7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) Multist outing lgoitm s on Extn Simult Annling Algoitm Jin-Ku Jong*, Sung-Ok Kim**, Ci-Hw Song*** * **Dpt. o Comput Eng, Hnnm Univsity 133 Ojong-ong Dok-gu, Djon 306-791, Ko ***Dpt. o Comput Sin Cungnm Ntionl Univsity 220 Gung-ong, Yusong-gu, Djon, 305-764 Ko Astt: - In tis pp, w popos mto tt is l to in goo multist outing t in wi ntwok. T polm omin tt w soul solv is mol s wigt, unit gp. T gp tt psnts wi ntwok s t no typ, sv tt sns t sm t to t ipints, som nos tt o not qust t to t sv n t st tt on't n t. Ou mto uss t xtn simult nnling lgoitm[esa]. Kywo : Extn simult nnling, multist outing, optimiztion 1. Intoution W popos n lgoitm tt ss out o sning t om on sv to spii multipl lints to minimiz t totl istn in ntwoks. Tis polm is int om t polm o ining out o ll nos in ntwoks. T omplxity o ining out t is insing mtilly wn mo nos oming into tion to, it is to in t st solution (out) wit titionl lgoitm. Rntly, t outing lgoitms o multisting ing stui wily, som o wit s ollows. Simult Annling mto[1], Applying SA on Dijkst o multi-onstint outing t[2], outing lgoitm o l-tim omputing using Hopil Nul Computing[3,7] n istiut lgoitm[4]. T simult nnling mto o tmining out uss n-to-n ly n o-t wit t onsition o ntwok sous. T istiut lgoitm tmins y t gouping o t nigoing nos tt tk ti pt in multisting. Ou popos lgoitm uss ESA lgoitm[5,6] to minimiz t sum o t istn ost twn t nos. W v mpp ntwok omin into t om o t gp n in ptution sm o ESA lgoitm wit vlution omul to in st multist t. T ost untion o t popos lgoitm onsis istn ost n no ost, ut it os not onsis t num o t u o out, vg ti quntity n tns ly. Howv, ts volums n ng into igus. 2. ESA Algoitm SA lgoitm xtts possil solution st y t mtopolis smpling sm n t tmoynmi vg is lult wit nonil vg. To, t possiility o ngy wit t sttus o n si s qution 1 w, oing to sttistil ynmis igu su s ix volum ( ), ix num o ptils ( ) n un t onstnt tmptu () wit in t los systm (1) Tis is t psnttion o t los systm. Tvling Slsmn Polm(TSP) is psnttiv polm tt solution oul oun wit t usg o t SA. TSP s ix num o t ity to visit n t slsmn must in t lst ost out. W will onsi t visiting ity s t num o moluls( ) tn it will nonil nsml. Wn, t moluls lututoin unit systm is ll gn nonil nsml. Volum( ), tmptu() n mil potntil () is ix wil ngy( ) n t num o moluls( ) is opn. T poility o stt wit ngy n moluls will in qution 2. (2) To, t igst poility o stt ppn is in onn wit ngy n num o moluls. T stuy o opn systm tt not only llows ngy ut lso t num o ptils is s on gn nonil nsml. Fo xmpl, on slsmn s to visit vy ity ( ) wit t lst ost n t lst istn out wi is t polm un nonil nsml n t slsmn s to visit wit t
7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) limittion o t ost s to visit itis ( n, ) tis onition it is gn nonil nsml. 3. Dinition o polm o ESA 3.1 psnttion o ntwok In ug ntwok on sv must st t sm t to multipl lints so it s to i t st out o vy no o t som no ( ). To in multisting out w psnt ntwok in gp. Evy no in ntwok inluing t sv is psnt s vtis. T pysil onntion o no is psnt s gs. E g is onnt to two ot nos s. Figu 1. Gpi Rpsnttion o Ntwok To psnt igu 1 s omul will s qution 3. (3) To slt t st out it is not nssy to ivi into sv n lint ut o t s o t tinking lt us onsi ist no s sv. No is no tt i not qust o svi ut in t wol tns out t to onnt to t nigoing no it oul inst to tns out. Wn no is not inlu in tnsing out it is not l to iv no n no, to, it must in t out. 3.2 Rpsnttion o tnsing out To solv t polm lik igu 1 in slt som o t no n g n o t no (sv) s oot n outing t. To st t tns out o vy no in ntwok systm it is gnl to us spnning t lgoitm. St som o t no o tns out. g T = ((()),g()) R = ((),(),(),()) Figu 2. Tns out t T t in igu 2 psnts tns out n psnts t nos tt is not inlu in outing t. T oot no in is onnt to t silings tt is xlu in. T sum o no in n is lwys t sm s t num o nos in. 3.3 ptution sm In gp itily slts on tns out t. W woul us s n initil solution o ESA lgoitm n tmin wt it is qutnss y vlution untion tt w popos. W us t vlution untion to viy. Until w in tt solution t systm ptu. T sis o ptu solution v to om Mkov in so t mtos n si s ollowing 3 typs. (1) Mto o movl on no (2) Mto o no ng in num o no (3) Mto o ing on no In t mto o (1) w oul mov ny no xpt oot no in t. T mov no is inst in vitul t. In mto o (2) t is two wys to ng. Fist, mov on no in t to t ot lotion. Son, intng on no in n on no in. In t mto o (3) slt on no ity in n inst no to. Lt s onsi t t o stt tnsition s igu 3. At tis point is no o t, n is t no o xtnl t. T=(()(()(()))) R=(g()()) Figu 3. Initil t T To mov on no in T, w onsi two typs on is to lt l no n t ot is to lt no o t mil on. In to mov mil no lik w must onsi w to sn il no's lotion. Fo xmpl, in wn no is lt t silings lotion will tmin y t ltion o itsl wn t ltion o t pnt is tking pl (igu 4-) o t onnt silings to t pnt o t pnt lik in igu 4-. Wn t ltion o vy no in su-t t ngy ng is so pi pning on t lotion o t no n oing to t spiition o its ntu it is to su optiml solution. An in t onition o igu 4- t oot no is onnt to t no g
7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) vi. In tis sitution witout onsition o ltion o no t oot must sn its t itly to n no is iving its t om no witout onsition o ltion o no. g () ltion o totl sut g () lt no t moving Figu 4. Dltion o t no To pou witout ng o t num o t no it xtts on ity no n ng its lotion n gins nw tns out in t. Figu 5, igu 6 n igu 7 sow t mov o t no. T two ss o moving no; igu 5 psnts t mov o t l no, n igu 6 n 7 psnt t mov o t mil no. T onition o ng o t mil no is tgoiz y w to mov its il no. Tis onition is psnt in igu 6 n igu 7. () () () mov l no to nonl no () mov l no to l no Figu 5. Mov o t l no It is mning lss tt t siling nos lt o igt. Figu 6- psnts mov o t l no to l no n no is onnt itly to t oot, ut in t pt o no is ins to, t t tns out is ws t t must tvl two mo no to gt ss to t oot. I t no os not v onntion g in = n in nw out t xists g w = t tns ost o is smll t s ost. In igu 7- it illustts mov o t non l no to l no. An igu 7- illustts non l no to non l no. T inl stt tnsition mto is to on mo no to t. In vitul t sltion o ity no ut o t oot no n inst into t o no it is illustt in igu 8. () mov to () mov to Figu 6. Mov o t su-t () l no moving () non-l no moving Figu 7. Mov o t no () inst s l () inst s non l Figu 8. A o t no 3.4 Cost untion In igu 1 g s its own wigt. Wigt psnts istn twn t nos. T tns ost in t onsi ntwok ly o possing tim o t out o nwit. W iv t om igu 1 s ollows. Figu 9. Tns t Tns ost o tis stt will t sum o t
7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) g s wigt o. To, it will. In t oiginl gp t is no g w. To, to lult totl ngy ost w must i t ost o g lik n it must gt tn ny ot vlus o g psnt in. So w us t vlu o g tt is not xist s In t onition o igu 1 t mximum g vlu is 2.0. Wn vil t g vlu tt is not psnt in is 3.0 to, t tns t in igu 10 will 8.2 Aoing to igu 1 t no must iv t t om t sv. But tns t in igu 10 o igu 11 no is nglt om tns t. To, t minimum ost wit t sm no lik igu 11 it will solution tt nnot pt. In t poss to lult optimiz tns t t nos n tgoiz into 4 tgois. Cs 1: It must povi wit svi n tt lis wit in t tns out. Cs 2: It must povi wit svi ut it is in vitul t. Cs 3: It os not n to svi ut witin t out o tns. Cs 4: It os not n to svi n it is not in t out o tns. In t popos lgoitm w us ooln typ inx to t no to know wt no