Luận văn phương pháp tối ưu đàn kiến giải bài toán định tuyến xe

kMđvt lso vthhu¾vtvtốpn lmeevtxaheehuerzilsvtzi3c vtovt pnhxavt hzi¾pn pnxamy 3có vthee 3cho ylòzi cgzixazi ivózi pđ® vtovt okélm 0.5% pđeepn1% lso ivózi ylòzi cgzixazi vtozi ưhu 3cho 3c

BÀI TOÁlN éĐỊlNH TUYẾlN XE

Ncgàpnh: Khoxa họ3c lmámy vtípnh

é ĐẠI HỌC QUỐC GIA HÀ l NỘI TRƯỜ l NG é ĐẠI HỌC CÔ l NG

NGHỆ

BÀI TOÁlN éĐỊlNH TUYẾlN XE

Ncgàpnh: Khoxa họ3c lmámy vtípnh

Cápn @bộ hướpncg gdẫpn: TS éĐỖ éĐỨC éĐÔlNG

Bàzi vtoápn pđ%pnh vthumyeepn pxee (VRP – Veehzi3cylee Rohuvtzipncg Pero@byleelm) ylziêpn qhuxapn vterpn3c vtzieesp

vtózi gd%3ch ivpn cgzixao hàpncg 3chuxa lm®vt 3côpncg vtmy Bàzi vtoápn myêhu 3cxahu vtìlm pđưòpncg pđzi vtozi

ưhu 3cho 3cá3c pxee 3cho hàpncg pxhuxavt sphávt vtù lm®vt ho¾3c pnhzieehu okho hàpncg pđee cgzixao hàpncg

3cho lm®vt vt¾sp okhá3ch hàpncg 3cho vterưó3c Có pnhzieehu vtziêhu 3chhuxapn vtozi ưhu, pnhưpncg

vthôpncg gdpnpncg pnhxavt ivxapn ylà vtozi vthzieehu hóxa 3chzi sphí iv¾pn 3chhumyeepn ho¾3c vtopncg pđ® gdàzi

qhuãpncg pđưòpncg gdzi 3chhumyeepn 3chuxa 3cá3c pxee

Bàzi vtoápn VRP 3có ý pncghĩxa ylópn vteropncg 3côpncg pncghzi¾sp Vzi¾3c vtozi ưhu 3cá3c vthumyeepn pđưòpncg iv¾pn

3chhumyeepn 3có vthee vtzieevt okzi¾lm 3cho 3cá3c 3côpncg vtmy vtózi 5% Thopncg okê 3cho vthxamy, 3chzi sphí iv¾pn

3chhumyeepn 3chzieelm vtzi V T E RQ P N C G ylópn 3cxahu vthàpnh vteropncg lm®vt lsxapn sphxalm (10%) Do pđó, L MQ Z I 3chzi

sphí vtzieevt okzi¾lm pđưo3c @bxapncg 3cá3ch cgzixazi vtovt VRP 3cho gdù pnho hơpn 5%, pđeehu 3có ý pncghĩxa ylópn

Bàzi vtoápn VRP 3cũpncg 3có pnhzieehu ý pncghĩxa vteropncg okhoxa HQ 3 C, @bàzi vtoápn pđã pđưo3c 3chúpncg

mzipnh ylà lNP-okhó Do pđó pnhhupncg vthhu¾vt vtoápn 3chípnh pxá3c gdùpncg pđee cgzixazi 3chúpncg 3chzi 3có vthee

cgzixazi pđưo3c @bàzi vtoápn ivózi okí3ch vthưó3c pnho éĐee cgzixazi pđưo3c @bàzi vtoápn ivózi okí3ch vthưó3c ylópn, pđã

vtoápn VRP, iví gdpn pnhư gdùpncg cgzixazi vthhu¾vt gdzi vterhumyeepn (GA – cgeepneevtzi3c xaylcgoerzivthlm), vtìlm okzieelm

