡆ۽;2)ࡆ۽࠹ൈष,෮Ⴕࠏఖ൞ॖྛ֥;3)؟ଢѓႪ߄໙ี,໓ᇏҐႨෛࠏಃᇗটഡᇂൡႋ؇Ӂഈ၂֡۽ࢲඏ֞༯၂֡۽ष,ᆭࡗ֥ሇݦඔ,Ⴈຓ҆ಕุ֥ࣚႇЌҦѩႨk-meansऊো[5-7]ߐൈࡗޭ҂࠹。ژݼקၬೂ༯。ෘمҊࡧࣚႇࠢটЌӻಕุ؟ဢྟ,๙ݖھࠁކ၌i಼ູྟ۽ၜਫ਼ཌщ;IູӁࡆ۽಼ྟ۽ၜԮෘم֥ࢌҵ、эၳ֩Ҡቔࣉྛ۽ၜਫ਼ཌथҦ。ਫ਼ཌࠢކ;jູ۽щ;Jֻູi่۽ၜਫ਼ཌ֥۽iࠢކ;Oֻູi่۽ၜਫ਼ཌഈֻ֥j֡۽;mູ۽ij1 ໙ี૭ඍაࡹଆO֥ॖ࿊ࡆ۽ࠏఖ;Mູࠏఖሹඔ;CW(m)ູࠏ ໙ี૭ඍఖmࡆ۽ֆ໊ൈࡗӮЧ;tູ۽Oᄝॖ࿊ࡆ۽ࠏijmijളӁࡆ۽ݖӱᇏႮႿࡆ۽۽ၜބࠏఖ֥࿊ᄴၛఖmഈ֥ࡆ۽ൈࡗ;sູ۽Oᄝॖ࿊ࡆ۽ࠏఖmijmijࠣࡆ۽۽ஆ಼֩ྟၹ֥թᄝ,֤၂ਬ҆ഈ֥षൈࡗ;NCMູӁࡆ۽эߐࠏఖՑඔ;CM-ࡱ֥ࡆ۽ऎႵ؟่ളӁਫ਼ࣥ。۽ၜܿ߃ࠧ൞ᄝളӁCIູࠏఖэߐ၂ՑӮЧ;CMູࠏఖࡆ۽ӮЧ;CMCൌ࠽ᇏ۴ऌथҦᆀ֥ླေ,ၛൈࡗቋ؋、ӮЧቋູ֮֩ࠏఖэߐӮЧ;TTູሹࡆ۽ൈࡗ;TCູሹࡆ۽Ӯູଢѓݦඔ,ؓቋႪ֥۽ၜਫ਼ࣥࣉྛႪ߄ა࿊ᄴ。Ч。؟۽ၜਫ਼֥ࣥіղٚൔࢠ؟,ׅ֥ႵPetriຩ、1,۽ࡱ࿊ᄴֻi่۽ၜਫ਼ཌࡆ۽;X=AND/ORބຩሑ֩。Ч໓ҕॉ໓ང[1],Ⴈڿࣉi0,ڎᄵ。֥AND/ORބຩሑཌྷࢲކ֥ٚൔ,ؓଖਬ҆ࡱ1,۽O࿊ᄴࡆ۽ࠏఖm;ijࡆ۽۽ၜႨຩሑіൕ,ೂ1෮ൕ。Z=ijm0,ڎᄵ。 Վຩሑ൞၂ᇕ٤࿖ߌ֥ֆཟ,S、Fູྴ1,x҂֩Ⴟy;֥षࢲඏࢫׄ,1、2、3֩іൕࡆ۽۽,ࡰіൕφ(x,y)=0,x֩Ⴟy。ࡆ۽ඨ,ORіൕॖ࿊ࡆ۽۽ၜ。ೂݔ၂۱ࢫׄႮ
ֻ3௹ਾᠱႰ,ํक़:ࠎႿࠁކ၌Ԯෘم֥ളӁ۽ၜܿ߃აथҦ໙ี 133і1 ਬࡱࡆ۽؟۽ၜਫ਼ཌཌྷܱඔऌі Datasheetforpartsmultipleprocessingroutesหᆘ۽ॖ࿊ࡆ۽ࠏఖ෮࿊ࠏఖࡆ۽ൈࡗหᆘࡗՑჿඏཌྷܱҕඔFM,M,M,M1112345,5,7,8෮Ⴕหᆘభ4 jFM,M,MᄝF、Fభ2223410,12,14344 M,M～M,M,M3～424124ᄝFభ6,9～8,10,74F3 5～6M,M,M～M,M5,7,6～12,9CW(1)=5;y]125355FM,M,M,M47124512,9,13,8CW(2)=10;4 