뗚25뻭뗚2웚(ퟜ뗚158웚)ꆡꆡꆡꆡꆡꆡ쾵ꆡ춳ꆡ릤ꆡ돌,쓪2퓂ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡSystemsEngineeringFeb.,2007컄헂뇠뫅:100124098(2007)0220036205컯쇷짨쪩톡횷컊쳢뗄쮫닣쒣쓢췋믰쯣램Ξ쟘ꆡ뷸,쪷ꆡ럥(훐쓏듳톧붻춨퓋쫤릤돌톧풺,뫾쓏뎤즳ꆡ410075)햪ꆡ튪:짨쪩톡횷컊쳢뗄쿠맘폅뮯쒣탍뗄놾훊,뚼쫇퓚ퟮ킡뮯쿠맘럑폃뗄잰쳡짏,듓뿉톡짨쪩벯뫏훐좷뚨짨쪩뗄탞붨캻훃,늢럖엤폃뮧뗄탨쟳,벴뚼뇘탫뷸탐톡횷뻶닟뫍탨쟳럖엤뻶닟ꆣ놾컄훷튪룹뻝짨쪩톡횷컊쳢뗄쳘뗣,짨볆쇋쫊뫏쟳뷢튻냣짨쪩톡횷컊쳢뗄춨폃탍쮫닣쒣쓢췋믰쯣램,쯣램뗄췢닣뛔짨쪩톡횷뻶닟뷸탐폅뮯,쓚닣퓲퓚짏닣좷뚨뗄짨쪩톡횷뻶닟믹뒡짏,뷸탐폃뮧탨쟳럖엤뗄폅뮯ꆣퟮ뫳뗄뛠룶쯣샽횤쏷쇋쿠뛔웤쯻폅뮯쯣램,쮫닣쒣쓢췋믰쯣램늻떫쫕솲쯙뛈뿬,뛸쟒쓜쟳좡룼룟훊솿뗄ퟮ폅뷢ꆣ맘볼듊:컯쇷릤돌;짨쪩톡횷컊쳢;춨폃;쮫닣쒣쓢췋믰쯣램훐춼럖샠뫅:F274ꆡꆡꆡ컄쿗뇪쪶싫:A1ꆡ틽퇔뿉톡뗄짨쪩탞붨뗘횷뗄벯뫏,I={1,2,ꆭ,n}쫇폃뮧뗣뗄벯뫏,쎿튻룶짨쪩톡횷jꇊJ뚼뛔펦폐튻룶만뚨뗄붨짨럑짨쪩톡횷컊쳢(FLP),튲뻍쫇컒쏇춨뎣쯹쮵뗄엤쯍믲폃fj뫍쓜솦쿞훆vj,쎿튻룶폃뮧iꇊI뚼폐튻룶탨쟳솿di,컯쇷훐탄뗈뗄톡횷컊쳢믲톡횷2럖엉컊쳢(LAP),튻횱틔쟒cij캪듓짨쪩j붫믵컯퓋쯍훁i뗄떥캻퓋쫤럑폃,춬쪱뚨살뻍뗃떽쇋듳솿톧헟뗄맘힢,헢튻랽쏦쫇평폚짨쪩톡횷뗄틥뻶닟뇤솿xj뫍yij,럖뇰뇭쪾죴뻶뚨탞붨짨쪩j,퓲xj=훘튪탔1,럱퓲xj=0;죴붫폃뮧i뗄탨쟳럖엤룸짨쪩j,퓲yij=1,,뛸쇭튻랽쏦퓲쫇틲캪FLP쟳뷢뗄삧쓑탔ꆣFLP놾짭뗄뢴퓓탔쪹듳엺톧헟짮죫웤훐,뒴퓬쇋튻쾵쇐뢴퓓뗄럱퓲yij=0,퓲짏쫶FLP뗄폅뮯쒣탍뿉틔뇭쫶캪쫽톧쒣탍뫍쟳뷢쯣램,죧훘탄램ꆢ믬뫏-헻쫽쿟탔맦뮮랽minꆡ7=ꇆmfjxj+ꇆnꇆmcijyijdi(1)램뗈\[1ꆣ\]뛸쯦ퟅ떱듺볆쯣믺벼쫵뗄룟쯙랢햹ꆢ듳맦쒣퓋쯣j=1i=1j=1돉캪뿉쓜,풽살풽뛠뗄퇐뺿죋풱쟷쿲폚닉폃틅뒫쯣램ꆢ쒣.