Txa@bhu (Txa@bhu lseexaer3ch), vthhu¾vt vtoápn ylhumy¾pn okzilm (Szilmhuylxavteegd xapnpneexaylzipncg) kM®vt lso vthhu¾vt

vtoápn lmeevtxaheehuerzilsvtzi3c vtovt pnhxavt hzi¾pn pnxamy 3có vthee 3cho ylòzi cgzixazi ivózi pđ® vtovt okélm 0.5% pđeepn1% lso ivózi ylòzi cgzixazi vtozi ưhu 3cho 3cá3c @bàzi vtoápn ylêpn vtózi hàpncg vterălm pđzieelm cgzixao hàpncg

Lhu¾pn ivăpn lsee pncghziêpn 3cúhu, vtìlm hzieehu 3cá3c sphươpncg sphásp lmeevtxaheehuerzilsvtzi3c pnózi 3chhupncg ivà

sphươpncg sphásp vtozi ưhu pđàpn okzieepn pnózi erziêpncg pđee cgzixazi qhumyeevt @bàzi vtoápn VRP

TÈ o khó xa: VRP, i v e eh z i 3 c y l e e e ro h u v t z i p n c g s p e ro @ b y l e e l m, CVRP, 3 c x a s p x a 3 c z i v t x a v t e e g d i v e eh z i 3 c y l e e e ro h u v t z i p n c g

s p e ro @ b y l e e l m.

1 Bà z i v toá p n VRP i và 3 c á 3 c @ b z i e e p n v th e e 1

1.1 kMo pđxahu 1

1.2 Bàzivtoápn VRP ivà 3c 3cokházipnzi¾lmylziêpn qhuxapn 3

1.3 Bàzivtoápn CVRP 5

1.4 Cá3c@bzieepn vthee 3chuxa CVRP 7

1.4.1 Thxamy pđozi3cxahuvterú3cvthumyeepn pxee 7

1.4.2 Thxamy pđozi hàlmlmpn3cvtziêhu 8

1.4.3 Thêlm3c 3ceràpncg @bhu®3c3cho 3c 3cvthumyeepn pxee 9

2 Cá 3 c 3 c ô p n c g v t e rì p nh p n c gh z i ê p n 3 c É h u y l z i ê p n q h u x a p n 10 2.1 Thhu¾vt vtoápn 3chípnh pxá3c 11

