[Đồ án - Hà]final

TRNG I HC BCH KHOA H NIVIN CNG NGH THNG TIN V TRUYN THNG * NTT NGHIP I HCNGNH CNG NGH THNG TINGII THUT DI TRUYN SP XP KHNG TRI GII BI TON THIT K MNG CHU LI TI U A MC TIUSinh vin thc hin:Nguyn S Thi H

Lp:CNTT1 K54

Gio vin hng dn:TS. Hunh Th Thanh Bnh

H NI 06-2014Sinh vin thc hin: Nguyn S Thi H 20090892 CNTT 1 K54i

PHIU GIAO NHIM V N TT NGHIP1. Thng tin v sinh vinH v tn sinh vin: NGUYN S THI Hin thoi lin lc 0918 635 834Email: [email protected]: CNTT1 K54 H o to: i hc chnh quy n tt nghip c thc hin ti: B mn Khoa hc my tnh, Vin CNTT&TT, i hc Bch Khoa H Ni.Thi gian lm ATN: T ngy 21/02/2014 n 25/05/20142. Mc ch ni dung ca ATN Nghin cu v bi ton thit k mng chu li ti u a mc tiu, gii thut di truyn sp xp khng tri gii bi ton.3. Cc nhim v c th ca ATN Nghin cu bi ton thit k mng chu li n v a mc tiu. Nghin cu gii thut di truyn sp xp khng tri gii bi ton ti u a mc tiu. xut gii thut di truyn sp xp khng tri gii bi ton thit k mng chu li ti u a mc tiu. Ci t gii thut di truyn sp xp khng tri gii bi ton thit k mng chu li ti u a mc tiu vi cc phng php m ha khc nhau. Tin hnh chy thc nghim v so snh kt qu.4. Li cam oan ca sinh vin:Ti Nguyn S Thi H - cam kt ATN l cng trnh nghin cu ca bn thn ti di s hng dn ca TS Hunh Th Thanh Bnh. Cc kt qu nu trong ATN l trung thc, khng phi l sao chp ton vn ca bt k cng trnh no khc.H Ni, ngy thng nmTc gi ATNNguyn S Thi H

5. Xc nhn ca gio vin hng dn v mc hon thnh ca ATN v cho php bo v:H Ni, ngy thng nmGio vin hng dnTS Hunh Th Thanh Bnh

TM TT NI DUNG N

n nay, trn th gii c nhiu cng trnh nghin cu v bi ton thit k mng chu li. Tuy nhin, hu ht trong s u chn hng tip cn ti u n mc tiu, trong khi hng tip cn ti u a mc tiu li c nhiu ngha thc t hn.Do , ti ny nhm nghin cu tng quan v vn thit k mng chu li, tip cn bi ton vi m hnh ti u a mc tiu. Trn c s , xut gii thut di truyn sp xp khng tri gii quyt vn , ci t v chy th nghim a ra kt qu cho mt m hnh mng chu li c th.Cu trc ca n gm 4 chng vi ni dung chnh nh sau:Chng 1 trnh by cc kin thc c s v th, bi ton ng i ngn nht, gii thut di truyn, bi ton ti u a mc vi mc ch lm nn tng l thuyt cho cc chng tip theo.Chng 2 trnh by v bi ton thit k mng chu li c m hnh ha bng th, lch s pht trin, cc ng dng v cc nghin cu lin quan.Chng 3 xut gii thut di truyn sp xp khng tri gii bi ton thit k mng chu li ti u a mc tiu.Chng 4 trnh by kt qu thc nghim, nhn xt v nh gi hiu qu ca gii thut xut.

LI M U

S ra i ca h thng mng, c bit l Internet, nh du mt bc ngot quan trng trong lnh vc cng ngh thng tin v truyn thng. K t , mng mang n cng ngy cng nhiu li ch trong mi lnh vc ca cuc sng nh kinh t, vn ha, qun i, Do , i khi ch mt s c mng cng c th gy ra mt lot nhng hu qu nghim trng, c bit l v kinh t. iu ny t ra yu cu cho cc nh cung cp mng l lm th no m bo tnh tin cy cho sn phm ca h. cng l l do cho s ra i ca , bi ton v thit k mng chu li (Survivable Network Design Problem - SNDP). Sau ny, khi h thng mng dn pht trin, SNDP ngy cng nhn c nhiu s quan tm ca cc nh khoa hc, cc nh quy hoch, qun l n nay c rt nhiu m hnh cho bi ton thit k mng chu li c a ra trn th gii. Mi m hnh i din cho mt ng dng v nhu cu c th trong thc t. n ny tp trung nghin cu m hnh mng chu li vi cc kiu kt ni unicast v anycast c chi ph bng thng theo m-un (All Capacities Modular Cost SNDP with Simultaneous Unicast and Anycast Flows - A-SNDP).

Hnh 1. Cc kiu kt ni c s dng trong m hnh mng chu li(a) Kiu kt ni unicast, kt ni t mt client n mt server(b) Kiu kt ni anycast, kt ni t mt client n nhiu server Nhm tng ngha thc t ca bi ton, n tin hnh nghin cu A-SNDP ti u a mc tiu, t xut gii thut di truyn sp xp khng tri gii quyt vn c t ra, ci t gii thut, so snh kt qu v kt lun v hiu nng ca gii thut.

LI CM N

Trc ht, em xin gi li cm n chn thnh ti TS Hunh Th Thanh Bnh, ngi tn tnh dy d v hng dn em trong qu trnh hon thnh n cng nh trong hc tp.ng thi, em xin by t lng bit n n cc thy c gio trong Vin Cng ngh thng tin v Truyn thng trng i hc Bch Khoa H Ni, nhng ngi tn tm ging dy, truyn t cho chng em nhng kin thc c bn lm nn tng cho vic thc hin n cng nh trong qu trnh cng tc sau ny.Em cng xin gi li cm n ti cc anh ch ti trng i hc Bch Khoa H Ni, cc bn, cc em trong nhm sinh vin nghin cu, nhng ngi lun bn cnh gip , ng vin em trong qu trnh hon thnh n.Cui cng, vi tt c s knh trng, con xin by t lng bit n su sc ti b m v anh ch em trong gia nh lun l ch da tinh thn vng chc v to mi iu kin cho con n hc nn ngi.H Ni, ngy 25 thng 05 nm 2014Nguyn S Thi H

MC LC

PHIU GIAO NHIM V N TT NGHIPiTM TT NI DUNG NiiLI M UiiiLI CM NivMC LCvDANH MC HNH VviiiDANH MC CC BNGxDANH MC CC T VIT TT V THUT NGxiCHNG 1: C S L THUYT11. Cc khi nim c bn v th11.1. nh ngha th11.2. ng i v tnh lin thng22. Bi ton tm ng i ngn nht22.1. Gii thut Dijkstra32.2. Gii thut Kruskal42.3. Gii thut Floyd-Warshall53. Gii thut di truyn53.1. Gen63.2. Nhim sc th (c th)63.3. Qun th63.4. Hm thch nghi73.5. t bin v lai ghp73.6. Chn lc t nhin73.7. S gii thut di truyn83.8. Cc vn ca gii thut di truyn84. Bi ton ti u a mc tiu94.1. Bi ton ti u t hp94.2. Bi ton ti u a mc tiu104.3. Mt s khi nim105. Gii thut di truyn sp xp khng tri115.1. Gii thut sp xp khng tri125.2. Khong cch quy t (Crowding Distance)13CHNG 2: BI TON THIT K MNG CHU LI TI U A MC TIU151. Tng quan v bi ton thit k mng chu li152. Cc ng dng ca bi ton thit k mng chu li162.1. Thit k mng truyn thng162.2. Thit k mng li giao thng173. Bi ton thit k mng chu li ti u a mc tiu184. Cc nghin cu lin quan19CHNG 3: GII THUT DI TRUYN SP XP KHNG TRI GII BI TON THIT K MNG CHU LI TI U A MC TIU211. M ha li gii211.1. M ha da trn c s d liu ng i (CDE)211.2. M ha ng i y (CCE)232. Php ton di truyn232.1. Php lai ghp232.2. Php t bin243. Hm thch nghi254. Chin lc chn lc t nhin255. Ci t gii thut25CHNG 4: KT QU THC NGHIM281. D liu thc nghim282. Thng s thc nghim293. Kt qu thc nghim303.1. nh gi m hnh bi ton303.2. So snh vi m hnh n mc tiu403.3. So snh cc phng php m ha44KT LUN47TI LIU THAM KHO48