ꆡꇆmyij=1,ꆡΠiꇊI(2)쓢췋믰쯣램뗈웴랢쪽쯣램살듯떽믲뇆뷼룃컊쳢뗄ퟮ폅j=1뷢ꆡꆡꆡyijꇜxj,ꆡΠiꇊI,ΠjꇊJ(3)\[2-9ꆣ\]웴랢쪽쯣램뗄튻룶쳘뗣퓚폚쟳뷢뷼쯆탔,뛔폚톡횷NP2쓑쳢,룷폐룷뗄뷏폅뷢,좴뚼컞램룸돶튻룶웕쫊뗄ꆡꆡꇆndiyijꇜxj,ꆡΠjꇊJ(4)i=1ퟮ폅뷢,헢퓚튻랽쏦죃죋룐떽췯쾧,뛸퓚쇭튻랽쏦좴돉캪ꆡꆡꆡyijꇝ0,ꆡΠiꇊI,ΠjꇊJ(5)컯쇷췸싧짨볆뗄쿠맘퇐뺿늻뛏쿲룼룟닣랢햹뗄췆뚯솦ꆣꆡꆡꆡxjꇊ{0,1},ꆡΠjꇊJ(6)쯤좻FLP뗄쿠맘폅뮯쒣탍뗄탎쪽뛠훖뛠퇹,뛸퓚쪵훊짏,쯹폐FLP뗄ퟮ훕쒿뗄,뚼쫇튪퓚ퟮ킡뮯쿠맘럑폃뗄2ꆡ쒣쓢췋믰쯣램\[10,11\]잰쳡짏,듓뿉톡짨쪩벯뫏훐좷뚨짨쪩뗄탞붨뗘횷,늢럖엤폃뮧뗄탨쟳,벴ퟮ훕쟳뷢뗄뷡맻탎쪽쫇쎻폐뇤뮯뗄,폐뇤SA(Simulatedannealing)쯣램쫇튻훖쟳뷢ퟩ뫏폅뮯컊쳢뗄쯦믺쯑쯷랽램ꆣ쯼퓚ퟮ폅뷢쯑쯷닟싔훐틽죫쇋쫊떱뗄뮯뗄횻쫇폅뮯쒣탍뗄쒿뇪몯쫽뫍풼쫸쳵볾ꆣ헢뻍쳡쪾컒쏇쯦믺틲쯘,뛔쒿뇪몯쫽튻냣늻탨튪쳘쫢뗄쿞훆쳵볾,뻟폐뿉룹뻝FLP뗄헢룶릲탔,짨볆튻룶헫뛔FLP뗄룟킧뗄춨뇈뷏맣랺뗄쫊펦탔ꆣ쯼쫇튻훖춨폃뗄쯣램,쒿잰틑퓚릤돌ꆢ폃탍쯣램ꆣ캪쇋뫳쏦쯣램쏨쫶랽뇣,쿂쏦쫗쿈룸돶FLP뗄뺭볃뗈쇬폲뗃떽쇋맣랺뗄펦폃,훮죧짺닺뗷뛈ꆢ뿘훆릤돌ꆢ뇤솿뚨틥뫏튻냣쒣탍ꆣ믺웷톧쾰ꆢ짱뺭췸싧ꆢ춼쿱뒦샭뗈쇬폲ꆣ캪쇋붨솢쒣탍,뚨틥뇤솿죧쿂:쇮J={1,2,ꆭ,m}쫇Ξ쫕ퟷ룥헟죕볲웚뷩:2006209206:쟘뷸(19782),쓐,훐쓏듳톧붻춨퓋쫤릤돌톧풺늩쪿퇐뺿짺,퇐뺿랽쿲:컯쇷릤돌,붻춨퓋쫤맦뮮폫맜샭뗈;쪷럥(19562)쓐,,훐쓏듳톧붻춨퓋쫤릤돌톧풺뷌쫚,늩쪿짺떼쪦,퇐뺿랽쿲:붻춨퓋쫤맦뮮폫맜샭,ퟩ뫏폅뮯뗈ꆣ
뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ쟘뷸,쪷럥:컯쇷짨쪩톡횷컊쳢뗄쮫닣쒣쓢췋믰쯣램37쯤좻평폚닉폃쯦믺쯑쯷닟싔,SA쯣램횻쓜퓚룅싊뗄뿘훆맦퓲ꆢ춬컂뛈쿂뗄뗼듺늽뎤틔벰쯣램훕횹ힼ퓲뗈뗄짨틢틥짏캪쟳뗃좫뻖ퟮ폅뷢쳡릩놣횤,떫쫇뿉틔횤쏷,SA쯣훃,뿉틔룹뻝뻟쳥쟩뿶뛸뚨,쟒컊쳢뗄돵쪼뷢뿉틔퓚싺ퟣ램ퟮ훕쓜틔룅싊캪1쫕솲폚좫뻖ퟮ폅뷢\[11,12ꆣ\]쿂쏦쿈뷩짜풼쫸쳵볾뗄잰쳡쿂,뷸탐폃뮧탨쟳뗄쯦믺럖엤뛸뗃떽ꆣ쿂SA쯣램뗄훷튪쓚죝ꆣ쏦훘뗣쳖싛쓚닣ꆢ췢닣SA쯣램뗄쇚폲릹퓬ꆣ맩쓉뛸퇔,SA쯣램쫇튻훖믹폚MonteCarlo뗼듺쟳평잰쏦탰쫶,췢닣SA쯣램쫇헫뛔짨쪩톡횷뷸탐폅뷢닟싔뗄쯦믺쯑쯷쯣램,웤돶랢뗣쫇믹폚컯훊뗄컯샭췋믰뮯,헢샯붫뷢훐톡퓱탞붨뗄짨쪩,뇭쪾캪튻룶헻쫽뗄벯뫏맽돌폫ퟩ뫏폅뮯횮볤뗄쿠쯆탔,쯣램평쒳튻뷏룟뗄돵쪼컂F,퓚웤훐쎶뻙쇋뻶뚨붨짨뗄짨훃,샽죧F={0,1,4,1,2},뛈뾪쪼,샻폃뻟폐룅싊춻뇤쳘탔뗄Metropolis돩퇹닟싔퓚퓲웤듺뇭쇋놻붨짨뗄짨쪩캪0,1,4,12,웤쯻뗄짨쪩퓲놻뷢뿕볤훐뷸탐쯦믺쯑쯷,냩쯦컂뛈뗄늻뛏쿂붵,랴뢴뷸탐맘뇕ꆣ듓뛸뛔췢닣쒣쓢췋믰쯣램뗄쇚폲릹퓬,퓊탭폃살탞룃돩퇹맽돌,ퟮ훕틔룅싊1쫕솲폚좫뻖ퟮ폅뷢ꆣSA쯣램뗄룄뷢뗄ힴ첬뗄쇚폲몯쫽,뿉틔뷸탐죧쿂죽훖늻춬뗄닙ퟷ:쪵퇩탔뻟폐훊솿룟ꆢ돵쪼뷢슳냴탔잿ꆢ춨폃탔뫃틔벰쯣램(1)붫벯뫏F훐뗄튻룶헻쫽폫쇭튻룶캴탞붨짨쪩뗄ힴ첬틗쪵쿖뗈폅뗣ꆣ뮥뮻;(2)쯦믺뗄톡퓱튻룶캴탞붨뗄잱퓚짨쪩,붫웤쳭볓뷸뚨틥s,sꇤγ,sꇥ,s캪쿠맘뷢뗄쿲솿뇭쪾,C(s)캪뷢s뗄죫벯뫏F훐,벴탂붨튻룶짨쪩;(3)붫벯뫏F훐뗄튻룶헻쒿뇪몯쫽횵,뇪ힼ뗄SA쯣램뗄튻냣늽훨쏨쫶죧쿂:쫽틆돽,벴맘뇕튻룶틑붨짨뗄짨쪩ꆣ퓚쪵볊훐쎿듎쯣램횴늽훨1:짨훃쒣쓢췋믰볆뮮뇭,쇮돵쪼컂뛈캪t,룸뚨탐쪱,뿉틔룹뻝쪵볊쟩뿶,쎿듎톡퓱웤훐튻쿮닙ퟷ벴뿉ꆣ샽돵쪼뷢s,춬쪱쇮s캪떱잰ퟮ폅뷢;죧,뛔폚p2훐탄컊쳢,뻍횻쓜톡퓱닙ퟷ(1)뷸탐쇚폲뷢뗄늽훨2:횴탐쇚폲몯쫽,뗃떽탂뷢sꇤ;짺돉ꆣ쎿듎횴탐짏쫶닙ퟷ뫳,뚼탨튪퓚벯뫏F뗄믹뒡짏,늽훨3:죴C(sꇤ)<C(s),퓲쇮s=sꇤ;럱퓲,듓(0,1)쯦훘탂뷸탐탨쟳뗄쯦믺럖엤,벴훘탂짺돉돵쪼뷢ꆣ믺닺짺튻룶쫽횵Θ,죴폐Θ<exp(-(C(sꇤ)-C(s))öt),퓲뛔폚쓚닣SA쯣램,웤쇚폲릹퓬튲폐솽훖랽램:(1)죎쇮s=sꇤ,럱퓲늻뷓쫜룃뷢;톡튻룶탨쟳럖엤뻶닟뇤솿yij,쟒싺ퟣyij=1,퓙죎톡튻룶늽훨4:죴캴싺ퟣ춬컂뛈쿂뗄돩퇹컈뚨ힼ퓲,략믘늽짨쪩jꇤꇊF,짨훃yijꇤ=1,yij=0,벴붫폃뮧뗄탨쟳쯦믺럖엤훨2;럱퓲횴탐붵컂닙ퟷ,뗃떽탂뗄컂뛈t;룸쇭튻룶짨쪩;(2)죎톡솽룶럖엤뻶닟뇤솿,싺ퟣyi1j=1늽훨5:쫕솲탔볬퇩ꆣ죴캴싺ퟣ쯣램훕횹ힼ퓲,퓲략믘1,yi=1,좻뫳짨훃yi=1,1j2yi1,2j=1yi0,1j=2j21yi2j=0,벴2늽훨2;럱퓲쯣램훕횹,쫤돶ퟮ폅뷢s.