2.2 Heehuerzilsvtzi3c 12

2.2.1 Heehuerzilsvtzi3cpxâmy gdpnpncg 12

2.2.2 Heehuerzilsvtzi3c3cxazivthzi¾pn 13

2.3 kMeevtxaheehuerzilsvtzi3c 14

2.3.1 Tìlmokzieelm Txa@bhu 14

2.3.2 Thhu¾vt vtoápn ylhumy¾pn okzilm 15

2.3.3 Gzixazivthhu¾vt gdzivterhumyeepn 15

2.3.4 Tozi ưhu hóxa pđàpn okzieepn 17

3 Phươ p n c g s phá s p ACO p đ e e p x h u x a v t 18 3.1 Tozi ưhu hóxa pđàpn okzieepn 18

3.1.1 Tù okzieepn vtpn pnhziêpn pđeepn okzieepn pnhâpn vtxao 18

3.1.2 Thhu¾vt vtoápn ACO 20

3.1.3 Tólmvtxavt vthhu¾vt vtoápn ACO 21

3.2 Ásp gdpnpncg ACO 3cho @bàzivtoápn CVRP 22

3.2.1 Bưó3c 1: Khozivtxao lmxa vter¾pn heehuerzilsvtzi3civà iveevt lmùzi 23

3.2.2 Bưó3c 2: Kzieepn vtxao ylòzicgzixazi 23

3.2.3 Bưó3c 3: C¾sp pnh¾vt iveevt lmùzi 24

4 K e e v t q h u x a v thE 3 c p n c gh z i ¾ l m i và o k e e v t y l h u ¾ p n 25 4.1 Dhuylzi¾hu 25

4.2 Thzieevt yl¾sp vthxalmlso 26

4.3 Keevt qhuxa vthpn3cpncghzi¾lm 28

4.3.1 Phâpn vtí3ch okeevt qhuxa 28

4.3.2 So lsápnh vthòzicgzixapn 3chxamy 31

4.4 Keevt ylhu¾pn 32

Dxapnh lsá3ch hìpnh

1.1 Chzisphí ylocgzilsvtzi3cvtípnh vtheeo sphxapn vterălm GDP 1

1.2 xa) kM®vt iví gdpn 3cho CVRP, vteropncg pđó hìpnh ivhu pncg ylà okho hàpncg, hìpnh vteròpn ylà okhá3ch hàpncg, lso cghzigdưózilmőziokhá3ch hàpncg ylà pnhhu3cxahuvtươpncg úpncg; @b) kM®vt ylòzicgzixazi hosp yl¾ 7

2.1 Thhu¾vt vtoápn vtzieevt okzi¾lm: vterưó3civà lsxahuokhzipnozivthumyeepn pxee 12

2.2 Thhu¾vt vtoápn qhuévt cgó3c 13

2.3 Sơ pđo 3chuxa cgzixazivthhu¾vt gdzivterhumyeepn 16

3.1 Thí pncghzi¾lm qhuxapn lsávt okzieepn 18

3.2 Thí pncghzi¾lm qhuxapn lsávt okzieepn 19

4.1 éĐo vth% lso lsápnh okhzivthxalmlso vthxamy pđozi 27

4.2 Bzieehupđo 3c®vt: lso lsápnh ivózi 3 vthhu¾vt vtoápn okzieepn okhá3c 29

Vzieevt vtxavt

VRP Veehzi3cylee Rohuvtzipncg Pero@byleelmCVRP Cxaspxa3czivtxavteegd Veehzi3cylee Rohuvtzipncg

Pero@byleelm TSP Terxaiveeylzipncg Sxayleelslmxapn Pero@byleelmACO Apnvt Coylopnmy

Ospvtzilmzizxavtziopn GA Geepneevtzi3c

B&B Berxapn3ch xapngd BohupngdVRPTW Veehzi3cylee Rohuvtzipncg Pero@byleelm Tzilmee Wzipngdowls

Chươpncg 1

Bàzi vtoápn VRP ivà 3cá3c @bzieepn vthee

1.1 kMee pđxahu

Locgzilsvtzi3c ylà qhuá vterìpnh ylêpn okee hoxa3ch, vterzieepn okhxazi ivà okzieelm lsoávt qhumy vterìpnh iv¾pn

3chhumyeepn, ylưhu vterhu hàpncg hóxa lm®vt 3cá3ch hzi¾hu qhuxa, vtzieevt okzi¾lm Lĩpnh ivpn3c ylocgzilsvtzi3c pđxapncg

pđưo3c erxavt pnhzieehu pnhà pncghziêpn 3cúhu qhuxapn vtâlm Teropncg vth¾sp okzi qhuxa, ylocgzilsvtzi3c pđã pđưo3c

Lĩpnh ivpn3c ylocgzilsvtzi3c vtziêhu vtopn erxavt pnhzieehu vtàzi pncghumyêpn ivee 3copn pncgưòzi 3cũpncg pnhư pnhziêpn ylzi¾hu.

Hìpnh 1.13cho vthxamy ylocgzilsvtzi3c 3chzieelm ylêpn vtózi 10% GDP 3chuxa Châhu Âhu vteropncg vth¾sp okzi qhuxa.H¾ vthopncg iv¾pn 3chhumyeepn ylà lm®vt h¾ vthopncg qhuxapn V T E RQ P N C G pnhxavt vteropncg h¾ vthopncg sphâpn sphozi,

3chzieelm ylêpn vtózi 50% 3chzi sphí ylocgzilsvtzi3c (Zhhu xapngd Zhxazi2017) Theeo vthopncg okê, 3chzi sphí ivee

iv¾pn 3chhumyeepn 3cxahu vthàpnh 10% 3chzi sphí vtxao erxa lm®vt lsxapn sphxalm (Rogderzicghuee, Colmvtozils, xapngd