DANH MC HNH V

Hnh 1. Cc kiu kt ni c s dng trong m hnh mng chu liiiiHnh 2. th v hng v th c hng2Hnh 3. S gii thut di truyn8Hnh 4. Minh ha hnh ch nht cuboid13Hnh 5. C s d liu cho mt yu cu ca khch hng th nht21Hnh 6. M ha CDE22Hnh 7. M ha CCE23Hnh 8. Lai ghp mt im ct gia c th cha P v c th m P' sinh ra con C.24Hnh 9. Lai ghp ng gia cha c th cha P v c th m P' sinh ra con C.24Hnh 10. Php t bin thay th xu th 2 ca c th cha P sinh ra c th con C.25Hnh 11. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_1.30Hnh 12. Trng thi th Polska ng vi cc im trong hnh 11.31Hnh 13. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_3.32Hnh 14. Trng thi th Atlanta ng vi im trong hnh 13.32Hnh 15. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Germany_2.33Hnh 16. Trng thi th Germany ng vi im trong hnh 15.33Hnh 17. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_3.34Hnh 18. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_4.35Hnh 19. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_5.35Hnh 20. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_6.36Hnh 21. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Germany_1.36Hnh 22. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Germany_3.37Hnh 23. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Germany_4.37Hnh 24. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Germany_5.38Hnh 25. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_1.38Hnh 26. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_2.39Hnh 27. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_4.39Hnh 28. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_7.40Hnh 29. So snh kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng vi th Polska.41Hnh 30. So snh kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng vi th Atlanta.41Hnh 31. So snh kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng vi th Germany.42Hnh 32. So snh kt qu thu c gia CDE-NSGA-II v CCE-NSGA-II vi b d liu Polska_1.45Hnh 33. So snh kt qu thu c gia CDE-NSGA-II v CCE-NSGA-II vi b d liu Germany_2.45Hnh 34. So snh kt qu thu c gia CDE-NSGA-II v CCE-NSGA-II vi b d liu Atlanta_3.46

DANH MC CC BNG

Bng 1. Thng s cc b d liu28Bng 2. So snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng th Polska.42Bng 3. So snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng th Germany.43Bng 4. So snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng th Atlanta.44

DANH MC CC T VIT TT V THUT NG

Ch vit ttVit y ngha

SNDPSurvivable Network Design ProblemBi ton thit k mng chu li

A-SNDPAll Capacities Modular Cost SNDPBi ton thit k mng chu li c chi ph bng thng theo m-un

MA-SNDPMulti-Objective A-SNDPBi ton thit k mng chu li c chi ph bng thng theo m-un ti u a mc tiu

GAGenetic AlgorithmGii thut di truyn

NSGA-IINon-dominated Sorting Genetic Algorithm IIGii thut di truyn sp xp khng tri

CDEConnection Database based EncodingPhng php m ha da trn c s d liu ng i

CCEComplete Connection EncodingPhng php m ha ng i y

CHNG 1: C S L THUYT

1. Cc khi nim c bn v thL thuyt th l mt lnh vc nghin cu c t lu i v c nhiu ng dng trong th gii hin i. Nhng t tng c bn ca l thuyt th c xut vo nhng nm u ca th k 18 bi nh ton hc li lc ngi Thy s - Leonhard Euler. Chnh ng l ngi s dng th gii bi ton ni ting v 7 cy cu thnh ph Konigsberg. th c s dng gii quyt cc bi ton trong nhiu lnh vc khc nhau. Chng hn, chng ta c th phn bit cc hp cht ha hc hu c c cng cng thc phn t nhng khc nhau v cu trc phn t nh th, hay nh chng ta cng c th s dng th gii gii quyt cc bi ton lp lch, thi kha biu, phn b tn s cho cc trm pht thanh v truyn hnh, phn tch mng li giao thng V bi ton thit k mng chu li cng c xy dng da trn th. c bit trong nhiu nm tr li y, vi s ra i ca my tnh in t v s pht trin nhanh chng ca cng ngh thng tin, l thuyt th ngy cng c quan tm nhiu hn.Sau y s trnh by cc khi nim c bn ca th, lm nn tng cho vic p dng cc gii thut gii quyt cc vn ca bi ton thit k mng chu li.1.1. nh ngha th th l mt cu trc ri rc gm cc nh v cch cnh ni gia chng. Cc loi th khc nhau c phn bit bi kiu v s lng cnh ni. Ta nh ngha cc loi th nh sau.nh ngha 1.1: n th v hng G = (V, E) bao gm V l tp khng rng cha cc nh, v E l tp cc cp khng c th t gm hai phn t khc nhau ca V gi l cnh. [Hnh 2. a]nh ngha 1.2: n th c hng G = (V, E) bao gm tp cc nh V v tp cc cnh E l cc cp c th t gm hai phn t khc nhau ca V. Cc cnh ca th c hng cn c gi l cc cung. [Hnh 2. b]

Hnh 2. th v hng v th c hngT y, tin s dng, ta s gi th thay cho n th v hng m khng c ch thch g thm.1.2. ng i v tnh lin thng

nh ngha 1.3: ng i di n t nh u n nh v, trong n l s nguyn dng trn th v hng G = (V, E) l dy x0, x1, x2, xn-1, xn trong u = x0, v = xn, (xi, xi+1) E, i = 1..n. nh u c gi l nh u, cn nh v c gi l nh cui ca ng i. ng i m c nh u trng vi nh cui c gi l chu trnh. Chu trnh c gi l n nu nh khng c cnh no lp li. xc nh xem c lun tn ti ng i gia 2 cp nh bt k trong th hay khng, ta a ra khi nim tnh lin thng ca th.nh ngha 1.4: th v hng G = (V, E) c gi l lin thng nu lun tm c ng i gia hai nh bt k ca n.nh ngha 1.5: th c hng G = (V, E) c gi lin thng mnh nu lun tm c ng i gia hai nh bt k ca n. th c hng G = (V, E) c gi l lin thng yu nu th v hng tng ng vi n l lin thng.2. Bi ton tm ng i ngn nhtPhn ny trnh by v bi ton tm ng i ngn nht t mt nh n cc nh khc hoc gia tt c cc cp nh ca th.

Pht biu bi ton: Cho th G = (V, E), tm ng i ngn nht t nh ngun sV n mi nh vV. c rt nhiu gii thut gii quyt vn ny. Sau y, s nhc li mt s gii thut ni ting v phn tch phc tp tnh ton ca chng.

2.1. Gii thut DijkstraGii thut Dijkstra cho php tm ng i ngn nht t mt nh s n cc nh cn li ca th c trng s v khng cha chu trnh m. tng ca gii thut l xc nh tun t cc nh c chiu di n s theo th t tng dn.Gii thut gn cho mi nh mt nhn tm thi. Nhn tm thi ca cc nh cho bit cn trn ca chiu di ng i ngn nht t s n nh . Nhn ca cc nh s bin i trong cc bc lp, m mi bc lp s c mt nhn tm thi tr thnh chnh thc chnh l chiu di ngn nht ca ng i t s n nh .Gii thut Dijkstra

for all vV do d(v) = color[u]= white end ford[s] = 0pred[s] = NullQ = V \ swhile (Q ) do u = nh c d[u] nh nht for all v l nh k ca u do if (d[u] + w(u,v) < d[v]) then d[v]= d[u] + w(u,v) pred[v] = u end if end for Color[u]= black Q = Q \ uend while

phc tp tnh ton:Thi gian chy ca gii thut Dijkstra ph thuc vo cch ci t hng i u tin nh nht Q. Xt trng hp ta duy tr hng i u tin nh nht bng cch tn dng cc nh c nh s t 1 n |V|. Khi , ta n gin lu tr khong cch t nh s n cc nh khc di dng mng. Mi thao tc chn hay xa cn O(1) thi gian, thao tc tm nh c khong cch so vi nh s nh nht cn O(V) thi gian (v cn tm kim trn ton b phn t ca mng). Nh vy tng thi gian cn thit ca gii thut s l O(V2+E) = O(V2).2.2. Gii thut KruskalGii thut Kruskal tm ng i ngn nht gia mi cp nh bng cch xy dng cy khung ca th ban u. tng ca gii thut ny nh sau: Vi th v hng G = (V, E) c n nh. Khi to cy T ban u rng. Xt tt c cc cnh ca th theo th t tng dn ca trng s. Mt cnh s c kt np vo T nu nh vic thm cnh khng to thnh chu trnh n trong T. Lp li bc ny cho n khi: kt np c n-1 cnh vo trong T.Cha kt np nhng xy ra trng hp c kt np thm mt cnh bt k trong s cnh cn li th s to ra chu trnh n. Trng hp ny th G l khng lin thng vic tm kim cy khung b tht bi.ng i gia mi cp nh trn cy khung chnh l ng i ngn nht gia chng.M hnh gii thut KruskalGii thut Kruskal

1. For all kV do Lab[k] := -1 // lab lu s nh ca gc cy k

For all (edge(u,v)E theo th t t cnh trng s nh ti cnh trng s ln) do R1:=getRoot(u) // r1 l gc ca cy cha nh u R2=getRoot(v) If r1 r2 then // cnh(u,v) ni hai cy khc nhau Kt np (u,v) vo cy, nu n-1 cnh th gii thut dng Union (r1,r2) // hp nht hai cy thnh mt cy End if End forEnd for