붫폃뮧i1,i2탨쟳뗄릩펦짨쪩뮥뮻ꆣ춬퇹뗄,퓚쪵볊닙ퟷ훐,죎톡웤훐튻쿮벴뿉췪돉쇚폲뷢뗄짺돉,떱좻,쎿튻듎닙3짨쪩톡횷컊쳢뗄쮫닣쒣쓢췋믰쯣램ퟷ훐뚼뇘탫싺ퟣ폃뮧탨쟳늻뗈듳폚짨쪩떱잰쪣폠쓜솦뗄3튪쟳,럱퓲략믘훘탂뷸탐듋닙ퟷꆣ.1ꆡBSA쯣램뗄쇚폲릹퓬죧잰쯹쫶BSA쯣램뗄쓚췢닣ퟓ쯣램뿉틔닉폃춬퇹뗄췋믰볆뮮,평폚SA쯣램뻟폐훮뛠폅뗣,틲듋놾컄붫틔SA쯣램캪믹뒡,짨볆FLP뗄춨폃쟒쓜쟳좡룟훊솿ퟮ폅뇭,벴BSA쯣램쯹쪹폃뗄닎쫽뿉뚼퓚췢닣SA쯣램훐뷸뷢뗄쮫닣쒣쓢췋믰쯣램ꆣ탐짨훃ꆣ죧잰컄훐쯹쫶,FLP뗄뷢뗄탎쪽냼삨솽늿럖:튻룶쫇ꆡBSA쯣램뻟쳥늽훨뇭쪾쫇럱탞붨짨쪩뗄뻶닟뇤솿Xj,쇭튻룶퓲쫇탨쟳뗄럖쿂쏦럖뇰쏨쫶BSA쯣램훐쓚닣폅뮯쯣램폫췢닣폅뮯엤뻶닟뇤솿Yij.뛸쟒솽헟횮볤쫇쿠뮥솪쾵뫍쿠뮥펰쿬쯣램뗄뻟쳥늽훨ꆣ뗄,튻냣살붲,탨쟳뇘탫럖엤룸틑뺭뻶뚨탞붨뗄짨쪩,틲듋췢닣폅뮯쯣램뗄뻟쳥볆쯣늽훨캪:뿉틔쮵Xjퟮ훕좷뚨Yij,헢튲뿉평잰쏦뗄폅뮯쒣탍훐뗄풼늽훨1:짨훃쒣쓢췋믰볆뮮뇭,쇮돵쪼컂뛈캪t,룸뚨쫸쳵볾(3)훐뗃떽쇋쳥쿖ꆣ틲듋컒쏇뿉틔퓚짨볆쯣램쪱,붫돵쪼뷢s,춬쪱쇮s캪떱잰ퟮ폅뷢;컊쳢럖캪솽룶닣듎뷸탐쟳뷢,뗚튻룶닣듎뛔짨쪩톡횷뇤솿늽훨2:횴탐췢닣쇚폲몯쫽,뗃떽탂뷢sꇤ;뷸탐폅뮯,뗚뛾룶닣듎퓲쫇퓚뗚튻룶닣듎좷뚨뗄짨쪩뻶닟늽훨3:횴탐쓚닣폅뮯쯣램;뗄믹뒡짏,뷸탐탨쟳럖엤뗄폅뮯볆쯣,뛸뛔폚쓚췢닣뗄폅늽훨4:죴C(sꇤγ)<C(s),퓲쇮γs=sꇤ;뮯,뻹쪹폃춨폃탍잿뗄쒣쓢췋믰쯣램쮼쿫,듓뛸뻍릹돉쇋늽훨5:죴C(sꇤ)<C(s),퓲쇮s=sꇤ;럱퓲,듓(0,1)쟸FLP뗄BSA(Bi2levelsimulatedannealing)쯣램ꆣ헢퇹붫컊볤쯦믺닺짺튻룶쫽횵Θ,죴Θ<exp(-(C(sꇤ)-C(s))öt),쳢럖캪솽닣살뷢뻶뗄틦뒦뻍퓚폚붫퇐뺿뗄컊쳢쾸뮯,쪹쎿퓲쇮s=sꇤ,럱퓲늻뷓쫜룃뷢;듎뗄쯣램쯑쯷뚼벯훐퓚뷏킡뗄뷢뿕볤쓚,헢퇹뻍퓶듳쇋퓚늽훨6:죴캴싺ퟣ춬컂뛈쿂뗄돩퇹컈뚨ힼ퓲,략믘늽춬퇹뗄퓋쯣쪱볤쓚쯑쯷떽좫뻖ퟮ폅뷢뗄뿉쓜탔,죧맻뷡뫏훨2;럱퓲횴탐붵컂닙ퟷ,뗃떽탂뗄컂뛈t;뫏쫊뗄쯣램훕횹닟싔,뮹뿉틔폐킧뗄뷚쪡퓋쯣쪱볤ꆣ늽훨7:쫕솲탔볬퇩ꆣ죴캴싺ퟣ쯣램훕횹ힼ퓲,퓲략믘뛔폚BSA쯣램뗄췋믰볆뮮뇭,벴돵쪼컂뛈ꆢ컂뛈쿂붵늽훨2;럱퓲쯣램훕횹,쫤돶ퟮ폅뷢γs.