Sylxa3cok2016) Vzi¾3c vtozi ưhu 3cá3c vthumyeepn pđưòpncg iv¾pn 3chhumyeepn 3có vthee vtzieevt okzi¾lm 3cho 3cá3c

3côpncg vtmy ylêpn vtózi 5% (Hxalsylee, Lziee, xapngd Qhuxaok2007) éĐzieehu pnàmy 3có ý pncghĩxa erxavt ylópn

Bàzi vtoápn pđ%pnh vthumyeepn pxee - VRP (Veehzi3cylee Rohuvtzipncg Pero@byleelm) ylà lm®vt ylósp 3cá3c @bàzi

vtoápn qhuxapn vtâlm vtózi ivzi¾3c vtìlm 3cá3ch pđ%pnh vthumyeepn 3cá3c pxee 3cho hàpncg pđee iv¾pn 3chhumyeepn

hàpncg hóxa vtù lm®vt ho¾3c pnhzieehu okho hàpncg vtózi 3cá3c pđ%xa pđzieelm 3cxapn 3chhumyeepn pđeepn Bàzi vtoápnVRP ylziêpn qhuxapn vterpn3c vtzieesp vtózi ivzi¾3c iv¾pn 3chhumyeepn, sphâpn sphozi hàpncg hóxa 3cho pnêpn pncghziêpn

B Â l NG 1.1: Khí v th x a z i 3 c h u x a p x e e v t x a z i

CO2 SO2 l NO p x P k M10

Xee vtxazi 26% 43% 38% 59%

Khôpncg 3chzi 3có xapnh hưopncg vtózi okzipnh vtee, 3chzi sphí iv¾pn 3chhumyeepn cgzixa vtăpncg pđopncg pncghĩxa ivózi

ivzi¾3c pnhziêpn ylzi¾hu vtziêhu vthpn cgzixa vtăpncg, gdxapn vtózi ylưopncg okhí vthxazi vtăpncg, vtù pđó xapnh hưopncg

ivee ylưopncg okhí vthxazi gdo pxee vtxazi pđưo3c 3cho o @bxapncg1.1(Dxa@bylxapn3c2013) Xee vtxazi vthưòpncg pđưo3c

gdùpncg pđee iv¾pn 3chhumyeepn hàpncg hóxa Do pđó, pncghziêpn 3cúhu @bàzi vtoápn VRP okhôpncg pnhhupncg 3có ý

pncghĩxa pđozi ivózi okzipnh vtee lmà 3còpn 3có ý pncghĩxa vtózi ivzi¾3c @bxao iv¾ lmôzi vterưòpncg

Lósp @bàzi vtoápn VRP 3cũpncg 3có pnhzieehu ý pncghĩxa vteropncg okhoxa HQ 3 C Bàzi vtoápn pđã pđưo3c 3chúpncg

lmzipnh ylà lNP-okhó Do pđó pnhhupncg vthhu¾vt vtoápn 3chípnh pxá3c gdùpncg pđee cgzixazi 3chúpncg 3chzi 3có vthee

cgzixazi pđưo3c @bàzi vtoápn ivózi okí3ch vthưó3c pnho éĐee cgzixazi pđưo3c @bàzi vtoápn ivózi okí3ch vthưó3c ylópn, pđã

vtoápn VRP, iví gdpn pnhư gdùpncg cgzixazi vthhu¾vt gdzi vterhumyeepn (GA – cgeepneevtzi3c xaylcgoerzivthlm), vtìlm okzieelm

Txa@bhu (Txa@bhu lseexaer3ch), vthhu¾vt vtoápn ylhumy¾pn okzilm (Szilmhuylxavteegd xapnpneexaylzipncg) kM®vt lso vthhu¾vt

vtoápn lmeevtxaheehuerzilsvtzi3c vtovt pnhxavt hzi¾pn pnxamy 3có vthee 3cho ylòzi cgzixazi ivózi pđ® vtovt okélm 0.5% pđeepn1% lso ivózi ylòzi cgzixazi vtozi ưhu 3cho 3cá3c @bàzi vtoápn ylêpn vtózi hàpncg vterălm pđzieelm cgzixao hàpncg (Vzigdxayl,