jFM,M,M,MᄝF、F、Fభ5813454,6,7,10CW(3)=7;6784 jFM,M,MᄝF、Fభ915,18,13CW(4)=12;4623478 M,M,MᄝFభ1013522,25,258CW(5)=8;F7 11M,M,M,M24,27,24,25CMCI=25;KZ2345jఃᇏCW(m)ູࠏఖmFM,M,M126,4,5K8245 ࡆ۽ֆ໊ൈࡗӮЧ;CMCIູࠏఖэߐ၂ՑFM,M,M,MᄝF、Fభ91312457,9,7,81011K jӮЧ。M,M,M～M,M14～1523425ᄝFభ8,9,8～6,711F1016M,M,M12,15,13K 345 FM,M,M176,7,5K11235 ໙ีଆ(3)ބ(4)ٳљіൕ۽ބࠏఖჿඏ;ൔ(5)іൕᆺՖሹࡆ۽ൈࡗቋ؋ބሹӮЧቋ֮ਆٚ૫ॉ੮,ି࿊ᄴ၂่۽ၜਫ਼ࣥ;ൔ(6)ູૄ֡۽ᆺିᄝ၂Ч໓ࡹ৫֥؟ଢѓ۽ၜਫ਼ࣥႪ߄ଆູॖ࿊ࠏఖഈࡆ۽。Pim2 ࢳෘمinTT=(t×X×Z),i∈[1,I],m∈ijmiijm∑j=1[1,M];(1)Ⴎၛഈ૭ඍॖᆩ,۽ၜܿ߃໙ี൞၂োऎႵ؟minTC=CM+CMC。(2)ଢѓ、؟эਈ、؟ჿඏ֥ቆކႪ߄໙ี,Ⴈࣚಒෘمఃᇏ,ࠏఖࡆ۽ሹӮЧCMބࠏఖэߐሹՑඔᄝॖྛൈࡗଽၛࢳ。Ч໓ิԛࠎႿჿඏטᆜ֥NCMބэߐሹӮЧCMCٳљູ؟ଢѓ၌Ԯෘم。ھෘم֥ܱ໙ี൞ؓԚ߄ބJiࢌҭэၳݖӱᇏ҂ॖྛࢳ֥ԩၛࠣ؟ଢѓ֥ླྀטCM=(t×CW(m)×X×Z),i∈[1,ijmiijm∑Ⴊ߄,༯૫ٳљؓऎุ໙ี֥ࢳथٚمࣉྛٳ༅。j=1I],m∈[1,M]; ჿඏטᆜෘمJ-1i০Ⴈ၌Ԯෘمࣉྛ؟۽ၜਫ਼ࣥࢳൈ,หᆘ۽NCM=φ(O,O),Oіൕ۽ij-mi(j+1)-m′ij-m∑ࡗஆႮႿӁളӁ۽ၜჿඏ,ෛࠏԚ߄ၛࠣj=1O෮࿊ࠏఖູm;ᆌؓหᆘԱ֥ࢌҭ、эၳݖӱᇏႵॖିӁളაࡆ۽ijCMC=NMC×CMCI。۽ၜཌྷᙣ֥۽ၜඨ。Ч໓Ⴈჿඏטᆜෘم,ؓႵ[8-9]ჿඏ่ࡱູᙣႿ۽ၜჿඏ֥ࡆ۽ඨࣉྛൡ֥֒ྩᆞ。ఃෘم҄ᇧೂ༯。