Bao Cao Baitap GA-libre

Bi tp ln mn hc Tr tu nhn to 0

TRNG I HC BCH KHOA H NI

VIN CNG NGH THNG TIN V TRUYN THNG

*

TR TU NHN TO

Gii thut di truyn vi bi ton ngi du lch

Sinh vin thc hin Trng Cng Ph 20101991

Cn Kim Tng 20102465

Nguyn Hong Long 20101802

inh Quang Vinh 20102786

Trn Hu Sn 20102109

o Trng Hun 20101600

H Ni - 2013


MC LC LI NI U .................................................................................................................................... 2 CHNG I : GII THUT DI TRUYN (Genetic Algorithm - GA) ................................................. 3

1. ng lc ..................................................................................................................................... 3

2. Thut gii di truyn ................................................................................................................... 4

3. Cc ton t di truyn ................................................................................................................... 8

4. u tranh sinh tn ....................................................................................................................... 9

CHNG II : BI TON NGI DU LCH (Travelling Salesman Problem - TSP) ....................... 10 1. Lch s bi ton : ....................................................................................................................... 10

2. Pht biu bi ton : .................................................................................................................... 12

3. Phn tch phc tp : .............................................................................................................. 12

CHNG III : XUT GII THUT DI TRUYN GII BI TON NGI DU LCH .......... 13 1. Gii thut xut : .................................................................................................................... 13

1.1 M ha bi ton : ................................................................................................................. 13

1.2 Khi to qun th : .............................................................................................................. 15

1.3 Lai ghp : ............................................................................................................................ 15

1.4 t bin : ............................................................................................................................ 17

1.5 Chn lc t nhin : .............................................................................................................. 18

1.6 Tin ha : ............................................................................................................................ 20

2. Gii thiu v chng trnh : ....................................................................................................... 21

3. Kt qu chy cc b d liu chu!n : ........................................................................................... 22

3.1 B d liu wi29.tsp : ............................................................................................................ 23

3.2 B d liu qa194.tsp: ........................................................................................................... 23

3.3 B d liu xit1083.tsp:......................................................................................................... 24

4. nh gi gii thut v cc ci tin trong tng lai: ..................................................................... 25

T"NG K#T ...................................................................................................................................... 26

TI LI$U THAM KHO ................................................................................................................. 27 PH% L%C ......................................................................................................................................... 28


LI NI U

Bi ton ng&i du lch l mt trong nh ng bi ton 'c nghin cu su nht trong l(nh vc t)i u ha. Bo co ny s* trnh by 1 hng tip cn gii quyt bi ton ng&i du lch s d+ng gii thut di truyn.

Gii thut di truyn v c bn mu)n m ph,ng li qu trnh tin ha c-a sinh vt trong t nhin vo cc bi ton t)i u ha t. a ra l&i gii t)t (c th khng l t)i u nht) khi m khng th a ra 'c 1 gii thut chnh xc hay vic vt cn cc tr&ng h'p l bt kh thi.

M/c d rt c) g0ng nhng v1n khng th trnh kh,i nh ng sai st, mong thy gio ch2 bo thm.


CHNG I : GII THUT DI TRUYN (Genetic Algorithm - GA) Gii thut di truyn c3ng nh tin ha da trn khi nim cho r4ng qu trnh

tin ha t nhin l hon ho nht, h'p l nht v t n mang tnh t)i u. S t)i u 'c th hin ch5 th h sau bao gi& c3ng pht trin t)t hn th h trc. Tin ha t nhin 'c duy tr nh& hai qu trnh c bn: sinh sn v chn lc t nhin, xuyn su)t qu trnh tin ha t nhin, cc th h mi lun 'c sinh ra b6 sung thay th th h c3, c th no thch ng vi mi tr&ng s* tn ti, ng'c li s* b o thi.

Gii thut di truyn bao gm 4 bc chnh: M ha l&i gii, khi to qun th, s d+ng cc php ton di truyn v nh gi thch nghi. Sau , chng ta li sinh ra mt qun th mi b4ng php chn lc ri tip t+c s d+ng cc php ton di truyn v nh gi thch nghi c-a cc c th (in hnh bi nhi7m s0c th - NST) trong qun th. Thut gii 'c thc hin qua cng nhiu th h th l&i gii a ra cng t)i u.