Xt v phc tp tnh ton, ta c th chng minh c rng thao tc GetRoot c phc tp l O(logn), cn thao tc Union l O(1). Gi s ta c danh sch cnh sp xp, khi vng lp dng cy khung duyt qua danh sch m cnh, vi mi cnh n gi 2 ln thao tc GetRoot, phc tp l O(mlogn). Nu th c cy khung (m n-1), chi ph thi gian ch yu s nm thao tc sp xp danh sch cnh bi phc tp ca HeapSort l O(mlogm). Tm li, phc tp tnh ton ca gii thut l O(mlogm) trong trng hp xu nht.2.3. Gii thut Floyd-WarshallGii thut gii quyt bi ton tm ng i ngn nht gia cc cp nh ca th. tng: Gii thut Floyd c thit k theo phng php quy hoch ng. Nguyn l ti u c p dng cho bi ton ny: Nu k l nh nm trn ng i ngn nht t i n j th on ng t i n k v t k n j cng phi ngn nht.Gii thut Floyd-Warshall

1. N:= rows (W)D0 WFor k 1 to n do For I 1 to n do For j1 to n do Dij(k) min (dij(k-1), dik(k-1) + dkj(k-1)) End for End forEnd forReturn D(n)

Thi gian tnh ca gii thut Floyd-Warshall c xc nh bi ba vng lp for lng nhau. V mi ln thc hin dng 6 cn thi gian O(1), nn gii thut chy trong thi gian O(n3).3. Gii thut di truynS pht trin mnh m ca ngnh khoa hc my tnh na cui th k trc ko theo s xut hin ca hng lot cc bi ton mi c nhiu ng dng thc t hn v cng phc tp hn. Do , nhng cch tip cn bit kh c th p ng cc nhu cu t ra. Bn cnh , vi s pht trin khng ngng ca cng ngh phn cng, my vi tnh c th hot ng vi cng sut ln hn cho php gii c cc bi ton c kch thc ln. Trn con ng tm kim cc phng php mi, cc nh nghin cu xut tng m phng cc qu trnh trong t nhin gii cc bi ton kh. Vi nn tng vng chc v l thuyt tin ha, nm 1975, John Holland xut gii thut di truyn (Genetic Algorithm, vit tt l GA) p dng cho cc bi ton ti u ha t hp.Gii thut di truyn m phng qu trnh tin ho trong t nhin da trn thuyt tin ha Neo-Darwinism nhm tm ra cc li gii xp x ti u cho cc bi ton ti u t hp kh. Gii thut di truyn l mt qu trnh tm kim v chn lc theo cc quy lun m phng tin ha trong mt tp phng n c, cc tiu chun chn lc c m t bi mt hm thch nghi vi mc ch tm ra phng n tt nht.Cc khi nim ca thuyt tin ho cng c s dng trong gii thut di truyn, nhm tm ra li gii mt cch t nhin. u tin cc phng n c th ca bi ton c m ha v khi to. Cc li gii ny c nh gi da trn thch nghi. Qu trnh chn lc s gi li cc li gii tt nh qu trnh chn cc c th thch nghi trong t nhin. Cc li gii c chn s qua qu trnh lai ghp, t bin to th h cc li gii mi vi k vng th h mi ny s tt hn th h trc. Qu trnh sinh sn v nh gi cc th h c tip tc cho n khi c s hi t th h, hay th h mi khng khc g th h c.Gii thut di truyn thc hin vi tp phng n hu hn, vi cc bi ton ti u c tp phng n lin tc hay v hn cn phi c ri rc ho c tp phng n hu hn thch hp. Tri qua gn 40 nm pht trin, gii thut di truyn phn no cho thy sc mnh ca mnh trong cc bi ton ti u nh tm ng i, lp lch,.Sau y s trnh by mt s khi nim c bn c s dng trong gii thut di truyn.3.1. GenCc gen biu din trong mt chui tuyn tnh, mi gen kim sot mt s c trng cho mt thnh phn ca li gii. Gen vi nhng c trng nht nh, c v tr nht nh trong nhim sc th. Bt c c trng no ca mi c th c th t biu hin mt cch phn bit v gen c th nhn mt s gi tr khc nhau.3.2. Nhim sc th (c th)Mi kiu (nhm) gen (ta gi l mt nhim sc th) s biu din mt li gii chp nhn c ca bi ton ang xem xt.

3.3. Qun thMt qun th chnh l mt tp hp cc li gii. Ti mi th h, qu trnh tm kim li gii mi s da trn nhng li gii (ang) c trong qun th.T mt qun th ban u, qu trnh tm kim li gii c m phng nh qu trnh tin ha trong t nhin. Qu trnh tm kim li gii chnh l qu trnh tin ha, v chn lc t nhin. Trong gii thut di truyn, qu trnh tm kim li gii ti u c thc hin theo nhiu hng, bng cch duy tr mt qun th li gii, v thc y qu trnh hnh thnh v trao i thng tin gia cc hng ny.3.4. Hm thch nghiHm thch nghi nhm nh gi thch nghi ca mt li gii. Hm thch nghi th hin mc tiu li gii ca bi ton cn t c.3.5. t bin v lai ghpVic sinh ra cc c th mi chnh l vic sinh ra cc li gii mi c thc hin bng cc p dng cc bin i ln mt s c th c trong qun th. Php lai kt hp cc tnh cht ca hai hay nhiu nhim sc th cha v m to ra cc nhim sc th con bng cch hon v cc on gen tng ng ca cha v m, hoc bng mt ton t kt hp cc gen ca cha v m theo mt cch no sinh ra cc gen ca c th con.Khc vi php lai, php t bin thay i mt cch ngu nhin mt hay nhiu gen ca nhim sc th c chn. Thay i ny c thc hin vi mt xc sut th hin tc t bin. Php t bin cho php a thm thng tin mi vo qun th lm cho cht liu di truyn phong ph hn.3.6. Chn lc t nhinQu trnh chn lc t nhin chnh l qu trnh chn lc cc c th trong qun th, nhm mc ch lm cho qun th mi ngy cng tt hn so vi nhng th h trc, bng nhng chin lc chn lc khc nhau nh: chn lc t nhin, gi li cc c th u t.

3.7. S gii thut di truyn

Hnh 3. S gii thut di truyn3.8. Cc vn ca gii thut di truynM ha li gii: Mi bi ton p dng gii thut di truyn gii quyt u gp nhng kh khn nht nh trong vic m ha mt li gii thnh c th. C nhiu phng php m ha, nhng i vi mt bi ton xc nh ch c th p dng mt hoc hai phng php thu c kt qu tt.V d nh phng php m ha chui nh phn c John Holland s dng ln u tin nm 1975 khi pht biu gii thut di truyn, hay phng php m ha chui hon v p dng rt thnh cng khi gii bi ton ngi du lch.Khi to qun th: Vic khi to qun th cng nh hng ln n kt qu cui cng, v vy vic khi to cc c th ban u ca qun th cng phi s dng phng php hp l ty theo bi ton.Cc php ton di truyn: cc php ton lai ghp, t bin, chn lc s quyt nh chiu hng tin ha ca qun th, do c c cc kt qu tt cui cng cng phi c cc php ton tin ha ph hp.

4. Bi ton ti u a mc tiu4.1. Bi ton ti u t hpMt bi ton ti u ha bao gm vic tm li gii tt nht (ti u) gii quyt bi ton. Cc bi ton ny c chia thnh hai loi:Loi th nht: min xc nh ca cc bin l lin tc.Loi th hai: min xc nh ca cc bin l ri rc, gi l bi ton t hp, tiu biu cho vic tm ra mt i tng bn trong mt tp hu hn, hoc l v hn m c.

i tng ca bi ton ti u t hp l mt cp (, f) vi l mt min N chiu, v f l mt hm nh x . Chng ta xem xt vic tm ra mt li gii sao cho:

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Mt li gii x* c gi l li gii ti u ton cc cho mt th hin ca bi ton vi f* = f(x*) biu th cho chi ph ti u, v biu th cho tp li gii ti u.

Tt c cc li gii tha mn cc rng buc ca bi ton c gi l cc li gii kh thi, v tp con ' l min kh thi. Trong trng hp ny, vn (1) phi tha mn:gi(x) 0, (2)hj(x) = 0,(3)

Vi hm gi(x) v hm hj(x) ln lt l bt ng thc v ng thc rng buc, nh ngha min kh thi . Xem hm f l hm mc tiu vi min l min li gii, v ' l min kh thi hay c gi l khng gian tm kim.Vic tm li gii ca bi ton ti u t hp theo cch n gin l ly ra tt c cc li gii c th, sau chn ra li gii tt nht cho bi ton. Tuy nhin, cng vic ny tn kh nhiu thi gian nu tp li gii kh thi qu ln. V d bi ton t hp m min xc nh l tp cc hon v ca N phn t th khng gian li gii kh thi ti a l N!, nu N qu ln th vic tm ra li gii ti u tn rt nhiu thi gian. V vy, gii quyt bi ton, chng ta c th s dng cc phng php xp x tm ra nhng li gii tt (khng bo m l tt nht) trong khong thi gian chp nhn c vi cc lp thut gii ph bin nh localsearch, heuristic, tin ha.4.2. Bi ton ti u a mc tiuBi ton ti u a mc tiu c nh ngha nh sau:

Trong :

l M hm mc tiu, cc hm g, h l cc rng buc ca bi ton.