is n to onnt t sv. T ost untion is psnt in t omul s ollows (4) 3.5 Algoitm To o t onvgn to t optiml vlu w us t stt tnsition untions. W slt vlu nomly mong 0,1,2 wn 0 is slt t untion will us n. In t onition o 2 t untion is us n In t onition o 3 untion is us. Ts untions stt tnsition untions n t ist untion is us t ution stt tnsition, n t ollowing is witout t ng o t tns no ut ng its lotion n t ltt is o t ng wit insting xtnl no in. W iv nw tns t T om xisting tns t T. T tns ost ontin t gin o no(t gin vlu o no in Gn nonil nsml psnts t mil potntil ). W tmin wit t ng o t ost wt t nw iv tns out t is pt o not. Ts posss onut until t tmptu is stiliz. Wn it oms into stil sitution in givn tmptu w u tmptu littl it n o t smpling. Wn t tmptu is ig t systm pt t most stt tt is ptu ut wn t tmptu is los to 0.0 it stts to pt t low ngy stt only wit non zo possiility. T systm will vok t sult o t psnt tns out t until it oms to low tmptu ( ) tt is not 0.0 possiilitis. Initil tmptu n α vil. n psnts tns out t n n psnts t ost o n. T systm uss n to gt nw stt tt is tmpol tns t n tns ost. I t nw solutions v lss ngy it will t nw solution. Wn is igg tn tt o wit t possiility o n will pl to n. Di initil pmt vlus : : gt nom pt t s initil solution, = initil tmptu, Stp 1 : slt vlu witin 0,1,2 nomly s 1 : s 2 : s 3 : Stp 2 : Stp 3 : i OR tn i (stt is in quiliium) tn s tmptu Rpt stp1~stp3 Until tmptu 0.0 Figu 10. ESA Algoitm 4. Expimnt n sults In igu 11 it psnts t t tt ws us in t xpimnt. T il psnts ntwok
7t WSEAS Int. Con. on MATHEMATICAL METHODS n COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING, Soi, 27-29/10/05 (pp129-133) no n t nums insi o t il stns o its inxs o t no. T inx os not ts o o t siz. T onntion twn t nos psnts pysilly onnt no n t wigt o g psnts istn n o t xpimntl it is us o t tns ost. Num 0 no is sv n t ots lints. ost is -8502.0. 8000 6000 4000 2000 0-2000 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86-4000 -6000-8000 -10000 Figu 13. T ost o tmptu lvl 5. Conlusion As in qution 4 it onigus no ost wit n it pvnt t typ s 3 nos om t inl out. Wn t vlu o is too ig o too smll w oul not gt goo solution us it istu tnsition to positiv stt us it ks t ln o no ost n istn ost. Ts gnl polm o Simult Annling Algoitm. In tis xpimnt w us t gn nonil nsml o ESA lgoitm. An w sow tns out polm o vy no n sltion o ity no n oul ooto t ining o t optimiz tns out. Figu 11. Expimntl Dt Figu 12. Finl onlusion o ntwok out Figu 12 is t inl output. In igu 12 t nos tt wnts to svi s olo o gy n t ot tt s wit il nos will t nos tt is not ing svi. No 1, 8, 28 psnt in tns outing t so tt lys t t to snnt nos. Figu 13 illustts t ng o tns ost uing possing tim. T tmptu stt om 1000000.0 n ool own to 0.01 n t initil tns ost is 2750.0 n t inl tns Rns : [1] Xingwi Wng, Hui Cng, Jinnong Co, Linwi Zng, Ming Hung, A Simultnnling s QoS Multisting Algoitm, Poings o ICCT2003 [2] Yong Cui, K Xu, Jinping Wu, Zongo Yu, Youjin Zo, Multi onstin Routing Bs on Simult Annling, ieee 2003 [3] Cotipt Ponvli, Goutm Ckoty, Noio Sitoi, A Nul Ntwok Appo to Multist Routing in Rl Tim Communition Ntwoks, 1995,IEEE [4] F Bu, Anujn Vm, Distiut Algoitms o Multist Pt Stup in Dt Ntwoks, IEEE/ACM Tnstion on Ntwoking, Vol. 4, No. 2, Apil 1996. [5] C.H.Song, K.H.L, W.D.L, An Algoitm o Augmnt Multipl Vil Routing Polm, WSEAS TRANSACTIONS ON SYSTEMS Issu 4, Vol. 2, pp 896 899, Ot. 2003 [6] Jong Suk Coi, Won Don L, Sukoon L, N Hyun Pk, Sng Il Hwng, Yo Duk Youn, "Extn Simult Annling s on Gn Cnonil Ensml", Jounl o t Ko Inomtion Sin Soity, Vol 17, No. 4, July 1990 [7] Pllp Vnktm, Suip Gosl, B.P. Vijy Kum, "Nul ntwok s optiml outing lgoitm o ommunition ntwoks", Nul Ntwoks 15, 2002, pp1289-1298