1. ng lc Thut gii di truyn cung cp mt phng php hc 'c thc !y bi s

tng t vi s tin ha sinh hc. Thay v tm kim cc gi thuyt t. t6ng qut n c+ th ho/c t. n gin n phc tp, GAs to ra cc gi thuyt k tip b4ng cch l/p vic t bin v vic ti h'p cc phn c-a gi thuyt 'c bit hin ti l t)t nht. 8 m5i bc, mt tp cc gi thuyt 'c gi l qun th hin ti 'c cp nht b4ng cch thay th vi phn nh, qun th bi c th con c-a cc gi thuyt t)t nht th&i im hin ti. S ph6 bin c-a GAs 'c thc !y bi cc yu t) sau:

Tin ha l mt phng php mnh, thnh cng cho s thch nghi

bn trong cc h th)ng sinh hc.


GA c th tm kim trn cc khng gian gi thuyt c cc phn tng tc phc tp, nh hng c-a m5i phn ln ton th thch nghi

gi thuyt kh c th m hnh.

Thut gii GA c th 'c thc hin song song v c th tn d+ng thnh tu c-a phn cng my tnh mnh.

2. Thut gii di truyn Bi ton dnh cho GAs l tm kim trn khng gian cc gi thuyt ng c

xc nh gi thuyt t)t nht. Trong GAs gi thuyt t)t nht 'c nh ngh(a

nh l mt gi thuyt t)i u ha mt i l'ng s) 'c nh ngh(a trc cho bi ton s0p ti, 'c gi l thch nghi c-a gi thuyt. V d+, nu tc v+ hc h,i l bi ton xp x2 mt hm cha bit cho tp m1u hun luyn gm d liu u vo v d liu u ra, th thch nghi c th 'c nh ngh(a nh l chnh xc c-a gi thuyt trn d liu hun luyn ny. Nu tc v+ l hc chin l'c chi c&, thch nghi c th l s) vn th0ng c-a chin l'c ny khi u vi cc chin

l'c khc trong qun th hin ti. M/c d cc thut gii di truyn 'c thc hin thay 6i theo bi ton c+ th,

nhng chng chia s9 chung cu trc tiu biu sau: Thut gii hot ng b4ng cch cp nht lin t+c tp gi thuyt 'c gi l qun th. 8 m5i ln l/p, tt c

cc c th trong qun th 'c c l'ng tng ng vi hm thch nghi. Ri

qun th mi 'c to ra b4ng cch la chn c xc sut cc c th thch nghi t)t nht t. qun th hin ti. Mt s) trong nh ng c th 'c chn 'c a nguyn

v:n vo qun th k tip. Nh ng c th khc 'c dng lm c s to ra cc c th con b4ng cch p d+ng cc tc ng di truyn: lai ghp v t bin.

GA( Fitness, Fitness_threshold, p, r, m)


{ // Fitness: hm gn thang im c lng cho mt gi thuyt // Fitness_threshold: Ngng xc nh tiu chun dng gii thut tm kim // p: S c th trong qun th gi thuyt // r: Phn s c th trong qun th 'c p d+ng ton t lai ghp m5i bc // m: T l c th b t bin

Khi to qun th: P To ng1u nhin p c th gi thuyt

c l'ng: ;ng vi m5i h trong P, tnh Fitness(h) while [max Fitness(h)] < Fitness_threshold do

To th h mi, PS 1. Chn c th: chn theo xc sut (1 r)p c th trong qun th P

thm vo PS. Xc sut Pr(hi) c-a gi thuyt hi thuc P 'c tnh bi cng thc:

1

( )Pr( )( )

ii p

jj

Fitness hhFitness h

=

=

2. Lai ghp: chn lc theo xc sut 2

r p c/p gi thuyt t. qun th

P, theo Pr(hi) tnh bc trn. ;ng vi m5i c/p , to ra hai con b4ng cch p d+ng ton t lai ghp. Thm tt cc cc con vo PS.