Crainic, Michel Gendreau, and Prins2014)

lNh¾pn vthxamy úpncg gdpnpncg vthpn3c vtzieepn vto ylópn 3chuxa ylósp @bàzi vtoápn VRP, ylhu¾pn ivăpn pnàmy pncghziêpn

3cúhu, vtìlm hzieehu @bàzi vtoápn CVRP (lm®vt @bàzi vtoápn pđơpn cgzixapn pnhxavt 3chuxa ylósp VRP) ivà 3cá3c

cgzixazi 3chúpncg pđã pđưo3c 3côpncg @bo, pđopncg vthòzi pđee pxhuxavt lm®vt vthhu¾vt vtoápn vtozi ưhu pđàpn okzieepn pđee

cgzixazi @bàzi vtoápn VRP

Lhu¾pn ivăpn lsee pđưo3c vto 3chú3c vthàpnh 4 3chươpncg pnhư lsxahu:

• Chươpncg pđxahu vtziêpn, 3chươpncg pnàmy, ylà sphxapn lmo pđxahu, cgziózi vthzi¾hu ylósp @bàzi vtoápn VRP

ivà úpncg gdpnpncg vto ylópn 3chuxa pnó vteropncg vthpn3c vtzieepn Bàzi vtoápn pđơpn cgzixapn pnhxavt vthhu®3c ylóspVRP ylà CVRP 3cũpncg lsee pđưo3c sphávt @bzieehu 3ch¾vt 3chee éĐopncg vthòzi, lm®vt lso @bzieepn vthee

okhá3c 3chuxa CVRP 3cũpncg pđưo3c cgziózi vthzi¾hu lsơ qhuxa,

• Chươpncg hxazi cgziózi vthzi¾hu lm®vt lso sphươpncg sphásp pđã pđưo3c ásp gdpnpncg vterưó3c pđó pđee

cgzixazi @bàzi vtoápn CVRP

• Chươpncg @bxa vterìpnh @bàmy vthhu¾vt vtoápn vtozi ưhu hóxa pđàpn okzieepn pđee pxhuxavt pđee cgzixazi @bàzi vtoápn CVRP

• Chuozi 3cùpncg, 3chươpncg @bopn ylà sphxapn okeevt qhuxa vthpn3c pncghzi¾lm 3chuxa vthhu¾vt vtoápn pđee

1.2 Bàzi vtoápn VRP ivà 3cá3c okházi pnzi¾lm ylziêpn qhuxapn

Bàzi vtoápn pđ%pnh vthumyeepn pxee (VRP) vthhu®3c ylósp @bàzi vtoápn vtozi ưhu vto hosp, qhuxapn vtâlm vtózi

ivzi¾3c iv¾pn 3chhumyeepn hàpncg hóxa vtù lm®vt ho¾3c pnhzieehu okho hàpncg vtózi lm®vt vt¾sp 3cá3c okhá3ch

hàpncg Bàzi vtoápn VRP pđưo3c pđee pxhuxavt ylxapn pđxahu vtziêpn @bozi Dxapnvtzzicg ivà Rxalmlseeer ivào pnălm

1959 (Dxapnvtzzicg xapngd Rxalmlseeer 1959), vteropncg pđó vtá3c cgzixa cgziózi vthzi¾hu lm®vt @bàzi vtoápn vthpn3c

vtzieepn ivee ivzi¾3c gdzi 3chhumyeepn pxăpncg vtózi 3cá3c vterxalm pxăpncg Vózi lso ylưopncg pxee 3cho pxăpncg 3cùpncg

vtopncg ylưopncg pxăpncg 3chhumyeepn 3cho vterxalm pxăpncg pđưo3c vthălm @bozi lm®vt pxee okhôpncg ivưovt qhuá

gdhupncg ylưopncg 3chúxa 3chuxa pxee pđó, ivà pđopncg vthòzi qhuãpncg pđưòpncg gdzi 3chhumyeepn 3chuxa 3cá3c pxee ylà

pnho pnhxavt 3có vthee Bàzi vtoápn pnàmy ylà gdxapncg pđơpn cgzixapn pnhxavt 3chuxa ylósp 3cá3c @bàzi vtoápn VRP, ivà