38쾵ꆡ춳ꆡ릤ꆡ돌ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2007쓪짏쏦췢닣쯣램훐뗄늽훨4,쫇붫BSA쯣램웹뷱캪횹쯹듓짏쏦뗄쯣램늽훨훐뿉틔랢쿖,쯣램뛔쒣탍뗄쒿뇪몯쟳뗄ퟮ폅뷢놣듦쿂살,뛸늻뾼싇룅싊탔톡퓱,헢퇹뻍뇜쏢쫽뫍풼쫸쳵볾뗈쎻폐죎뫎뻟쳥튪쟳,틲듋룃쯣램뿉틔쮵쫊쇋쯣램룅싊탔쳸샫떱잰ퟮ폅뷢뗄컊쳢,ퟮ듳돌뛈뗄샻폃쯣폃폚쯹폐샠탍뗄짨쪩톡횷컊쳢,헢튻랽쏦쫇평폚SA쯣램램쯹쟳좡뗄쯹폐뷢ꆣ뗄춨폃탔쯹뻶뚨뗄,쇭튻랽쏦튲퓚폚쯣램쪹폃쇋쟉쏮뗄쇚뛸쓚닣폅뮯쯣램뗄볆쯣늽훨캪:폲몯쫽짨훃,훁폚뛔폚뻟쳥컊쳢뗄늻춬뗣,횻쫇퓚폚쇚폲늽훨1:틔sꇤ캪떱잰돵쪼뷢뫍ퟮ폅뷢,릹퓬쓚닣닣쇚몯쫽뗄쪹폃짏,샽죧뛔폚p2훐탄컊쳢,췢닣SA쯣램훐횻폲뷢,뗃떽탂뷢sꇥ;쓜닉폃뗚튻훖쇚폲몯쫽,뛸뛔폚CFL쒣탍뫍UFL쒣탍,늽훨2:죴C(sꇥ)<C(sꇤ),퓲쇮sꇤ=sꇥ;럱퓲,듓(0,1)퓲쯹폐뗄쇚폲몯쫽뻹뿉쪹폃ꆣ쟸볤쯦믺닺짺튻룶쫽횵Θ,죴폐Θ<exp(-(C(sꇥ)-C(sꇤ))öt),퓲쇮sꇤ=sꇥ,럱퓲늻뷓쫜룃뷢4ꆡ쯣샽럖컶;늽훨3:죴캴듯떽춬컂뛈쿂뗄돩퇹컈뚨ힼ퓲,퓲략믘쿂쏦폃솽룶쯣샽뛔BSA쯣램뷸탐닢쫔ꆣ짏쫶쒣탍뫍늽훨2;럱퓲쯣램훕횹,략믘췢닣폅뮯쯣램ꆣ쯣램쪹폃VisualC#뇠돌쪵쿖,퓚놼,256M쓚듦짏쏦쏨쫶뗄쪵볊짏횻쫇BSA쯣램뗄뿲볜,쯣램쯹튪뗄PC믺짏퓋탐ꆣ쪹폃뗄뻟쳥닎쫽짨훃,뮹탨튪룹뻝컊쳢뗄맦쒣뗈쪵볊쟩뿶뗚튻룶쯣샽뗄쫽뻝뻹살ퟔ폚OR2Library(Beasley,뛸퓙ퟷ좷뚨ꆣ쇭췢듓짏쏦뗄쯣램늽훨훐뿉틔뾴돶,쪵볊짏1990),듓훐릲톡퓱12룶FLP뗄쫽뻝뷸탐볆쯣럖컶,헢킩쓚닣SA쯣램횻쫇횴탐쇋샠쯆뻖늿쯑쯷뗄릦쓜,떫쫇퓚웤컊쳢쳡돶헟틑뺭쪹폃Lindo죭볾쟳뗃웤ퟮ폅뷢ꆣ쇭췢BSA훐죔좻펦폃쇋SA쯣램훐ퟮ캪훘튪뗄Metropolics돩퇹ힼ쯣램뗄닎쫽뚼닉폃뇈뷏볲떥뗄짨훃랽램,틔뷸튻늽퇩횤쯣퓲,헢퇹폐훺폚쓚닣SA쯣램쯑톰룼폅뷢,틲듋뿉틔죏캪램뗄폐킧탔:돵쪼컂뛈짨훃캪100;컂뛈쿂붵맦퓲닉폃뗈웤쫇튻룶볲싔냦SA쯣램ꆣ쇭췢,쓚췢닣쯣램뗄뗼듺늽뎤뇈샽쿂붵,쿂붵쾵쫽Α=;췢닣쯣램뗄뗼듺늽뎤캪m,뿉틔늢늻튻퇹,틲캪췢닣쯣램횻폫짨쪩벯뫏J폐맘,뛸쓚쓚닣뗼듺늽뎤퓲캪5n;쯣램훕횹ힼ퓲캪떱잰컂뛈뗍폚훕닣쯣램폫벯뫏F뫍폃뮧벯뫏I폐맘,틲듋뿉틔룹뻝쪵볊탨횹컂뛈tf=1쪱,쯣램훕횹,춬쪱폃뇪ힼSA(StandardSA,튪럖뇰짨훃,샽죧,뿉틔붫췢닣뗼듺늽뎤짨훃캪kûJû,웤SSA)쯣램뷸탐쯣램닢쫔,웤춬컂뛈쿂뗄뗼듺늽뎤캪5mn,훐k캪듳폚1뗄헻쫽,뛸쓚닣뗼듺늽뎤짨훃캪ûFûûIû,헢웤쯼짨훃폫BSA쿠춬,듓뛸쪹웤ퟜ뗼듺듎쫽폫BSA튻퇹뗄짨훃볈쓜싺ퟣ돤럖돩퇹뗄튪쟳,폖뿉틔뷚풼볆쯣쪱훂ꆣ뻟쳥뗄볆쯣뷡맻죧뇭1쯹쪾ꆣ볤ꆣ뇭1ꆡBeasly닢쫔컊쳢볆쯣뷡맻럖컶믹ힼ컊쳢SSABSA컊쳢맦쒣(mꇁn)Lindoퟮ폅횵볆쯣뷡맻쿠뛔컳닮(%)CPUTime(s)볆쯣뷡맻쿠뛔컳닮(%)CPUTime(s)Cap7116ꇁꇁꇁꇁꇁꇁꇁꇁꇁꇁꇁꇁꆡꆡ평뇭1뗄쫽뻝뿉틔뾴돶,BSA쯣램쓜쟳뷢떽짏쫶쯹SSA쯣램캴쓜쟳좡죎뫎ퟮ폅뷢,떱좻,죧맻룄짆SA쯣램폐12룶FLP뗄ퟮ폅뷢,떫쫇평폚뗼듺듎쫽뷏짙뗄풭틲,뗄닎쫽짨훃,웤튲뿉쓜쟳좡ퟮ폅뷢,떫헢헽쫇SSA폫BSA
뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ쟘뷸,쪷럥:컯쇷짨쪩톡횷컊쳢뗄쮫닣쒣쓢췋믰쯣램39횮볤뗄닮뻠ꆣ뛸쟒퓚쪵볊퓋쯣훐컒쏇뮹랢쿖,BSA쯣램뗄쫕솲쯙뛈,튪쏷쿔뗄뿬폚SSA쯣램,뫳쏦뗄춼1뫍춼2럖뇰쫇컊쳢Cap101뫍Cap131횴탐BSA쯣램쪱,뗼듺볆쯣듎쫽폫쒿뇪몯쫽횵횮볤뗄맘쾵춼,헢샯뗄뗼듺듎쫽쫇횸췢닣뗼듺듎쫽,뛸쎻폐뾼싇쓚닣뗼듺뗄틲쯘ꆣ평쿂쏦뗄춼훐뿉틔뾴돶,BSA쯣램쫕솲럇뎣톸쯙,췹췹퓚쯣램뗄잰냫늿럖뻍틑뺭쫕솲폚ퟮ폅뷢,헢쿔좻쫇웤쯻폅뮯쯣램쯹컞램뇈쓢뗄폅쫆ꆣ춼2ꆡCap131뗼듺쯣램뗚뛾룶쯣샽퓲쫇컄쿗\[5\뫍]컄쿗\[7\훐]쪹폃뗄Ghosh닢쫔컊쳢\[12\],쯼붫벸훖FLP뗄폅뮯쯣램뗄킧맻뷸탐쇋뇈뷏,쿂쏦뗄뇭2퓲쫇샻폃룃탅쾢,붫웤쯹쳡떽뗄벸훖폅뮯쯣램뗄볆쯣킧맻폫놾컄쯹쳡돶뗄BSA쯣램뷸탐뇈뷏ꆣ듓뇭2훐뿉틔뾴떽,Ghosh닢쫔컊쳢뚼쫇듳맦쒣뗄,웤훐뛔돆쫇횸퓚웤쯦믺짺돉뗄퓋쫤럑폃훐뇘폐cij=cji,Πi,j,뛸춼1ꆡCap101뗼듺쯣램럇뛔돆퓲쫇컞듋뇘튪쳵볾,뛸AꆢBꆢC뗄럖샠퓲횻쫇웤룷샠훐컊쳢훐쯦믺짺돉룷훖쫽뻝뗄쟸볤쫇늻튻퇹뗄ꆣ뇭2ꆡGhosh닢쫔컊쳢볆쯣뷡맻럖컶맦쒣컊쳢HybridCLMGTSTSBSA(m=n)샠탍쏻돆쒿뇪횵CPUTime1쒿뇪횵CPUTime1쒿뇪횵CPUTime1쒿뇪횵CPUTime1쒿뇪횵뛔돆럇뛔돆뛔돆럇뛔돆뛔돆럇뛔돆힢:CPUTime1캪SunEnterprise3000럾컱웷(4ꇁCPU,6G쓚듦)ꆣꆡꆡ듓뇭1뿉틔뾴돶,퓚ퟜ릲18룶닢쫔컊쳢훐,BSA뛔웤뗄ퟮ폅뷢튻훂(폃킱쳥뇭쪾),벴튻릲폐13룶컊쳢뗄ퟮ폅훐12룶컊쳢쟳뗃쇋떽쒿잰캪횹뗄ퟮ폅뷢(폃듖쳥뇭쪾),뷢뗄훊솿늻뇈웤쯻쯣램쯹쟳뗃뗄ퟮ폅뷢닮ꆣ뛸퓚쇭췢5룶쇭췢폐1룶컊쳢쟳뗃뗄ퟮ폅뷢,폫잰쏦쯄훖쯣램훐쯹쟳뗃쯹늻쓜쟳뗃ퟮ폅뷢뗄컊쳢훐튲뿉틔뾴떽,BSA쯹쟳뗃뗄
40쾵ꆡ춳ꆡ릤ꆡ돌ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2007쓪ퟮ폅뷢폫웤쯻쯣램쯹쟳뗄ퟮ폅뷢뗃닮뻠,늢늻쫇럇뎣쏷FLP뗄릲폐쳘뗣,릹퓬쇋뛔튻냣뗄FLP뻟폐춨폃탔뗄쮫쿔,듓쿂쏦뗄볆쯣쟩뿶살뾴,ퟮ듳쿠뛔닮뻠뷶캪(2502럇뛔닣쒣쓢췋믰쯣램BSA,웤훐췢닣폅뮯쯣램쫇헫뛔짨쪩톡돆2C)ꆣ횷뇤솿뗄폅뮯,쓚닣폅뮯쯣램퓲쫇퓚췢닣폅뮯쯣램좷뚨뗄탞붨짨쪩뻶닟짏,뛔폃뮧탨쟳럖엤뷸탐폅뮯,헢퇹붫쯣램5ꆡ뷡싛쎿듎뗄쯑쯷,뚼벯훐퓚뷏킡뗄뷢뿕볤쓚뷸탐,듓뛸퓶듳쇋퇐뺿FLP뗄ퟮ훕쒿뗄쫇퓚싺ퟣ폃뮧탨쟳뫍쫜컯쇷뷚쯑쯷떽좫뻖ퟮ폅뷢뗄뿉쓜탔,늢뷚쪡쇋쯣램뗄쯑쯷쪱볤ꆣ뗣쓜솦쿞훆뗄잰쳡쿂컄훐ퟮ뫳뗄쯣샽튲횤쏷BSA쯣램쫇튻훖헫뛔짨쪩톡횷컊,뛔짨쪩톡횷뫍폃뮧탨쟳럖엤뷸탐폅뮯뻶닟,틔쟳ퟮ킡뮯쾵춳뗄퓋펪뫍춶럑폃뗈ꆣ놾컄룹뻝쳢뗄룟킧뗄쯣램ꆣ닎뾼컄쿗:\[1\ꆡ]쯯퇦.쿖듺컯쇷맜샭벼쫵ꆪꆪ붨쒣샭싛벰쯣램벼쫵[M\].짏몣:춬볃듳톧돶냦짧,2004.\[2\ꆡ]MakKL,WongYS,[J\].ComputerIntegratedManu2facturingSystems,1998,11(2):113ꆫ127.\[3\ꆡ]Gen,ödistributionplanning[J\].Computers&IndustrialEngineering,2005,48(4):799ꆫ809.\[4\ꆡ]얣믝쏱,뫺낲훞.튻샠뎵햾톡횷컊쳢뗄럇쿟탔폅뮯쒣탍벰틅뒫쯣램[J\].붻춨퓋쫤릤돌톧놨,2002,2(1):80ꆫ84.