s×X×Z-s×X×Z≥t×X×ijmiijmijmiijmijmi22121Step1:ࡼԚหᆘԱ(FeatureList,FL)ᇏაఃZ,i∈[1,I],j,j∈[1,J],m∈[1,M];(3)ijm12i1หᆘીႵჿඏܱ༢֥หᆘ,ᄝ҂ڿэః໊ᇂ֥ൈs×X×Z-s×X×Z≥t×i(j+1)mii(j+1)mijkiijmijm22111็࿊ԛট;X×Z,i∈[1,I],j,j+1∈[1,J],m,m∈[1,iijmi121Step2:ࡼఃႵՑჿඏ֥หᆘՖFLᇏοః֒M];(4)భඨิ౼ԛট,ቆӮྍ֥ਙіLL,ѩࡼૌᄝFLX=1;(5)i∑ᇏ໊֥ᇂഡᇂູॢ;Z=1。(6)ijk∑Step3:Ֆުཟభ,၇ՑҰਙіLLหᆘՑჿൔ(1)ބ(2)ٳљູሹࡆ۽ൈࡗބӮЧቋཬ;ൔඏܱ༢,ѩࡼ֒భҩหᆘݼѓ്ູ“CurrentBit”,ೂ
۽ ြ ۽ ӱֻ16ज 134[11]ݔᄝ“CurrentBit”ᆭభ֥หᆘԱᇏ,Ⴕ؟۱หᆘބః༯。ՑႵᙣ,ླᄝఃު,ᄵࡼᆃུหᆘԱᄝหᆘԱLLStep1:Q={q,q,…,q}ູЇݣn۱ᇕಕ֥12nิԛቆӮ၂۱ྍ֥LL_1ਙі,ѩࡼఃᄝLLᇏԢࣚႇࠢ,N(n>N,ູࡼ࿊౼֥ܥקܿଆඔ֥ຓeliteelite֥ൈࡼLL_1٢ᄝLLᇏ֥Cu҆ࣚႇࠢ,ᄵ࿊౼ऊো۱ඔູN。rrentBitު૫,ൈࡼeliteېҩ֥ପ۱หᆘഡᇂູStep2:ՖࣚႇࠢQᇏෛࠏ࿊קN۱৬ሰቔູ“Handed”。eliteԚऊোᇏྏc,c,…,c。Step4:ᇗگstep3Ҡቔ,ᆰ֞LLഈ෮ႵࠎၹФ12Neliteѓ്ູ“Handed”;Վൈ,LLᇏ෮ႵหᆘՑၘડStep3:۴ऌൔ(7)ࡼࣚႇࠢQᇏ֥ؓའq(i=iቀჿඏܱ༢1,2,…,n)၇Ցο൦एٳ۳एቋ֥࣍၂۱,ࡼLLοඨ၇ՑҬೆFLᇏ,ࠧॖ֤ડቀჿඏྩᆞު֥ॖྛࢳऊোᇏྏc(1≤j≤N),ఃᇏkູ৬ሰົඔ;。 ؟ଢѓႪ߄Ҧ=m2in。q-cij(q-c),1≤j≤Niljlelite∑1)ຓ҆ࣚႇࠢࠣః۷ྍҦ。l=1ᆌؓࢌҭ、эၳݖӱᇏॖି߶ߊ֒భᇕಕ֥(7)ቋႪ۱ุ,ᄯӮቋႪ۱ุᄝ၌Ԯݖӱᇏשാط֝ᇁStep4:οൔ(8)࠹ෘN۱ऊোྍ֥ᇏྏc(1≤elitej֥ෘم҂ି൬৻֞ಆअቋႪࢳ֥౦ঃ,Ч໓ႋႨࣚj≤N),ఃᇏNֻູj۱ऊোSᇏ෮Їݣ֥৬ሰ۱elitejjႇҦ,൮༵,Ֆຓ҆ࣚႇࠢᇏگᇅሸކ۽ၜି৯ቋඔ;Ⴊ֥၂קඔਈ۱ุ֞༯၂սᇏ;ఃՑ,০Ⴈٚ1c=q,j=1,2,…,N。