3. t bin: Chn m% c th c-a PS vi xc sut cho m5i c th l nh nhau. ;ng vi m5i c th bin 6i mt bit 'c chn ng1u nhin trong cch th hin c-a n.

4. Cp nht: P PS. 5. c lng: ;ng vi m5i h trong P, tnh Fitness(h)


Tr v gi thuyt trong P c thch nghi cao nht.

} Figure 1 : Cc bc c bn ca gii thut


Khi to qun th

La chn cha m:

Lai ghp

t bin

iu kin d.ng

u tranh sinh tn

Cc c th t)t nht

TRUE

FALSE

Figure 2 : Lu gii thut c bn


3. Cc ton t di truyn 3.1 Lai ghp : Php lai l qu trnh hnh thnh NST mi trn c s NST cha m:, b4ng cch

ghp mt hay nhiu on gen c-a hai (hay nhiu) NST cha m: khc nhau. Cc c/p cha m: 'c la chn ng1u nhin v xc sut xy ra lai ghp vi

m5i c/p 'c quy nh t. trc.

C nhiu cch lai ghp khc nhau:

Lai ghp mt im c0t, nhiu im c0t.

Lai ghp nhiu on.

3.2 t bin : t bin l tnh trng NST con khng c mt (ho/c mt s)) tnh trng c

trong m di truyn c-a cha m:. Cc c/p cha m: 'c la chn ng1u nhin v xc sut xy ra t bin vi

m5i c/p 'c quy nh t. trc, th&ng l rt nh,.

Cc php t bin th&ng 'c s d+ng:

o bit.

Hon v: 6i v tr c-a cc gen vi nhau.

6i gi tr: Thay 6i gi tr ti mt im gen.

o on: o th t c-a mt on NST bt k.


4. u tranh sinh tn Chn nh ng NST t. qun th kt qu theo mt quy t0c no thay th cho

cha m: sinh ra th h mi. Mt s) phng thc u tranh sinh tn c bn:

Tro 6i hon ton cha m: b4ng con.

Tro 6i ng1u nhin: Chn ng1u nhin k cha m: v thay th b4ng k con mi.

Chn nh ng c th u t nht trong qun th.


CHNG II : BI TON NGI DU LCH (Travelling Salesman Problem - TSP)

1. Lch s bi ton : Bi ton ng&i bn hng (ting Anh: travelling salesman problem - TSP) l

mt bi ton NP-Hard thuc th loi t)i u t6 h'p 'c nghin cu trong l thuyt khoa hc my tnh. Ni dung bi ton c th hiu khi qut nh sau : Cho trc mt danh sch cc thnh ph) v khong cch gi a chng, tm chu trnh ng0n nht i qua tt c cc thnh ph) ng 1 ln.

Figure 3 22,775 Cities in Vietnam, derived from data from the National Imagery and Mapping Agency database of

geographic feature names.

Bi ton 'c nu ra ln u tin n


c v d+ cho chu trnh trong nc c v Th+y S(, nhng khng cha bt k ni dung ton hc no.

Bi ton ng&i bn hng 'c nh ngh(a trong th k2 19 bi nh ton hc Ireland William Rowan Hamilton v nh ton hc Anh Thomas Kirkman. Tr&ng h'p t6ng qut c-a TSP c th 'c nghin cu ln u tin bi cc nh ton hc Vienna v Harvard trong nh ng nng c0t v nhnh cn.

Trong thp nin 1990, Applegate, Bixby, Chvtal, v Cook pht trin mt chng trnh mang tn Concorde gii 'c nhiu tr&ng h'p c ln k2 l+c hin nay. Gerhard Reinelt xut bn mt b d liu cc tr&ng h'p c kh khc nhau mang tn TSPLIB n


nghin cu so snh kt qu. N


CHNG III : XUT GII THUT DI TRUYN GII BI TON NGI DU LCH

1. Gii thut xut : Nhm xut gii thut di truyn n gin gii bi ton ng&i du lch. Gii

thut 'c ci /t b4ng ngn ng java. Cc b d liu kim th 'c ly ti http://www.tsp.gatech.edu/ (cung cp

cc b d liu chu!n trn thc t)

1.1 M ha bi ton : 1.1.1 M ha th : th 'c m ha b4ng danh sch mng cc im v ta tng ng

c-a chng. Di y l v d+ v b d liu th chu!n.