Mt li gii l mt vector . Gi tr l chn di v l chn trn.

Tp hp cc li gii tha mn cc rng buc: (5), (6) v (7) c gi l khng gian quyt nh (Dicision space, search space, feasible space) .

Tp hp M hm mc tiu c gi l khng gian mc tiu (objective space) .4.3. Mt s khi nimKhng ng mc tiu: Cc mc tiu trong (4) khng ng tc l vic ti u mt mc tiu no dn n ti u tt c cc mc tiu cn li. Lc ny, tp hp li gii ch l mt li gii.ng mc tiu: Cc mc tiu trong (4) ng tc l vic ti u mt mc tiu s gim vic ti u cc mc tiu khc. Lc ny, tp hp li gii s gm nhiu li gii khc nhau.Trong bi ton ti u a mc tiu, ngi ta ch xt n nhng bi ton c cc mc tiu ng vi nhau. V trn thc t, cc mc tiu lun ng . (v d bi ton s c cp CHNG 2).Tri (Dominate): Mt li gii x gi l tri hn li gii y nu tha 2 mnh sau:Li gii x khng xu hn y ti mi mc tiu.Li gii x tt hn cht ti t nht mt mc tiu.Tp khng tri: Tp cc li gii m khng c li gii no tri hn chng. Bin khng tri: Cc li gii thuc tp khng tri s c biu din thnh cc im trong khng gian quyt nh. Thng th cc im ny s to thnh mt bin gi l bin khng tri.Bin pareto: L bin nghim nghim ti u ca bi ton ti u a mc tiu.5. Gii thut di truyn sp xp khng triGii thut di truyn sp xp khng tri (Non-dominated Sorting Genetic Algorithm II, vit tt l NSGA-II) l mt bin th ca gii thut di truyn nhm gii quyt cc bi ton ti u a mc tiu, c Deb v Agarwal xut vo nm 2000. tng ca gii thut xoay quanh vic sp xp qun th thnh cc tp khng tri (rank) v tnh ton mt phn b ca cc li gii trn rank tin hnh qu trnh chn lc t nhin.NSGA-II k tha cc c tnh ca gii thut di truyn v c pht trin ph hp vi vic gii quyt cc bi ton ti u a mc tiu. Sau y, n s trnh by cc bc c bn ca NSGA-II.Cc bin ca gii thut:Pt qun th cha ca th h t.Qt qun th con c to thnh t Pt bng cc php ton di truyn.Fj tp khng tri, j = 1,,R.N s lng c th trong qun th Pt.Cc bc ca gii thut:Bc 1:Khi to qun th P1 vi |P1| = N.Gn t = 1.Bc 2:p dng cc php ton di truyn to qun th Qt t qun th cha Pt.Bc 3:Kim tra iu kin dng, nu tha mn th xut ra qun th Pt, nu khng chuyn sang bc 4.Bc 4:

t Rt = Pt Qt.Bc 5:S dng gii thut sp xp khng tri sp xp cc c th trong Rt thnh cc tp khng tri F1, F2,, Fk.Bc 6:Tnh khong cch quy t cho cc cc th trong Fj, j = 1,,k.To qun th Pt+1 bng cch thm cc c th t cc tp Fj vo Pt+1 cho n khi N c th. S c 2 trng hp nh sau: Trng hp 1: |Pt+1| + |Fj| N th Pt+1 = Pt+1Fj. Trng hp 2: |Pt+1| + |Fj| > N th ch b sung N - |Pt+1| c th t Fj vo Pt+1, cc c th c la chn da vo khong cch quy t ca chng.Gn t = t+1.Quay li bc 2.5.1. Gii thut sp xp khng triCc bin ca gii thut:P qun th ng xt.Fj tp khng tri, j=1,,R.

Su tp c th tri hn c th u, uP.Cc bc ca gii thut:Khi u gii thut gn j = 1.Bc 1:

Vi gn Su = .Bc 2:

Vi v , xt xem u c tri hi v hay khng, nu tri hn th Sv = Sv{u}.Bc 3:

Vi , Fj = Fj {u} nu Su = .P = P\Fj.Bc 4:Nu P = th kt thc.Nu P th j = j+1 v quay li bc 1.5.2. Khong cch quy t (Crowding Distance)Khong cch quy t ca c th i nm trn mt bin l chiu di trung bnh cc cnh ca mt hnh ch nht (cuboid) c to ra t hai c th gn k n trn bin khng tri.

Hnh 4. Minh ha hnh ch nht cuboidPhng php tnh khong cch quy t c thc hin nh sau:ng vi cc hm mc tiu fk ta sp xp cc nghim trong bin F theo th t tng dn : Ik = sort(fk(.), >).t l = |F|, x[i, k] l nghim th i trong Ik.Gn dk(x[1, k]) = 0 v dk(x[l, k]) = .ng vi mi i = 2,, l-1 tnh:

Tnh tng khong cch quy t tng ng vi mi hm mc tiu:

Vi phng php tnh khong cch quy t ny, cc c th trong cc tp Fj c khong cc quy t cng ln th cng c u tin chn vo qun th cha th h tip theo hn. Nhng cc th c khong cch quy t thp, ng ngha vi vic cc c th ny nm gn nhau trn bin nghim v to thnh mt vng gi l vng quy t. Cc c th thuc vng quy t thng c kiu gen tng t nhau, nu u tin la chn cc c th thuc vng ny th s khng mang s a dang v kiu gen trong qu trnh tin ha qua cc th h sau.

CHNG 2: BI TON THIT K MNG CHU LI TI U A MC TIU

1. Tng quan v bi ton thit k mng chu liS ra i ca h thng mng, c bit l Internet, nh du mt bc ngot quan trng trong lnh vc cng ngh thng tin v truyn thng. K t , mng mang n cng ngy cng nhiu li ch trong mi lnh vc ca cuc sng nh kinh t, vn ha, qun i, Do , i khi, ch mt s c mng cng c th gy ra mt lot nhng hu qu nghim trng, c bit l v kinh t. iu ny t ra yu cu cho cc nh cung cp mng l lm th no m bo tnh tin cy cho sn phm ca h. cng l l do cho s ra i ca , bi ton v thit k mng chu li (Survivable Network Design Problem - SNDP). Sau ny, khi h thng mng dn pht trin, SNDP ngy cng nhn c nhiu s quan tm ca cc nh khoa hc, cc nh quy hoch, qun lBi ton thit k mng chu li ni chung c nghin cu t nhng nm 60 ca th k trc. Cho n nay, c nhiu bin th ca bi ton chu li ny. Mi mt bin th ca bi ton c i su nghin cu v a ra cc gii thut c th p dng cho mi m hnh. Tt c cc gii thut tng ng vi mi hng tip cn c m t chi tit trong Design of survivable network: A survey nm 2005 [18].Xt m hnh mng chu li c a ra u tin. Trong m hnh ny, ng vi mt nt mng u s c gn gi tr khng m r(u) i din cho quan trng ca n trong mng. iu kin mng chu li c pht biu: tn ti ti thiu r(s, t) = min{r(s), r(t)} ng ri rc (khng c nt chung v cnh chung) gia bt k cp nt s,t no trong mng. Nhiu gii thut chnh xc, xp x c a ra gii quyt m hnh ny. Trong , phi k n l gii thut chnh xc da trn phng php branch-anh-cut v branch-and-bound ca Chou and Frank (1992) v Hsu and Kao(1990), heuristic ca Kenneth Steiglitz (1969). Tuy nhin, cc gii thut ny cng ch mi gii quyt vi mng kch thc nh, s lng nt t. Gn y, vi s pht trin ca cng ngh thng tin v nhu cu truy cp ca con ngi cng thay i, m hnh chu li ny hu nh khng cn ph hp trong thc t, thay vo , nhiu m hnh mng chu li mi c ra i. n ny cng s a ra mt m hnh thit k mng chu li mi, khng n thun ch ti u mt mc tiu chi ph nh trc y m ng thi cn ti u cc mc tiu khc. M hnh thit k mng chu li ti u a mc tiu ha hn s l mt xu th mi trong qu trnh pht trin ca lp bi ton SNDP.