(8)jielite∑[10]Nx∈SjمটൌགྷఃჅ۱ุ֥گᇅ。ܱႿຓ҆ࣚႇ֥ࠢijStep5:ೂݔ۲۱ऊোᇏྏc(1≤j≤N)҂ᄜэjeliteקၬࠣఃᄝ၌Ԯݖӱᇏ֥۷ྍҦೂ༯。߄,ሇᇀStep6,ڎᄵْ߭Step3。קၬ1(Paretoᆦ) ӫ၂۱ཟਈu=(u,u,12Step6:ٳљՖN۱ऊোᇏෛࠏ࿊౼၂۱ᇕಕ,elite…,u)ᆦ(ࠇ٤ਜႿ)ཟਈv=(v,v,…,v),֒m12m֤֞N۱ᇕಕ。ࣚႇࠢᇏЌ࿊౼֥ᆃN۱ᇕeliteeliteࣇ֒ؓႿ i∈(1,2,…,m),u≤v i∈(1,2,iiಕ,Ԣఃᇕಕ,Ֆطࣚႇࠢᇏᇕಕ۱ඔູ…,m)֤u<v,࠺ູu v。iiN。eliteקၬ2(ParetoቋႪ) ᄝॖྛࢳთଽ҂թ3)ෛࠏಃᇗم。ᄝޅ၂۱x֤f(x) f(x′)ᄵx′ॖӫູ؟ଢѓ؟ଢѓ၌ԮෘمࢹParetoቋႪં,๙ݖؓսႪ߄໙ี֥ParetoቋႪࢳ。і۱ุࢳ֥ᇕಕࣉྛႪ߄,ၛଽᄝѩྛ֥ٚൔෆ෬٤קၬ3(ParetoቋႪࠢ) ParetoቋႪࢳࠢ൞ᆷਜࢳ,ෆ෬֥֞ᇕಕࢳऎႵParetoቋႪࠇࢤ࣍Pare-෮ႵParetoቋႪࢳ֥ࠢކ。[12]toቋႪ。Ч໓ҐႨෛࠏಃᇗمؓ၌Ԯෘم֥؟ଢקၬ4(ຓ҆ࣚႇࠢ) ႨၛЌթࠎၹᄝ၌Ԯݖѓหྟࣉྛԩ,၌ԮෘمऎႵॖэෆ෬ٚཟ,ࠧӱᇏӁള֥٤ਜࢳ֥ࠢކӫູຓ҆ࣚႇࠢ。[13]ᄝᆜ۱Paretoభခ૫ഈࣉྛनᄋҐဢ֥ି৯。ෘمૄՑםսݖӱᇏ࿊౼ܥקܿଆඔ֥ຓ҆ࣚࡌഡႵq۱ቋཬ߄ଢѓݦඔ,ࡼ۲ଢѓڮჍෛႇࠢটЌ֞ଢభູᆸ෮ᅳ֥֞٤ᆦࢳ,ѩෛሢࠏಃᇗ,ࡼఃሇߐӮֆଢѓݦඔູࣉ߄ݖӱ҂؎۷ྍھಕุ。္ࣼ൞ඪૄളӮྍ၂սqಕุ,༵ᅳԛྍಕุᇏ֥෮ႵParetoቋႪࢳ,ಖުࡼy=ωf(x)。(9)kk∑k=1ᆃུ۱ุ၇Ցაຓ҆ࣚႇࠢᇏ֥۱ุࣉྛбࢠ。ೂෛࠏಃᇗωູkݔھ۱ุ҂ିФຓ҆ࣚႇࠢ෮Ⴕ۱ุᆦ,ᄵࡼqเࡆ֞֒భຓ҆ࣚႇࠢᇏ,ѩԢຓࣚႇࠢ෮ႵФω=r/r,k=1,2,…,q。(10)kkj∑j=1ھ۱ุᆦ֥ࢳ。ᄝࣉ߄֥ު௹,෮ᅳ֥֞٤ᆦఃᇏ,r൞٤ڵෛࠏඔ。ᄝ࿊ԛࣉྛᄖࢌ֥۱ุభ,jࢳ֥ඔଢສສޓն,ေӑݖຓ҆ಕุ֥ܥקܿଆ。Ⴎൔ(10)ളӮ၂ቆෛࠏಃᇗඔ,۴ऌൔ(9)࠹ෘૄՎൈॖҐႨࠎႿk-meansऊো֥ࣚႇࠢҊࡧෘم。