\[5\ꆡ][J\].Computers&OperationsRe2search,2006,33(9):2563ꆫ2589.\[6\ꆡ]JayaramanV,[J\].Euro2peanJournalofOperationalResearch,2003,144(3):629ꆫ645.\[7\ꆡ][J\].EuropeanJournalofOp2erationalResearch,2003,150(1):150ꆫ162.\[8\ꆡ]HokeyMin,HyunJeungKo,[J\].Omega,2006,34(1):56ꆫ69.\[9\ꆡ]헅엠쇖,캺쟉퓆.컯쇷엤쯍훐탄톡횷쒣탍벰웤웴랢쪽쯣램[J\].붻춨퓋쫤릤돌톧놨,2003,3(2):65ꆫ68.\[10\ꆡ]탏컄통,킻뷰탇.쿖듺폅뮯볆쯣랽램[M\].놱뺩:쟥뮪듳톧돶냦짧,1999.\[11\ꆡ]췵쇨.훇쓜폅뮯쯣램벰웤펦폃[M\].놱뺩:쟥뮪듳톧돶냦짧,2001.\[12\ꆡ]:öööꆫmastjjböjeböorliböfilesö,1990.\[13\ꆡ]:öööunitsöag1öprojectsöbenchmarksöUflLibö,2006.\[14\ꆡ]쟘뷸,쪷럥,죎열.쿞훆쳵볾쿂뗄엤쯍훐탄쓚늿맦뮮퇐뺿[J\].쾵춳릤돌,2004,22(11):29ꆫ-levelSimulatedAnnealingAlgorithmforFacilityLocationQINJin,SHIFeng(SchoolofTrafficandTransportationEngineering,CentralSouthUniversity,Changsha410075,China)Abstract:Theessenceofthefacilitylocationisdecisionoftheopenofthefacilityandtheallocationofthedemandsofcustomers,,,andtheinneralgorithmisoptimizationfortheallocationofcustomerꆯ:LogisticEngineering;FacilityLocationProblem;All2purpose;Bi2levelSimulatedAnnealingAlgorithm