2. Cc ng dng ca bi ton thit k mng chu liSNDP c nhiu ng dng trong thc t nh: thit k mng truyn thng, mng phn tn khi quan tm n tin cy ca mng,. Ngoi ra, cng c th s dng m hnh ha mt s bi ton ng dng th v p dng bi ton ny trong cc ng dng . Mt s bi ton ng dng thng c quan tm gn lin vi khi nim sng st (Survivable) nh: ng dng thit k mng li giao thng chng tc nghn, ng dng trong h thng li in, ng ng, ng nc v mng truyn thng kim sot c s h tng gim thiu chi ph sa cha h thng khi i mt vi cc s c hng hc thit b v ng dy Phn tip theo gii thiu cc ng dng c th ca bi ton SNDP: trong thit k mng truyn thng v trong mng li giao thng.2.1. Thit k mng truyn thngMng truyn thng l mt tp cc my tnh c lp v cc phng tin giao tip gia chng. Mng truyn thng thng c s dng bi nhiu ngi, c th truy cp ti bt c v tr my tnh no trong mng. Vn bo mt ca n l vn cn quan tm khi quyt nh thit k chng. Gi thit rng chng ta c th phn tch tnh cht b tn cng ca mt cu trc mng truyn thng d liu. Mng truyn thng c th c i din bi mt th vi trng s bng tham s cht lng ca dch v (Quality of Service - QoS), v d nh tc d liu ti a. Mc ch c th m bo tc d liu mong mun, thm ch khi c mt vi link b li. i vi mt m hnh mng truyn thng, gi thit rng cc hot ng tn cng lm ph hy lin kt truyn thng l iu kh trnh khi. m bo tnh tin cy, tnh an ton ca mng, ph thuc vo ng i gia cc my tnh trong mng. Bi ton SNDP c dng p ng c mc xy ra li hay h hng ng truyn trong mng, p ng c tin cy cn thit cho vic thit k mng truyn thng c bn.Trong trng hp, ch c mt my tnh m nhn chc nng nh my ch (server) v cc my tnh khc kt ni n my tnh ny trong mng, chng ta m hnh ha h thng ny nh mt cy khung, gc ca n chnh l my tnh c (m nhn nh chc nng ca mt server), cc nh l cc my tnh (cc khch hng mun kt ni n mng) hay cc router, switch (tng ng nh l cc nh khng cn thit trong khng gian), cc cnh l kt ni gia hai my. Nh vy, m bo c tnh tin cy ca mng, ty thuc vo chc nng ca tng loi my tnh, chng ta phi quyt nh c s ng i cn thit n my tnh gc m bo khi gp bt k s c hng hc hay b tn cng no, th cng khng nh hng n ton b mng truyn thng.Trong trng hp, c mt c s h tng tn ti (mng truy cp), c nhiu my tnh sn c trong mng, vic kt ni cc my tnh mi cho mng truyn thng ny cn phi gii quyt qua bc tin x l:Thu gn c s h tng tn ti ban u xem nh n ch c nhn thy trn mng l mt my tnh duy nht.Vic kt ni thm my tnh vo mng tng t nh trng hp ban uKt thc chng ta li phi x l a n v ti u kt ni vi mt trong tp hp cc my c.Trong c hai trng hp va nu, nu dng mt cy Steiner v sau tng thm ng ty thuc vo nhu cu kt ni, th s tit kim chi ph v p ng c cc nhu cu chu li ca mng truyn thng.2.2. Thit k mng li giao thngMng li giao thng l mt thnh phn khng th thiu trong mi thnh ph, mi a im dn c. Cng vi s gia tng dn s cc khu vc thnh th, mng li giao thng ngy cng tr nn phc tp v c ch trng nhiu hn. Chng hn, hin nay tnh trng tc nghn giao thng xy ra thng xuyn trn a bn H Ni. c nhiu phng n c a ra nh phn lung, chn ng ba, ng t Tuy nhin, cc phng php ny cng ch mi t c hiu qu trong mt thi gian ngn. To ra mt c s h tng giao thng ti u, hn ch tc nghn l nhim v quan trng ca CIP (Critical Infrastructure) v mng li truyn thng. c bit ti bo co nm 1997 ca y ban Tng thng v bo v c s h tng quan trng (PCCIP-Presidential Commission on Critical Infrastructure Protection) xc nh cc yu t c s h tng cn thit cho quc phng, an ninh, kinh t ca Hoa K. Xc nh cu hnh c s h tng ti thiu l cn thit p ng yu cu c bn. Quay li vi m hnh mng li giao thng trong mt thnh ph, vic xc nh cc tnh trng nguy c d xy ra tc nghn mt nt, on ng giao thng no l yu t quan trng quyt nh xy dng m hnh c s h tng giao thng c bn. Mt phng thc thit k hiu qu bt u bng vic sinh ra mt cu trc th y c trng s cc cnh da trn khong cch Euclide, trong cc nh biu din cc nt giao thng, v trng s cnh biu din khong cch Euclide gia cc nt giao thng ny. Tip theo phng thc s dng th con nhm v kt ni cc nt giao thng vi nhau. Sau , ty thuc vo c im nng lc giao thng cn thit, xc nh s lng cc con ng phn chia thch hp kt ni gia hai nt giao thng. Kt qu l mt th con ca bi ton SNDP s h tr c qu trnh thit k ti u cho mng li giao thng.Ngoi ra, cc ng dng nh h thng li in, ng ng, ng nc cng c xem xt nh l vn chu li ca bi ton.Qua hai phn trn, ta c th thy vai tr quan trng ca bi ton SNDP vo ng dng tin hc cng nh cc lnh vc khc trong i sng. Vi tnh cht hu dng nh th nn khng t cc nghin cu c tin hnh a ra li gii tt cho bi ton. Phn sau xin trnh by m hnh pht trin mi ca bi ton SNDP.3. Bi ton thit k mng chu li ti u a mc tiu n trnh by bi ton thit k mng chu li da trn m hnh All Capacities Modules Cost (ACMC) cho hai kiu kt ni unicast v anicast c pht biu trong [1], vit tt l A-SNDP. Qua xut m hnh thit k mng chu li di dng m hnh bi ton ti u a mc tiu (MA-SNDP): gim chi ph xy dng ng thitng tnh n nh ca h thng mng.Bi ton ny c pht biu nh sau:u vo: th v hng G = (V, E), trong V l tp cc nt, tp cnh E = {e| e = (u, v)} vi u, v V.Tp yu cu ca cc khch hng D = {ti, si, di, bi}, i = {1,,|D|} trong : si, di V ln lt l nt ngun v nt ch ca yu cu i. bi l bng thng cn dng ca yu cu i. Be,k, Ce,k ln lt l bng thng v chi ph tng ng mc k ca cnh e vi k = {1,...,K}, K l mc cao nht.Tp cc nt replica S = {ui, vi} vi vi l nt replica ca nt ui v ui, vi V.Rng buc:Tt c cc yu cu kt ni ca khch hng u c tha mn.Mi yu cu kt ni c hai ng i khng chung cnh.Mc tiu:NCost min, NFail minVi

(8)

Trong , ce = Ce,k nu , ngc li ce = 0;

(9) y, ce l chi ph ca cnh e; Rei l bng thng m yu cu i s dng trn cnh e E, v i = {1,, |D|}; failn l s cc yu cu b nh hng khi nt n gp li.u ra:Tp cc ng i tng ng vi mi yu cu ca khch hng.Mun gim chi ph xy dng mng NCost, th cn tn dng mt s cnh m bng thng cn d cho cc yu cu khc. Tuy nhin, iu ny s lm cho s kt ni i qua mt nt tng ln, hay ni cch khc s lm cho NFail tng ln, tc l mng gim tnh n nh. V vy ti u ng thi c hai mc tiu l iu rt kh.Bi ton SNDP l bi ton ti u thuc lp NP-kh nn cha c gii thut hiu qu no c th tm c li gii ti u trong thi gian a thc. tm ra tp cc li gii hon chnh ca bi ton MA-SNDP, n s trnh by cch tip cn s dng gii thut di truyn sp xp khng tri (Non-Dominated Sort Genetic Algorithm II NSGA II).4. Cc nghin cu lin quanBi ton SNDP c trnh by tng quan trong [10], trong c yu t kinh t v tin cy u c cp trong vic thit k mng truyn thng. SNDP phi m bo tnh chu li ca h thng mng v ng thi phi ti thiu chi ph xy dng. Trong nhiu nghin cu, ch xy dng mt ng d phng cho mt kt ni c yu cu, tc l vi mi kt ni s c hai ng i khng chung cnh, trong mt ng s c s dng khi ng cn li gp s c [2-5].Trong [1], SNDP da trn m hnh ACMC (gi tt l A-SNDP) ch gii quyt mt mc tiu l gim chi ph xy dng mng. Cng c nhiu nghin cu khc v SNDP s dng mc tiu ny nh trong [2], [8], [10]. H dng phng php nhnh cn tm ra li gii ti u cho bi ton. Tuy nhin, phng php ny ch t ra hiu qu vi cc mng c kch c nh. Vi nhng mng ln hn, h s dng cc phng php ti u xp x nh cc gii thut tm kim cc b [2], gii thut tin ha [10]. Visen v Gold [10] p dng thnh cng chin lc tin ha gii quyt SNDP, song ch s dng c vi cc yu cu l Unicast. Vi nhng mng c c unicast v anycast, Walkowiak v cc cng s trnh by mt gii thut xp x gii A-SNDP [13]. tng ca gii thut c da trn Flow Deviation [8] v gii thut tm kim cc b [14]. H tm c kt qu kh tt cho mng Polska (12 nt, 18 cnh, 65 unicast, 12 anycast), c th so vi kt qu ti u, th kt qu ca h trung bnh cao hn 7.11 %. Ngoi ra, h cn xy dng gii thut Tabu Search da trn gii thut leo i vi mt s mo gii bi ton A-SNDP [2]. Sau khi thc nghim vi ba mng khc nhau, Polska (12 nt, 18 cnh, 65 unicast, 12 anycast), Germany (17 nt, 26 cnh, 119 unicast, 13 anycast) v Atlanta (26 nt, 41 cnh, 234 unicast, 22 anycast), cc kt qu m h tm c cho thy nhiu ha hn. Tuy nhin, gii thut Tabu Search ny vn cn kh n gin v kt qu tm c khng hon ton ti u. Trong [15], nhm tc gi cng xut hai gii thut xp x l FBB1 v FBB2 cho bi ton A-SNDP. tng ca FBB1 l tn dng bng thng cn d tng ng vi mc chi ph phi tr trn mi cnh. FBB2 l mt t hp ca FBB1v Tabu Search. Kt qu thc nghim trn ba mng khc nhau, Polska, Germany v Atlanta [2-13] c trnh by trong [15]. Vi mi mng , h to ngu nhin 10 b d liu thc nghim. Kt qu cho thy hng tip cn h xut kh hiu qu vi A-SNDP. Trn tt c cc mng, FBB1 v FBB2 c kt qu tt hn so vi Tabu Search trong hu ht cc b d liu. n pht biu bi ton A-SNDP di dng mt bi ton ti u a mc tiu da trn hai mc tiu chi ph v tnh n nh. ti u hai mc tiu cng mt lc l mt vic rt kh. Cho ti by gi, cha c nghin cu no theo hng a mc tiu cho bi ton ny. Trong chng tip theo, n s trnh by v vic p dng gii thut NSGA-II gii quyt bi ton MA-SNDP.

CHNG 3: GII THUT DI TRUYN SP XP KHNG TRI GII BI TON THIT K MNG CHU LI TI U A MC TIU

1. M ha li giiTrong gii thut di truyn, mi li gii ca bi ton c m ha di dng mt c th, qua thc hin cc php ton di truyn nhm tm ra li gii ti u t tp li gii ban u. Vi bi ton MA-SNDP, mi li gii bao gm hai tp ng i: tp ng lm vic (working path) v tp ng d phng (backup path), v vy vic m ha mt li gii c th s dng hai phng php l m ha da trn c s d liu ng i (Connection Database based Encoding, vit tt l CDE) v m ha ng i y (Complete Connection Encoding, vit tt l CCE).1.1. M ha da trn c s d liu ng i (CDE) phn ny, n s trnh by v CDE c nhc n trong [21]. tng ca phng php m ha ny l vi mi mt yu cu ca khch hng cc ng lm vic v d phng s c khi to v lu tr trc khi m ha li gii cho gii thut di truyn. lm c iu ny, trc ht phi gii quyt cc vn sau:Cu trc lu tr ng i: mi yu cu ca khch hng s c mt bng lu tr cc ng lm vic gm hai hng ID v ng i tng ng. Mi mt ng lm vic s c tham chiu n mt bng ng d phng ring bit, vi rng buc cc ng i trong bng ny khng c trng cnh vi ng lm vic tng ng.

Hnh 5. C s d liu cho mt yu cu ca khch hng th nhtvi wi.1 l ng lm vic, bi.1.j l ng d phng cho ng lm vic w1.1, i = 1 nPhng thc khi to bng ng lm vic: qu trnh khi to s dng phng thc FindOtherWays, tng ca phng thc nh sau: u tin, khi to mt bng gm hai hng ID v path, cc ng i t nt A n B s c lu tr trong bng ny (A l nt ngun, B l nt ch ca yu cu). ng i u tin trong bng l ng i ngn nht, sau s xa ngu nhin mt cnh trn th v thuc ng i tm c trc v tip tc tm ng i in vo bng trn th c thay i. Vic xa cnh v tm ng s c thc hin cho n khi khng tm c ng t A n B na hoc s ng i lu trong bng t n s lng nht nh. Lu rng, cc ng i trong bng khng c ging nhau.Phng thc khi to bng ng d phng: Vi mi mt ng lm vic, khi to bng ng d phng tng ng, u tin s xa tt c cch cnh ca ng lm vic trn th, sau s dng phng thc FindOtherWays khi to bng. ng vi mi ng i trong bng ng lm vic s tm c mt bng ng d phng tng ng.Vi vic khi to cc bng lu tr ng i nh trn, vn m ha li gii cho bi ton ny s tr nn n gin hn rt nhiu. Mt li gii ca bi ton s c m ha nh sau:Mt c th T m ha mt li gii hon chnh ca bi ton, T s gm mt tp cc xu, vi mi xu Ti s ng vi yu cu kt ni th i, vi i=1,..,|D|.Mi xu Ti gm hai phn IDwPi v IDbPi nh hnh 5, trong IDwPi v IDbPi ln lt l ID ca ng lm vic chnh v ng d phng ca yu cu i, vi i=1,..,|D.C th thy cc xu Ti l c lp vi nhau. Nh vy mun khi to cc th T, ch cn khi to tng xu Ti. Vi mt xu Ti, IDwPi s c khi to trc bng cch chn mt ID thuc bng ng lm vic ca yu cu i, sau chn mt ID thuc bng ng d phng tng ng vi ng lm vic c chn gn cho IDbPi.

Hnh 6. M ha CDECch m ha CDE mang li nhiu u im nh c th c t chc n gin gip cho vic thc hin cc php ton tin ha d dng v nhanh chng, s dng c s d liu ng i s m bo li gii tm c hp l v khng mt qu nhiu thi gian kim tra cc rng buc cng nh gii m. Nhng bn cnh nhng u im cng tn ti hn ch nh khng gian tm kim khng c m rng trong qu trnh thc hin gii thut di truyn dn n kt qu tm c cha thc s tt, c s d liu ng i ci t phc tp, vi CCE c trnh by phn tip theo s khc phc nhng hn ch ny.1.2. M ha ng i y (CCE)Vi phng php m ha CCE mt li gii ca bi ton MA-SNDP s c m ha nh sau:Mt c th T m ha mt li gii hon chnh ca bi ton, T s gm mt tp cc xu, vi mi xu Ti s ng vi yu cu kt ni th i , vi i=1,..,|D.Mi xu Ti gm hai phn workingPath wPi v backupPath bPi nh hnh 6, trong wPi v bPi ln lt l ng lm vic chnh v ng d phng ca yu cu i, vi i=1,..,|D.Cng ging nh m ha CDE xu Ti cng c lp vi nhau. khi to cc th T, c th khi to tng xu Ti nh sau: wPi s c khi to trc bng cch tm mt ng i tha mn yu cu i, sau cc cnh ca ng i ny s c loi b khi th v tip tc tin hnh tm mt ng i khc tha mn gn cho bPi.

Hnh 7. M ha CCE tin theo di nhng phn tip theo ca n, chng ta s gi gii thut NSGA-II c ci t vi m ha CDE l CDE-NSGA-II v vi m ha CCE l CCE-NSGA-II.2. Php ton di truyn2.1. Php lai ghpC CDE-NSGA-II v CCE-NSGA-II u s dng hai php lai ghp: lai ghp ng v lai ghp mt im ct.Php lai ghp mt im ct: vi php lai ghp ny, ta chn mt im trn cc c th cha m P v P' tng ng, sau ghp phn u ca c th P vi phn ui ca c th P' to thnh con C.

Hnh 8. Lai ghp mt im ct gia c th cha P v c th m P' sinh ra con C.Php lai ghp ng: php lai ghp ny c phn phc tp hn php lai ghp mt im ct. Vi php lai ghp ng, tin hnh ghp phn wP ca cha P vi phn bP ca c th m P' to c mt c th con C mi. Tuy nhin, vi php lai ghp ng s xy ra trng hp wPi v bPi ca c th con khng tha mn rng buc l hai ng i khng chung cnh, v th phi thc hin kim tra trong khi lai ghp, vi nhng trng hp khng tha mn rng buc nh th th c th con s s dng li ton b xu t c th cha.

Hnh 9. Lai ghp ng gia cha c th cha P v c th m P' sinh ra con C.

2.2. Php t binKhc vi vic chn nhiu php lai ghp ch c mt php t bin c s dng. Php t bin ny tuy kh n gin nhng cng mang li hiu qu nht nh. C th, php t bin c thc hin nh sau: chn ra mt s c th trong qun th, vi mi c th P c chn li tip tc chn ngu nhin mt xu i bt k. Sau khi chn c xu i, tin hnh thay th xu ny bng mt xu khc to ra mt cc th C mi.