3cho okhá3ch hàpncg pđó VRP hozi sphxazi pđzieehu sphozi pxee 3cho hàpncg pnhư vthee pnào pđee 3có vthee vtozi

Dưózi pđâmy vterìpnh @bàmy 3chzi vtzieevt ivee 3cá3c vthàpnh sphxapn ylziêpn qhuxapn vteropncg @bàzi vtoápn VRP.

hzi¾pn ivzi¾3c cgzixao hàpncg kMőzi pxee 3có lm®vt lso vthhu®3c vtípnh cgxapn ivózi pnó, iví gdpn pnhư ylà

ylưopncg hàpncg hóxa vtozi pđxa lmà pnó 3có vthee 3cho, ho¾3c ylưopncg okhá3ch hàpncg vtozi pđxa lmà

• Kho hàp n c g (D e e s po v t).

Kho hàpncg pđưo3c @bzieehu gdzieepn @bozi iv% vterí pđ%xa ylý, pnơzi hàpncg hóxa pđưo3c 3chúxa Thôpncg

vthưòpncg, okho hàpncg 3cũpncg ylà pnơzi pxhuxavt sphávt ivà okeevt vthú3c 3chuxa pxee 3cho hàpncg

• k M x a p n c g y lưé z i c g z i x ao v thô p n c g.

Xee iv¾pn 3chhumyeepn pđzi ylxazi cgzihuxa 3cá3c okhá3ch hàpncg vthôpncg qhuxa lmxapncg ylưózi cgzixao vthôpncg

pnàmy kMxapncg ylưózi cgzixao vthôpncg vthưòpncg lsee pđưo3c @bzieehu gdzieepn @bxapncg pđo vth%, vteropncg pđó

Hàlm lmpn3c vtziêhu 3chuxa @bàzi vtoápn VRP vthưòpncg ylà vtozi vthzieehu hóxa/vtozi pđxa hoxa lm®vt pđ

%nh lưong nào đó Mnc tiêu cơ ban và thông dnng nhat là toi thieu hóa tong

pđ® gdàzi qhuãpncg pđưòpncg lmà pxee gdzi 3chhumyeepn kM®vt hàlm lmpn3c vtziêhu 3có vthee okhá3c ylà vtozi

pđxa hóxa ylozi pnhhu¾pn vthhu pđưo3c @bxapncg 3cá3ch sphpn3c ivpn lm®vt vt¾sp okhá3ch hàpncg

• Lèz i c g z i x a z i 3 c h u x a VRP.

kM®vt ylòzi cgzixazi 3cho @bàzi vtoápn VRP vthưòpncg ylà lm®vt vt¾sp 3cá3c vthumyeepn pxee 3cùpncg ivózi pxee

3cho vtươpncg úpncg lsee gdzi 3chhumyeepn vtheeo vthumyeepn pxee pđó kM®vt lso @bzieepn vthee sphú3c vtxasp

okhá3c 3chuxa @bàzi vtoápn VRP 3cxapn 3có vthêlm lm®vt lso vthôpncg vtzipn okhá3c pđee @bzieehu gdzieepn ylòzi

• Ràp n c g @ b h u® 3 c.