۱۱ุ֥ൡႋᆴ,ᄵֻi۱۱ุФ࿊ᇏ֥ۀੱpູi2)ࠎႿk-meansऊোෘم֥ࣚႇࠢҊࡧҦ。y-yiminp=。(11)inࠎႿࣚႇ֥ࠢ؟ଢѓႪ߄ෘم҂ေऎႵޓݺ(y-y)jmin∑֥൬৻ྟି,ߎေෘم֤֥ࢳऎႵޓݺ֥ٳ҃j=1ྟ,ၹՎЧ໓ҐႨk-meansऊোෘمҊࡧࣚႇࠢ,ၛఃᇏ,yູ֒భᇕಕቋҵ۱ุൡႋᆴ;nູᇕಕ۱min௹ᄝҊࡧݖӱᇏЌӻࢳ֥ٳ҃ྟି。ఃෘم҄ᇧೂඔ。
ֻ3௹ਾᠱႰ,ํक़:ࠎႿࠁކ၌Ԯෘم֥ളӁ۽ၜܿ߃აथҦ໙ี ࢳ۽ၜܿ߃໙ี֥၌ԮෘمၜԱࢳູF(O)-F(O)-F(O-O)-F(O)-112235647၌Ԯෘم(GeneticAlgorithm,GA)൞Ⴎૅݓ֥(O)-F(O)-F(O)-F(O)-F(O)-5869711812913HollandႿ1975۴ऌളࣉ߄ܿੰิԛ֥ෛࠏႪ߄F0(O)-F(O)。ॖ࿊ࠏఖԱࢳູO(M)-116111712ෆ෬ٚم。ھෘمᄎෘੀӱЇওщ、ԚಕุളO(M)-O(M)-O(M)-O(M)-O(M)-2432445263Ӯ、ൡႋ؇ᆴࡎ、၌ԮҠቔഡ࠹(࿊ᄴ、ࢌҭ、эၳ)O(M)-O(M)-O(M)-O(M)-O(M)-758493103115֩。གྷ۴ऌ෮໙ีᇗׄࣼщࢳ、ࢌҭބэၳO(M)-O(M)-O(M)-O(M)-O(M)-125131143152164[14]ࣉྛӂඍ。O(M)。ಖުؓหᆘԱࣉྛࢳॖᆩ,หᆘ֥ࡆ۽1751)щބࢳ。ඨູF-F-F-F-F-F-F-F-F-F-F。ቋުႮ1567823491011ၛສ֥࣮໓ངᇏ,նҐႨࠢӮщ֥ٚൔ3҆ٳ֥ࢳࢲݔॖ֤ھщٚσ۽ၜਫ਼ཌູࡼࠎၹіൕູ(j,k),ఃᇏ,jіൕ۽ݼ;kູ෮࿊ࡆO(M)-O(M)-O(M)-O(M)-O(M)-1224526375۽ࠏఖݼ。ھщٚൔႮႿૄ۱ࠎၹེջ֥ྐ༏ਈO(M)-O(M)-O(M)-O(M)-O(M)-8493115125131ݖ؟,ᄯӮ၌ԮҠቔگᄖ,ིੱࢠ֮。Ч໓ҐႨ؟҆O(M)-O(M)。Ⴎі1ଽ֥ࡆ۽ൈࡗބӮЧඔ164175ٳщٚم,ࡼࡆ۽หᆘ、ॖ࿊۽ၜ、ॖ࿊ࠏఖٳ3ऌ,ьॖԛ෮ؓႋ֥۽ၜਫ਼ཌ֥ሹࡆ۽ൈࡗބӮ[12]҆ٳࣉྛٳ؍щ。Ⴎ۽ၜਫ਼ࣥ1ބཌྷܱඔЧ。ऌі1,ॖၛ֤ԛھਬࡱ၂۱ॖྛ֥щٚσ,ೂ2)ࢌҭބэၳ。3෮ൕ。ᆌؓЧ໓ิԛ֥؟