NAME : xit1083 COMMENT : Bonn VLSI data set with 1083 points COMMENT : Uni Bonn, Research Institute for Discrete Math COMMENT : Contributed by Andre Rohe TYPE : TSP DIMENSION : 1083 EDGE_WEIGHT_TYPE : EUC_2D NODE_COORD_SECTION

1 0 105

2 0 111

3 0 15


Trng s) trong ct u tin l s) hiu c-a 2nh, trong s) th 2 l honh ,

trng s) th 3 l tung . Khong cch gi a 2 2nh ( , ) v , c-a th (trng s) cho cnh) 'c tnh theo cng thc :

, = + 1.1.2 M ha chu trnh (c th - gen) : Chu trnh 'c m ha b4ng mng c th t cc s) hiu c-a 2nh. Vi

th n 2nh th mng c kch thc n phn t. V d+ chu trnh c-a th 10 2nh :

C1 1 3 2 4 6 9 8 7 5 10

C2 10 7 9 6 4 2 8 3 1 5

Ngoi ra m5i chu trnh cn phi c thm thng s) v chi ph c-a ton b chu trnh . Chi ph ny 'c tnh b4ng t6ng di tt c cc cnh to nn chu trnh (theo cng thc tnh khong cch cp trn).

M5i chu trnh l 1 l&i gii, trong gii thut di truyn coi nh 1 c th. Vic tin ha v sau ta s* da trn tp chu trnh khi to ban u v tm ra kt qu t)t nht sau mt s) th h.

Di y l v d+ v b d liu chu trnh chu!n.

NAME: xit1083 COMMENT: Tour length 3558 TYPE: TOUR DIMENSION: 1083 TOUR_SECTION


1

23 55 24

2

56 64 79

1.2 Khi to qun th : Qun th ban u 'c khi to b4ng cch sinh ng1u nhin cc chu trnh, s)

l'ng chu trnh khi to l mt na s) kch thc c th t)i a. Vic sinh ng1u nhin s d+ng hm t bin (s* ni r pha di). S) kch thc c th t)i a c th ty bin theo s) 2nh c-a th cn gii, sau nhiu ln chy nhm chn kch thc qun th l 100 c th.

1.3 Lai ghp : Phng thc lai ghp 'c thc hin da trn 2 c th u vo :

C1 1 3 2 4 6 9 8 7 5 10

C2 10 7 9 6 4 2 8 3 1 5

Thc hin lai ghp 1 im c0t vi v tr c0t l ng1u nhin :

C0t t. im p n ht chu trnh c-a C2 a vo chu trnh mi, ly mt v d+ p = 5 :


Con 2 8 3 1 5

Xt t. u n cu)i chu trnh 1, np dn cc im cha c trong con lai theo th t duyt ta 'c chu trnh mi :

Con 2 8 3 1 5 4 6 9 7 10

Tnh li chi ph cho chu trnh mi sinh.

(*) Cch lai ghp ny m bo con lai mi l 1 chu trnh tha mn. Ci /t code :

!"#

$%$&$

'())

!*%+!*+

%))

,

'$())

'%$%(#%))

'!*+!*%+

&

-

'%##

&))

!*%)&+!*+

,

,

,


.

,

1.4 t bin : Phng thc t bin 'c thc hin da trn 1 c th u vo :

C1 1 3 2 4 6 9 8 7 5 10

Thc hin t bin b4ng tro 6i cc im trn gen cho nhau. S) ln tro )i 'c sinh ng1u nhin t. trong khong 5% chiu di chu trnh (tc l c t)i a 10% v tr trn 1 gen c th b t bin), v tr im tro c3ng 'c sinh ng1u nhin trong qu trnh chy.

V d+ vi t bin C1 b4ng tro 6i 2 ln : tro 3 v 9, tro 4 v 10. Khi ta 'c chu trnh mi :

C2 1 9 2 10 6 3 8 7 5 4

(*) Cch t bin ny m bo c th mi sinh l 1 chu trnh tha mn. Ci /t code :

.