Hnh 10. Php t bin thay th xu th 2 ca c th cha P sinh ra c th con C.3. Hm thch nghiTrong gii thut NSGA-II, thch nghi ca mt c th c nh gi theo hai tiu ch l bin m c th thuc cng tri th c th cng thch nghi v nu hai c th thuc cng mt bin th c th no c khong cch quy t ln hn th thch nghi hn.4. Chin lc chn lc t nhinMt chin lc chn lc tt s gip cho kt qu thu c cui cng tt hn. i vi bi ton ny, n trnh by mt chin lc kh n gin nhng li mang li hiu qu tt. Chin lc ny da trn vic phn lp khng tri trnh by trn. Sau khi tin hnh qu trnh sinh sn, t qun th ban u s thu c mt qun th mi gm cc c th mi c sinh ra, tin hnh gp hai qun th ny li s c mt qun th mi P' c kch thc ln hn qun th ban u. Tin hnh phn lp cho qun th P' s thu c tp cc lp Fj. Tin hnh chn ln, u tin chn nhng c th thuc cc lp c ch s j nh vo qun th th h tip theo v chn cho n khi no qun th t kch thc quy nh th dng. Cc c th khng c chn s b loi b.5. Ci t gii thut gii quyt bi ton MA-SNDP gii thut NSGA-II cng c tinh chnh t c kt qu tt nht. Nhn chung c CDE-NSGA-II v CCE-NSGA-II u c nhng bc thc hin ging nhau.Gii thut CDE-NSGA-II v CCE-NSGA-II

1. P intiPopulation1. t = 01. While (t < generation) do1. Q reproduction P1. R = PQ1. j = 11. While (R ) do1. For all u P do1. Su = 1. End for1. For all u P do1. For all v P\{u} do1. If (u Dominate v) then1. Sv = Sv{u}1. End if1. End for1. End for1. Fj = 1. For all u P do1. If (|Su| = 0) then1. Fj = Fj{u}1. R = R\{u}1. End if1. End for1. For all u Fj do1. D[j, u] CrowdingDistance u1. End for1. j = j+11. End while1. P = 1. j = 11. While (|P| < N) do1. If (|P| + |Fj| N) then1. P = PFj1. Else1. While (|P| < N) do1. D[j, u] FindMax D[j,.]1. D[j, u] 01. P = P {u}1. End while1. End if1. End while1. End while

CHNG 4: KT QU THC NGHIM

1. D liu thc nghimTrong n ny, tc gi s dng cc b d liu th thc t c ng ti trn website http://sndlib.zib.de v c nhiu nhm nghin cu trn th gii s dng. Cc b d liu th thc nghim gm Polska (12 nt, 18 cnh), Germany (17 nt, 26 cnht), and Atlanta (26 nt, 41 cnh). Vi mi th, tc gi sinh ngu nhin 10 b yu cu kt ni tin hnh thc nghim. Sau y l bng lit k cc thng s ca cc b d liu thc nghim. Bng 1. Thng s cc b d liuTn b d liuYu cu UnicastYu cu AnycastS replica th

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2. Thng s thc nghimChng trnh thc nghim c ci t bng ngn ng Java, chy trn mi trng h iu hnh Windows 7. Cc thng s phn cng: b vi x l Intel Core 2 Duo U7700, RAM 2GB. Vi mi b d liu yu cu kt ni s c thc nghim 50 ln. Cc ch s di truyn: qun th c 300 c th, tin ha qua 300 th h, xc sut lai ghp mt im ct l 33%, xc sut lai ghp ng l 33%, xc sut t bin l 3%.3. Kt qu thc nghim3.1. nh gi m hnh bi tonKhi xy dng m hnh v gii quyt mt bi ton ti u a mc tiu, th ta phi xt xem liu cc mc tiu c ng hay khng, nu khng ng th vic a ra m hnh khng mang li nhiu ngha. V vy trc ht, n s trnh by mt s kt qu thu c khi thc nghim CCE-NSGA-II phn no tr li cu hi: Liu hai mc tiu NCost v NFail c ng nhau hay khng?.

Hnh 11. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_1.Hnh 11 mnh ha cho kt qu thu c khi s dng CCE-NSGA-II gii quyt bi ton MA-SNDP vi b d liu Polska_1. Kt qu thu c l mt tp cc gii php khng tri (Pareto) ca bi ton. N cho thy rng hai mc tiu c chn ng vi nhau, ngha l khi mun gim chi ph xy dng th mc n nh ca mng s gim v ngc li mun mc n nh cao th chi ph xy dng s tng theo.Hnh 11 th hin gi tr cc mc tiu ca cc c th thuc tp Pareto sau 300 th h khi thc nghim vi b d liu Polska_1, vi trc tung th hin gi tr mc tiu NFail v trc honh th hin gi tr NCost. Nh vy mt ln na c th thy rng khng th ti u ng thi c hai mc tiu ny c.

Hnh 12. Trng thi th Polska ng vi cc im trong hnh 11.(a) Trng thi th Polska ng vi im A trong hnh 11.(b) Trng thi th Polska ng vi im B trng hnh 11.Trong hnh 12 (a), cc nt ca th trong ng mu c nhiu yu cu kt ni s dng, c bit l nt s 7. S chnh lch s lng yu cu kt ni s dng cc nt trong v ngoi ng mu l kh ln. Nu trong ng mu , s yu cu s dng mt nt trung bnh l 9 th ngoi ch c 3.5. Vi iu ny, khi mt nt trong ng mu b li th s c kh nhiu yu cu kt ni b mt tnh chu li gy nh hng ln n ton mng.Nhng trong hnh 12 (b) li c s khc bit. Khng c s chnh lch ln v s lng yu cu s dng cc nt trong mng. Nh trong hnh cc nt trong mng c chia thnh ba tp, tp mu vng s yu cu s dng mt nt trung bnh l 7.4, tp mu xanh l 6.6 v tp mu l 6. Vic ny s gim nh hng ca vic mt nt b li gy ra cho ton mng. Tuy nhin, chi ph xy dng li kh cao. V vy, trong hnh 11 cc im cng v bn phi th s chnh lch s yu cu s dng mt nt cng gim nhng chi ph xy dng cng tng.Hnh 13 th hin gi tr cc mc tiu ca cc c th thuc tp Pareto sau 300 th h khi thc nghim vi b d liu Atlanta_3.

Hnh 13. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_3.

Hnh 14. Trng thi th Atlanta ng vi im trong hnh 13. (a) Trng thi th Atlanta ng vi im A trong hnh 13.(b) Trng thi th Atlanta ng vi im B trng hnh 13.Cng tng t kt qu thu c vi b d liu ng vi th Polska, trong hnh 14 (a), cc nt ca th trong ng mu c nhiu yu cu kt ni s dng nht, c bit l nt s 8. S chnh lch s lng yu cu kt ni s dng cc nt trong v ngoi ng mu cng rt ln, c th l 23.6 v 8.9. Nhng mt trng thi hon ton khc cng c th hin trong hnh 14 (b), khi m s lng cc yu cu s dng cc nt c tri u cho c th. th Atlanta cng c chia ra lm 3 tp nt, tp mu vng s yu cu s dng mt nt trung bnh l 11.1, tp mu xanh l 12 v tp mu l 13.5. V phn no cho thy vic m bo tnh n nh ca mng th chi ph xy dng l kh tn km.Hnh 15 th hin gi tr cc mc tiu ca cc c th thuc tp Pareto sau 300 th h khi thc nghim vi b d liu Germany_2.

Hnh 15. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Germany_2.

Hnh 16. Trng thi th Germany ng vi im trong hnh 15.(a) Trng thi th Germany ng vi im A trong hnh 15.(b) Trng thi th Germany ng vi im B trong hnh 15.Trong hnh 16 (b), tp nt mu vng s yu cu s dng mt nt trung bnh l 7.5, tp nt mu xanh l 8.9 v tp nt mu l 8.9. S chnh lch ny l khng cao, do s gim c nh hng khi mt nt b li n ton mng, nhng chi ph xy dng li cao.Cn hnh 16 (a), chi ph xy dng mng thp hn, nhng n nh ca mng li thp hn. Nhng nt trong ng mu c cc yu cu kt ni s dng kh nhiu, nhiu nht l nt 10. Vi s yu cu s dng mt nt trong ng mu trung bnh l 17.2, cn ngoi ch c 4.9. R rng nu mt nt trong ng mu li th s nh hng n ton mng ln hn rt nhiu so vi mt nt bn ngoi b li.Mt s kt qu khc:

Hnh 17. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Polska_3.











Hnh 28. Tp Pareto thu c ca CCE-NSGA-II ng vi b d liu Atlanta_7.Vi cc kt qu thc nghim trn, phn no tr li cho cu hi v s ng gia cc mc tiu ca bi ton. S ng ny cho thy khng th ng thi va tng tnh n nh ca thit k, va gim chi ph. Cc kt qu trn mang li mt ci nhn tng qut hn cho cc bi ton mng chu li thc t. Trong tng lai, vic b sung nhiu mc tiu cho bi ton s thu hp khong cch gia cc nghin cu v l thuyt v ng cc ng dng thc t. 3.2. So snh vi m hnh n mc tiuNh trnh by chng 2, bi ton A-SNDP c pht trin thnh mt bi ton a mc tiu MA-SNDP v gii quyt n bng hng tip cn a mc tiu. Vy cu hi c t ra l phng php tip cn a mc tiu c t c hiu qu nh phng php tip cn n mc tiu vi mt mc tiu truyn thng hay khng?. Do phn ny, n s trnh by kt qu thc nghim v so snh gii thut di truyn theo phng php m ha CCE (CCE-GA) cho A-SNDP vi CCE-NSGA-II cho MA-SNDP trn mc tiu chi ph xy dng.