҆ٳٳ؍щٚൔ,གྷٳљ[15]ؓࢌҭބэၳٚൔࣉྛӂඍ。ؓႿॖ࿊۽ၜԱބࠏఖԱ֥ࢌҭٚم,ູਔЌᆣૄ໊ࠎၹ֥༵ުඨЌӻ҂э,໓ᅣႨਆׄࢌҭ3 ၌Ԯෘمࢳ۽ၜܿ߃໙ี֥؟҆ٳщٚσم,ෛࠏ࿊ᄴ2۱ࢌҭׄ,ࡼڳսਆಙุФٳӮቐ EncodingschemaofgeneticalgorithmtoᇏႷ3҆ٳ,۲ڳսᇏࡗ֥҆ٳࠎၹ҂эگᇅ֞ሰsolvetheprocessplanningproblemսᇏ,ࡼభުਆ҆ٳࠎၹٳљࢌҭگᇅ֞ሰսᇏ,ၛ ॖ࿊۽ၜԱ:ھಙุӉ؇ູਬࡱࡆ۽หᆘሹഈ֥ࢌҭٚൔЌᆣਔॖ࿊۽ၜބࠏఖԱૄ໊ࠎၹ֥ඔ༵ުඨ҂э,֤֥֞ሰս൞ॖྛ֥。,໓ᇏਬࡱ܋Ⴕ11۱ࡆ۽หᆘ,ܣॖ࿊۽ၜԱӉؓႿหᆘԱ֥ࢌҭҠቔ,ҐႨၛ༯ࢌҭ҄ᇧ。؇ູ11,ఃࠎၹ໊ഈඔሳٳљοඨіൕՖหᆘF-1൮༵ෛࠏ࿊ᄴ2۱ࢌҭׄࡼڳսಙุٳӮቐF֥֒భหᆘ෮࿊ᄴ֥۽ၜᄝھหᆘؓႋॖ࿊۽ၜ11ᇏႷ҆ٳ,ೂ4෮ൕ,ࡼᇏࡗ҆ٳگᇅ֞۲ሱ֥ࠢᇏ֥ඨݼ。ೂֻ3۱ࠎၹ໊ඔሳູ2,іൕֻ3ሰսᇏ,ࡼڳսPᇏሰսOၘႵ֥ࠎၹԢ;ಖު۱ࡆ۽หᆘ21F࿊ᄴ֥൞ֻ2่۽ၜਫ਼ཌ,ࠧO-O。356ࡼڳսPᇏഺჅ֥ࠎၹοჰඨ၇Ցแೆ֞ሰս2ॖ࿊ࠏఖԱ:ಙุӉ؇֩Ⴟਬࡱ෮Ⴕࡆ۽۽Oᇏ,ьॖ֤֞ሰսO。ဢ֥ࢌҭٚൔॖၛ֤֞11ሹބ,໓ᇏਬࡱ܋Ⴕ17۱۽,ܣӉ؇ູ17。აሰսO。ᄝࢌҭުႨჿඏטᆜෘمҩ,ѩؓႵᙣ2ॖ࿊۽ၜԱཌྷර,ఃࠎၹ໊ഈඔሳٳљοඨіൕႿ۽ၜหᆘჿඏ֥ඨࣉྛטᆜ。۽O-O֥֒భ۽෮࿊֥ࠏఖᄝھ۽෮ؓႋ117֥ॖ࿊ࠏఖᇏ֥ඨݼ,طѩ٤ॖ࿊ࠏఖݼ。ೂֻ1۱ࠎၹ໊ඔሳູ2іൕֻ1۱ࡆ۽۽O࿊ᄴ֥1ࠏఖູھ۽ஆֻ2֥ࠏఖࠧM;,ֻ12۱2ࠎၹ໊ඔሳູ3іൕֻ12۱ࡆ۽۽O࿊ᄴ֥ࠏ12ఖູھ۽ஆֻ3֥ࠏఖࠧM。5หᆘԱ:ಙุӉ؇ູਬࡱࡆ۽หᆘሹބࠧ4 หᆘԱࢌҭҠቔ11, Crossoveroperationofthefeaturestringૄ۱ࠎၹ໊ഈඔሳіൕ၂۱หᆘݼ,൞෮Ⴕหᆘડቀ۽ၜჿඏ֥၂۱ஆਙ。ᇏ෮ൕหᆘԱಙุࡆ ؓႿॖ࿊۽ၜބࠏఖԱ֥эၳ,༵ෛࠏ࿊ᄴॖ۽ඨູF-F-F-F-F-F-F-F-F-F-F。1567823491011࿊۽ၜࠇࠏఖԱഈ֥၂۱ࠎၹ໊,ՖھหᆘԱ֥ॖࢳൈ൮༵ؓॖ࿊۽ၜԱބॖ࿊ࠏఖԱࢳ,࿊۽ၜࠢࠇᆀھ۽֥ॖ࿊ࠏఖࠢᇏ,࿊ᄴ၂۱ॖՖቐ֞Ⴗ၇Ցॖၛ֤֞F-F۲หᆘ֥ॖ࿊۽ၜၛ111࿊۽ၜࠇॖ࿊ࠏఖটูս֒భ۽ၜࠇᆀࠏఖࠧॖ。ࠣO-O۲۽֥ॖ࿊ࠏఖ。Ⴎі1ॖᆩ,ॖ࿊۽117طؓႿหᆘԱ֥эၳҠቔҐႨਆׄࣉྛࢌҭࢌߐ,