!

!-

.!" .'')

./$

!"

!"

!!*+

!!*+!!*+

!!*+


.##

,

.!

,

1.5 Chn lc t nhin : Kch thc qun th l c) nh qua cc th h. 8 m5i th h ta li c cc c

th mi sinh b4ng lai ghp v t bin do cn phi c s chn lc m bo tnh cn b4ng c-a qun th c3ng chnh l trnh cc l5i pht sinh v b nh khi kch thc qun th qu ln.

! $ & 1 & , = -$ &$ 1$ , + ! $ & 1 5, Cch thc chn lc c th 'c nh gi da trn chi ph c-a m5i chu trnh.

C th 'c chn lm l&i gi cu)i cng l c th c chi ph nh, nht trong qun th sau mt s) th h tin ha.

Ban u ton b qun th s* 'c s0p xp t


Cch thc chn lc ny m bo s phong ph c-a qun th sau nhiu th h. B4ng ci /t c+ th, cch thc chn lc ny em li kt qu ti u hn rt nhiu so vi cch chn lc trc vi mt s) b d liu.

(*) Ti u Chn lc t nhin : Cch thc chn lc cn n vic s0p xp cc c th theo chi ph. Vic s0p xp l rt t)n km khi qun th c kch thc

ln. Gii thut s0p xp 'c s d+ng l Selection Sort ( phc tp ()). Ban u, m5i bc chn lc u s0p xp li ton b qun th. Tuy nhin c th

ch2 cn thc hin s0p xp -$ &$ 1$ , c th u tin gim bt s) l'ng php so snh v 6i ch5.

-- // Selection sort cha ti u $%$

'$(.-#))

'%)%(.-%))

'.%-(. -

%

,

.

..

. )

.

.

,

,

T)i u th- t+c s0p xp trn b4ng thay vng l/p th nht :


T. : '$(.-#))

Thnh : '$( !0.#))

.- l ! $ & 1 & , cn !0. l -$ &$ 1$ ,.

Ci tin ny em li hiu nng tt hn cho gii thut v th&i gian chy. Tuy nhin so snh trong 1 s) tr&ng h'p, cch chn lc ny cho kt qu ti hn

khong 5%.

1.6 Tin ha : Vi qun th khi to ban u, chng 'c tin ha mt cch ng1u nhin v

thch nghi vi iu kin chn lc, cc c th km thch nghi s* b loi thi v c th t)t nht 'c chn lm l&i gii.

Vic tin ha di7n ra qua mt s) th h, m5i th h ta thc hin lai ghp v t bin ng1u nhin trn ton qun th.

Lai ghp : ng1u nhin trong 50% s) c th ng u tin c-a qun th (La chn cha m: ng1u nhin).

t bin cho ton b qun th 100% (tuy iu ny c v9 tri t nhin nhng vic tm ra ngun gen mi cn u tin hn ht).

Sau mt s) th h nh trc (10,000 n 10,000,000) chng trnh s* d.ng v xut ra kt qu.

(*) Ci tin a lung : tn d+ng hiu n


2. Gii thiu v chng trnh :

Figure 4 : Giao din chng trnh

Chng trnh vi giao din n gin gm 1 c-a s6 nhp thng tin v hin kt qu. M/c nh chng trnh s* c d liu trong cc tp tin i km : th u vo inputGraph.txt v 1 chu trnh m1u so snh kt qu inputCircle.txt. D liu trong cc tp tin phi nh dng chu!n nh cp trong cc m+c m ha th, m ha chu trnh. Nu thng tin khng ng nh dnh, chng trnh s* khng chy.

Ngoi ra chng trnh cung cp thm 1 s) thit lp thng s) v s) l'ng c th trong qun th (Population size) v s) l'ng th h tin ha (Max Generation). S) liu m/c nh ban u l 100 c th v 10.000 th h. gii hn cc l5i v b nh v hn ch th&i gian chy qu lu, chng trnh /t s?n s) l'ng c th ln nht l 1.000 v s) th h l 10.000.000 (nu nhp ln hn s* t ng s d+ng gi tr ln nht).