Hnh 29. So snh kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng vi th Polska.

Hnh 30. So snh kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng vi th Atlanta.

Hnh 31. So snh kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng vi th Germany.Cc kt qu so snh vi mc tiu NCost ca CCE-GA v CCE-NSGA-II l khng chnh lch nhiu. Thm ch vi cc b d liu ca th Polska, cc kt qu tt nht v chi ph ca CCE-NSGA-II cn tt hn c CCE-GA. Vi cc th c kch thc ln hn, th CCE-NSGA-II t ra thua km so vi CCE-GA, nhng s chnh lch ny khng qu ln. Vi th Germany, cc kt qu ca CCE-GA ln hn CCE-NSGA-II trung bnh ch 1%, vi th Atlanta l 3%. Vi t l tng i nh, s khc bit gia cc kt qu ca hai gii thut l khng ln.Di y l cc bng so snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost.Bng 2. So snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng th Polska.B d liuCCE-GACCE-NSGA-II

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Bng 3. So snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng th Germany.B d liuCCE-GACCE-NSGA-II

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Bng 4. So snh t l kt qu thu c gia CCE-GA v CCE-NSGA-II vi mc tiu NCost ng th Atlanta.B d liuCCE-GACCE-NSGA-II

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3.3. So snh cc phng php m haVi mt gii thut k tha t gii thut di truyn, cc kt qu ca NSGA-II cng b nh hng ln t phng php m ha. Trn con ng gii quyt bi ton MA-SNDP, vic tm ra mt phng php m ha ph hp nhm tm ra cc li gii tt l ht sc cn thit. phn ny, n s trnh by v so snh cc kt qu thc nghim ca hai phng php m ha trnh by.

Hnh 32. So snh kt qu thu c gia CDE-NSGA-II v CCE-NSGA-II vi b d liu Polska_1.

Hnh 33. So snh kt qu thu c gia CDE-NSGA-II v CCE-NSGA-II vi b d liu Germany_2.

Hnh 34. So snh kt qu thu c gia CDE-NSGA-II v CCE-NSGA-II vi b d liu Atlanta_3.

Kt qu thc nghim cho thy vi phng php m ha CCE c phn hiu qu hn so vi CDE. iu ny c th c gii thch, do bn cht ca phng php CDE hn ch i rt nhiu v vic m rng khng gian tm kim trong qu trnh thc nghim gii thut.KT LUN

V mt l thuyt, n trnh by c cc ni dung sau:Cc khi nim c bn v th, tng quan v bi ton ng i ngn nht gia cc cp nh trn th.Tng quan v bi ton ti u ha t hp, ti u a mc tiu.Tng quan v gii thut di truyn.Trnh by gii thut di truyn sp xp khng tri gii quyt bi ton ti u a mc tiu (NSGA-II).Tng quan v bi ton thit k mng chu li (SNDP).Trnh bi v m hnh bi ton thit k mng chu li a mc tiu (MA-SNDP). xut gii thut NSGA-II gii quyt bi ton MA-SNDP.V mt thc nghim, n thu c mt s kt qu sau:Ci t thnh cng gii thut NSGA-II vi hai phng php m ha CDE v CCE, ngoi ra cn ci t thm gii thut di truyn vi phng php m ha CCE tin hnh so snh kt qu trn mt mc tiu NCost.a ra mt s nh gi v m hnh v cc mc tiu ca MA_SNDP.So snh hai phng php m ha t cc kt qu thu c.Nh vy, kt qu thc nghim l kh ph hp vi nhng g trnh by trong l thuyt. Tuy vy, do cn nhiu hn ch v kin thc, kinh nghim ca bn thn, cng nh thi gian thc hin, n cn cc hn ch:Cha ci t th nghim cc gii thut khc so snh vi gii thut xut.i vi gii thut NSGA-II cha a ra c nhiu phng php lai ghp, t bin so snh v nh gi mc hiu qu.Cha thng k c mc nh hng ca cc tham s khi tin hnh th nghim.Hng pht trin n l hon thin cc hn ch trn. Ngoi ra, n s pht trin hng tip cn a mc tiu i vi nhiu m hnh mng chu li khc nhau, vi nhiu mc tiu khc nhau, nhm tip cn c vi cc yu cu m trong thc t t ra.

TI LIU THAM KHO

Krzysztof Walkowiak, A Flow Deviation Algorithm for Joint Optimization of Unicast and Anycast Flows in Connection-Oriented Networks. In: Osvaldo Gervas, Computational Science and Its Applications ICCSA 2008. LNCS,vol. 5072, pp. 797-807, Springer, Perugia, Italy (2008).Jakub Gadysz, Krzysztof Walkowiak, Tabu Search Algorithm for Survivable Network Design Problem with Simultaneous Unicast and Anycast Flows. In: Intl Journal Of Electronics And Telecommunications, vol. 56, no. 1, pp. 41-48, Versita Publisher, Warsaw (2010).Krzysztof Walkowiak, A New Function for Optimization of Working Paths in Survivable MPLS Networks. In: Computer and Information Sciences ISCIS 2006, pp. 424-433, Springer, Istanbul (2006)W. Grover, Mesh-based Survivable Networks: Options and Strategies for Optical, MPLS, SONET and ATM Networking, Prentice Hall PTR, Upper Saddle River, New Jersey (2004).V. Sharma, F. Hellstrand, Framework for MPLS-based recovery, RFC 3469 (2003).J. Vasseur, M. Pickavet, P. Demeester, Network Recovery: Protection and Restoration of Optical, SONET-SDH, IP and MPLS, Morgan Kaufmann, San Francisco (2004).A. Kasprzak, Algorithms of flow, capacity and topology structure in computer networks, Monography, Wroclaw, Polish(1989).M. Pioro, D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks, Morgan Kaufmann Publishers(2004).K. Walkowiak, Anycast Communication A New Approach to Survivability of Connection-Oriented Networks. In:Communications in Computer and Information Science, pp. 378389, Springer, Berlin(2003).Volker Nissen, Stefan Gold, Survivable network design with an evolution strategy. In:Success in Evolutionary Computation, pp. 263283, Springer, Berlin (2008).Garcia Najera, Abel, Multi-Objective evolutionary algorithms for vehicle routing problems. Ph.D. thesis, University of Birmingham (2010).Deb, K. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley-Interscience Series in Systems and Optimization. Chic hester, John Wiley & Sons, 2001.Johnson & Deering, Reserved IPv6 Subnet Anycast Addresses, RFC 2526 (1999). Anycast vs Unicast, http://communitydns.eu/Anycast.pdfJakub Gladysz, Krzysztof Walkowiak: Optimization of survivable networks with simultaneous unicast and anycast flows, ICUMT, pp. 1-6, Poland(2009).Roberto Battiti, Mauro Brunato, Franco Mascia, Reactive Search and Intelligent Optimization, Springer, New York, USA (2008).Huynh Thi Thanh Binh, Pham Vu Long, Nguyen Ngoc Dat, Nguyen Sy Thai Ha: Heuristic Algorithms for Solving Survivable Network Design Problem with Simultaneous Unicast and Anycast Flows. ICIC 2012: 137-144.Herv Kerivin, A.Ridha Mahjoub. Design of Survivable Networks : A Survey. Research Report LIMOS/RR-05-04, 3 mars 2005.Eduardo G. Carrano, Luiz A. E. Soares, Ricardo H. C. Takahashi, Rodney R. Saldanha, and Oriane M. Neto: Electric Distribution Network Multi-objective Design Using a Problem-Specific Genetic Algorithm, IEEE Transactions On Power Delivery, vol. 21, no. 2, pp. 995-1005.Eckart Zitzler, Marco Laumanns, Stefan Bleuler: A Tutorial on Evolutionary Multi-objective Optimization, (2003) n tt nghip: Nguyn Th Minh, ng dng cc gii thut hng tt thit k mng chu li, trng HBKHN, b mn KHMT-CNTT, nm 2012.Huynh Thi Thanh Binh, Ngo Hong Son, Nguyen Ngoc Dat, Genetic Algorithm for Solving Survivable Network Design with Simultaneous Unicast and Anycast Flows, In the Proceedings of the Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2013), pp. 1237-1247.Huynh Thi Thanh Binh, Bui Thu Lam, Nguyen Sy Thai Ha, Hisao Ishibuchi, Multi-Objective Genetic Algorithm for Solving Survivable Network Design Problem with Simultaneous Unicast and Anycast Flows, Applied Soft Computing, submitted (SCIE).

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