۽ ြ ۽ ӱֻ16ज 136ࠧᄝڳսหᆘԱᇏෛࠏ࿊ᄴਆׄ,ࢌҭھਆׄࠎၹمᇏਆಃᇗω=,ω=,ૄᇕෘمᄎྛ2012֤֞ሰս。ႮႿՎҠቔٚൔॖିӁളႵᙣ۽ၜჿඏՑ,࠹ෘࢲݔೂі2෮ൕ。֥҂ॖྛࢳ,ܣᄝࢌҭު,ླႨഈ໓ิ֥֞ჿඏטᆜі2 ൌ২ᄎྛࢲݔෘمࣉྛ҂ॖྛࢳ֥ྩگაטᆜ。 ෘم҄ᇧቋݺࢳᄎྛ20ՑିղनቋႪࢳनᄎෘٚمࢲކၛഈิԛ֥۽ၜܿ߃໙ี֥؟҆ٳٳ؍щሹൈࡗሹӮЧ֞ቋݺࢳ֥ՑඔሹൈࡗሹӮЧൈࡗCPU/s、ࢌҭაэၳٚمၛࠣෛࠏಃᇗ֥؟ଢѓࣚႇЧ໓ٚم nI\ؓбٚم nI\ࢳҦ,ࢳ؟ଢѓ಼ྟ۽ၜܿ߃໙ี֥ෘم҄ᇧቋݺ֥۽ၜਫ਼ཌູ:O(M)-O(M)-O(M)-O(M)-O(M)-O(M)O(M)-O11135231655565718ೂ༯。(M)-O(M)-O(M)-O(M)-O(M)193101125175Step1ҕඔഡᇂ(parametersetting):ಕุܿଆູN,ࢌҭۀੱູp,эၳۀੱູp,ૄսᇕಕ࿊ԛcm Ⴎഈඍൌဒࢲݔॖၛ֤֞ၛ༯ࢲં。֥ቋႪࣚႇ۱ඔູN,ቋնࣉ߄սඔູMaxGen;elite1)Ֆᄎྛ20Ցު֥ࢲݔбࢠഈটु,2ᇕٚمStep2Ԛ߄(initialization):ࣉ߄սඔt←0,ෙିղ֞໙ี֥ቋݺࢳ,Ч໓෮ิԛ֥ٚمିҐႨࢫ֥ჿඏטᆜෘمෛࠏളӮN۱ԚᇕЌᆣૄՑᄎྛࢲݔ֤֞໙ี֥ቋݺࢳ,طԮ֥ಕ;ؓбٚم20ՑᄎྛࢲݔᇏᆺႵ2Ց֤֞ቋݺࢳ。Step3ࡎ(evaluationg):ؓૄ۱۱ุ۴ऌൔ(1)ᆃඪૼაԮ֥ٚمཌྷб,Ч໓෮ิෘمᄎྛࢲݔބ(2)ٳљ࠹ෘఃଢѓݦඔᆴ,ႨParetoቋႪҦ۷ࣚሙ໗ק,طԮ֥ܥקಃᇗ؟ଢѓ၌Ԯෘمᄎྍຓ҆ࣚႇࠢ;ྛࢲݔ҂໗ק,ޓ֤֞໙ี֥ቋႪࢳ。ᆃᆞ൞ႮStep4࿊ᄴ(selection):Ⴈൔ(9)ᆷקෛࠏಃᇗ,ႿЧ໓ᄝԩ၌Ԯෘم֥؟ଢѓ໙ีൈҐႨຓ҆ࣚᄜ۴ऌൔ(10)、(11)࠹ෘൡႋᆴބ࿊ᄴ֥ۀੱ,ၛႇҦ,ૄՑ၌Ԯݖӱᇏࡼ၂קඔਈ֥ຓ҆ࣚႇࠢഈҠቔᆳྛN-NՑ,࿊ᄴN-Nؓڳս۱ุ;eliteeliteگᇅ֞༯၂սᇏ,ࡼഺჅ֥ࠎၹ۱ุႨෛࠏಃᇗٚStep5ᄖࢌ(crossover):ؓႿ࿊ԛ֥ૄؓ۱ุ,مࣜݖࢌҭэၳࠆ֤。