Mt thng s) n a cn 'c nhp vo l Threads : thng s) thit lp cho s) lung chy song song c-a chng trnh (s) qun th cng tin ha cng lc).


Thng s) ny m/c nh thit lp l 2 v cho php thit lp trong khong t. 1 n

4. Thit lp y - cc thng s), bm calculate thc hin tnh ton. Kt qu tr v gm chi ph cho &ng i t)t nht m chng trnh tnh ton

'c v chi ph tnh ton t. chu trnh m1u nhp vo (c th khng cn nhp chu trnh u vo). Ngoi ra chng trnh hin th th&i gian chy theo giy v ton b chi tit v chu trnh tnh 'c 'c lu trong tp tin outputCircle.txt, bm nt show circle hin xem ni dung chu trnh.

Trong qu trnh tnh ton, chng trnh s d+ng cc file tm lu kt qu tnh ton trung gian v kt qu t)t nht sau cc ln chy. Khi khi chy nu nhp s?n 1 chu trnh vo tp tin tempCircle.txt tng ng vi th th chng trnh c th s* nhanh chng tm 'c kt qu t)t hn.

3. Kt qu chy cc b d! liu chu"n : S d+ng cc b d liu chu!n cho bi ton TSP 'c ti v t. trang

http://www.tsp.gatech.edu/ D liu trong m5i b bao gm thng tin v tn b d liu, s) 2nh, dng

th v danh sch 2nh cng vi ta m5i 2nh. Nhm la chn cc b d liu sau th nghim gii thut :

Tn b d liu S) 2nh Chi ph c-a l&i gii t)i u tm 'c

wi29.tsp 29 27603

qa194.tsp 194 9352

xit1083.tsp 1083 3617,26/3558

Gii thut 'c ci /t b4ng ngn ng java (jdk 7u9 - win64)


Cu hnh my tnh chy gii thut :

Intel(R) Core(TM) i5-3210M CPU @ 2.50GHz RAM DDR3 4GB bus 1600MHz

OS Windows 7 x64

Trong qu trnh chy s d+ng thit lp s) c th t)i a l 100 v s) th h ln l't cc mc 10.000, 50,000, 100.000, 500.000, 1.000.000, 5.000.000 ty b d liu. M5i mc thit lp cho chy 10 ln v ly ra gi tr nh, nht so snh vi chi ph t)i u m1u (ly t. b d liu chu!n). Chi tit v kt qu cc ln chy c trong Ph+ l+c i km bo co ny.

Sau y l th)ng k kt qu chy chng trnh vi mt s) b d liu :

3.1 B d! liu wi29.tsp : Tn b d liu wi29.tsp (Western Sahara) Kch thc th : 29 2nh

Chi ph chu trnh t)i u : 27603 Kt qu chy :

Pop size Max Gen Min cost % Time Optimal found

100 10.000 27601,17 99,99 59 Yes

100 500.000 27601,17 99,99 903 Yes

(*) C th do kt qu t)i u 'c cung cp theo b d liu khi tnh ton lm trn nn c sai s).

Kt lun : tm thy chu trnh t)i u.

3.2 B d! liu qa194.tsp: Tn b d liu qa194.tsp (Quatar) Kch thc th : 194 2nh


Chi ph chu trnh t)i u : 9352 Kt qu chy :


100 1000 11465,45 122,6 17 No

100 10000 10147.12 108,5 192 No

100 100.000 10137,51 108,4 1783 No

Kt lun : cha tm thy chu trnh t)i u

3.3 B d! liu xit1083.tsp: Tn b d liu xit1083.tsp (VLSI - XIT1083 Vi mch tch h'p) Kch thc th : 1083 2nh

Chi ph chu trnh t)i u : 3617,26/3558 Kt qu chy :


100 1000 10774,26 297,86 80 No

100 10000 8694,27 240,36 241 No

Kt lun: cha tm thy chu trnh t)i u


4. nh gi gii thut v cc ci tin trong tng lai: Gii thut xut p ng c bn cc bc trong gii thut di truyn.

Kt qu chy gii thut cho kt qu t)i u trong cc tr&ng h'p s) 2nh nh, di 100 v a ra kt qu kh tim cn vi cc tr&ng h'p s) 2nh khong 1000. Cn vi nh ng tr&ng h'p s) 2nh ln hn 1000 gii thut v1n cha tm ra 'c l&i gii.

Gii thut di truyn xut phn ln v1n ph+ thuc vo s may m0n tm ra kt qu. Do tm 'c kt qu t)i u vi cc tr&ng h'p s) 2nh

ln l rt hn ch. Trong tng lai, nhm s* tm hiu v ci /t cc gii thut heuristic gip tm ra 'c l&i gii t)i u vi th c kch thc ln hn, cng

vi l cc ci tin v gii thut GA nh qun th ng, a qun th tng tc


T#NG K$T

Bo co lm r cc khi nim v gii thut di truyn v cc bc thc hin khi p d+ng vo gii quyt bi ton ng&i du lch. Kt qu gii thut ci /t v1n cn nhiu hn ch khi th&i gian gii quyt cc b d liu ln hn c@ 10~20 nghn 2nh. Trong tng lai nhm s* tip t+c ci tin thut ton b4ng cc gii thut heuristic h5 tr' tm &ng, ci tin gii thut di truyn b4ng c ch a qun th c tng tc.


TI LI%U THAM KHO

[1] Phm Vn Hi - Slide bi ging Tr tu nhn to.

[2] Nguyn nh Thc - Lp trnh tin ha.

[3] Wikipedia.

http://vi.wikipedia.org/wiki/B%C3%A0i_to%C3%A1n_ng%C6%B0%E1%BB%9Di_b%C3%A1n_h

%C3%A0ng.

[4] Cc ti liu lin quan v cc b d liu mu ti http://www.tsp.gatech.edu/index.html.


PH LC

K$T QU CH&Y GII THUT TRN CC B' D( LI%U

1. B d liu wi29.tsp :

B d! liu wi29.tsp S )nh : 29 Chi ph chu trnh ti u : 27603 Chi ph chu trnh tt nht : 27601,17 Tm thy chu trnh ti u

Pop size

Max Gen Re_01 Re_02 Re_03 Re_04 Re_05 Re_06 Re_07 Re_08 Re_09 Re_10

Average run time Min cost

Optimal cost

Min/opt %

100 10000 27748,71 27748,71 27748,71 27748,71 27748,71 27748,71 27601,17 27601,17 27601,17 27601,17 59 27601,17 27603 99,99

100 100000 27601,17 27601,17 27601,17 27601,17 27601,17 27601,17 27601,17 27601,17 27601,17 27601,17 903 27601,17 27603 99,99

2. B d liu qa194.tsp

B d! liu qa194.tsp S )nh : 194 Chi ph chu trnh ti u : 9352 Chi ph chu trnh tt nht :

Cha tm thy chu trnh ti u

Pop size



Optimal cost

Min/opt %


100 1000 15000,60 14800,71 13448,23 13098,30 12495,81 12207,76 12048,84 11747,44 11505,10 11465,45 17 11465,45 9352 122,6

100 10000 11265,86 11158,49 11104,15 10738,32 10585,48 10483,64 10188,88 10147.12 10147.12 10147.12 192 10147.12 9352 108,5

100 100000 10147.12 10137,51 10137,51 10137,51 10137,51 10137,51 10137,51 10137,51 10137,51 10137,51 1783 10137,51 9352 108,4

3. B d liu xit1083.tsp :

B d! liu xit1083.tsp S )nh : 1083 Chi ph chu trnh ti u : 3617.26 Chi ph chu trnh tt nht :

Cha tm thy chu trnh ti u

Pop size



Optimal cost

Min/opt %

100 1000 14774,42 13064.93 12304.03 11987.84 11658.09 11387.66 11176.63 10957.42 10899,42 10774.26 80 10774.26 3617,26 297,86

100 10000 9599.92 9526.40 9374.46 9281,23 9119,28 9063,45 9005,01 8694,27 8914,20 8859,74 841 8694,27 3617,26 240,36

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