طԮ֥ܥקಃᇗمᄝԩႨ໓ᇏ֥ᄖࢌҦࣉྛᄖࢌҠቔ;؟ଢѓൈ,ࣇࣇᆺ൞Ⴈܥקಃᇗࡼ໙ีሇ߄ӮֆଢStep6эၳ(mutation):ؓᄖࢌު֥۱ุ,၇ऌ໓ѓটԩ,ᆃᇕҵљ߄֥ෘمҦ֤భᆀିޓݺᇏ෮ࢃ֥эၳҦᆳྛэၳҠቔ;ֹࡼ၌ԮݖӱᇏႪਅࠎၹ၌Ԯ༯ಀ,طުᆀ߶ᄯӮStep7ࣚႇҦ(elitiststrategy):ૄՑэၳࢲඏ,၌ԮݖӱᇏႪਅࠎၹ֥שാ。Ⴈຓ҆ࣚႇࠢ۷ྍҦ۷ྍຓ҆ࣚႇࠢ,ѩႨk-2)Ֆनᄎྛൈࡗഈु,Ч໓෮ิԛ֥ෘمҦmeansऊোٚمҊࡧԛN۱۱ุ,࿊ԛھN۱۱eliteeliteӉႿԮ֥ܥקಃᇗ؟ଢѓ၌Ԯෘم。ᆃ൞Ⴎุเࡆ֞భ૫Ӂള֥N-N۱۱ุᇏၛܒӮN۱eliteႿЧ໓෮ิٚمᄝԩ؟ଢѓ၌Ԯ໙ีൈ,ᄎႨਔ۱ุ֥ᇕಕ;ຓ҆ࣚႇҦ,֒ຓ҆ࣚႇࠢܿଆնႿყקᆴൈ,ູStep8ᇔᆸҩ൫(terminationtest):ೂݔડቀ൙༵ਔҊࡧݖӱᇏЌӻࢳ֥ٳ҃ྟି,ߎҐႨk-meansऊᇅק֥๔ᇌ่ࡱ,ᄵᇔᆸෘم,ڎᄵْ߭Step3。োෘمҊࡧࣚႇࠢ。ᆃུෘمҦა၌Ԯෘمཌྷࢲކ,ิശਔ၌Ԯෘمᄝࢳ؟ଢѓႪ߄໙ี࿙Ⴊି3 ൫ဒࢲݔაٳ༅৯֥ൈ,൝с߶႕ཙෘم֥؇,Ֆෘمࣚ؇ഈൌဒҐႨMicrosoftVisualC#2008ൌགྷЧ໓ิটु,Ч໓෮ิෘمૄՑᄎྛࢲݔିಒЌ֤֞໙ԛ֥ෛࠏಃᇗ؟ଢѓ၌Ԯෘم֥ࣚႇЌҦ,ൌี֥ቋݺࢳ,ၹՎЧ໓ิԛ֥ෘمҦ൞ॖྛႵဒߌູPentium4/ ࢲંҦٚمބԮ֥ܥקಃᇗ؟ଢѓ၌Ԯෘمࣉྛбࢠ。ဒᆣൌ২ҐႨഈඍ1ބі1෮ൕඔऌ,ऎุᆌ಼ؓྟ۽ၜܿ߃აथҦ໙ีࠣఃNPหྟ,ෘمҕඔഡᇂೂ༯。ᇕಕܿଆNູ100,ࢌҭۀੱᄝٳ༅ݓଽຓၘႵ࣮໓ང֥ࠎԤഈ,൮಼༵ؓྟpູ,эၳۀੱpູ,ቋնࣉ߄սඔMaxGencm۽ၜܿ߃໙ีࣉྛਔབྷ༥ٳ༅,ѩᄝՎࠎԤഈิູ100,ᄝෛࠏಃᇗ֥؟ଢѓࣚႇ၌Ԯෘمᇏ,ૄԛਔջ۽ၜჿඏ֥؟۽ၜਫ਼ཌ、؟ଢѓ಼֥ྟ۽ၜս࿊ԛ֥ࣚႇ۱ඔNູ5,ܥקಃᇗ؟ଢѓ၌Ԯෘeliteਫ਼ཌܿ߃໙ี֥ඔ࿐ଆ。ቋު,ᆌؓ෮ิԛ֥ඔ
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