Ràpncg @bhu®3c ylà pnhhupncg pđzieehu okzi¾pn lmà ylòzi cgzixazi 3cho VRP 3cxapn sphxazi pđưo3c vthoxa

1.3 Bàzi vtoápn CVRP

Bàzi vtoápn éĐ%pnh vthumyeepn pxee ivózi gdhupncg ylưopncg iv¾pn 3chhumyeepn cgziózi hxapn - CVRP

(Cxaspxa3czivtxavteegd Vzi- hee3cylee Rohuvtzipncg Pero@byleelm) ylà lm®vt @bàzi vtoápn 3cơ @bxapn pnhxavt vthhu®3c ylósp

3cá3c @bàzi vtoápn VRP lNhư pđã pđưo3c pđee 3c¾sp, CVRP pđưo3c pđee pxhuxavt ylxapn pđxahu vtziêpn @bozi

Dxapnvtzzicg ivà Rxalmlseeer ivào pnălm 1959 (Dxapnvtzzicg xapngd Rxalmlseeer1959), vteropncg pđó vtá3c cgzixa cgziózi

vthzi¾hu lm®vt @bàzi vtoápn vthpn3c vtzieepn ivee ivzi¾3c 3cho pxăpncg pđeepn 3cá3c vterxalm pxăpncg CVRP 3cũpncg ylà

CVRP

CVRP myêhu 3cxahu sphávt hàpncg 3cho 3cá3c okhá3ch hàpncg, lmőzi okhá3ch hàpncg 3có lm®vt pnhhu 3cxahu

3cho vterưó3c, @bxapncg 3cá3ch gdùpncg 3cá3c pxee ivózi gdhupncg ylưopncg 3chúxa cgziózi hxapn Cá3c pxee 3cho hàpncg

pđưo3c pđ¾hu vtxazi lm®vt okho hàpncg, 3cá3c vthumyeepn pxee lsee pxhuxavt sphávt ivà okeevt vthú3c vtxazi okho hàpncg pđó

kMpn3c vtziêhu ylà pxá3c pđ%pnh 3cá3c vthumyeepn pxee lsxao 3cho L MQ Z I okhá3ch hàpncg pđưo3c sphpn3c ivpn, pxee okhôpncg

3cho qhuá gdhupncg ylưopncg 3chúxa ivà vtopncg okhoxapncg 3cá3ch gdzi 3chhumyeepn 3chuxa 3cá3c pxee ylà pnho pnhxavt

Bàzi vtoápn CVRP pđưo3c pđ%pnh pncghĩxa vterêpn lm®vt pđo vth% G = (V , E) @bzieehu gdzieepn lmxapncg

pxee pđó vthălm: e r = ( 3 c1, 3 c2, , 3 c v t ) Ký hzi¾hu e r l s z iz e eylà lso ylưopncg okhá3ch hàpncg lmà vthumyeepn

pxee e r vthălm Khá3ch hàpncg vthú l s pđưo3c vthălm @bozi vthumyeepn pxee e r, oký hzi¾hu @bozi e r[ l s], ylà 3 c l s Vì

lm®vt vthumyeepn pxee sphxazi pxhuxavt sphávt ivà okeevt vthú3c vtxazi okho hàpncg 0, pđee 3cho vthhu¾pn vtzi¾pn, vtxa

So ylưopncg vthumyeepn pxee okhôpncg pđưo3c qhuá lso ylưopncg pxee pđxapncg 3có ylà K.

2 e \{0} r z i ∩ e r j = 0/ kMőzi ivóokházi 3∀ch hàe r z i , e r pnjcg ∈ Sosphxazi y lp, đưoe r z i ƒ= 3c vthăe r lm jivà pđú∪pne rcz i∈Sog lm®y l e r z i = Vvt ylxapn

kM®vt ylòzi cgzixazi vthoxa lmãpn L MQ Z I pđzieehu okzi¾pn vtù 1 pđeepn 3 o vterêpn pđưo3c C GQ Z I ylà lm®vt ylòzi cgzixazi

h x a s p y l¾ lNcgưo3c ylxazi, ylòzi cgzixazi pđó pđưo3c C GQ Z I ylà o khô p n c g h x a s p y l¾.

Chxavt ylưopncg 3chuxa lm®vt ylòzi cgzixazi So y l pđưo3c pđápnh cgziá @bozi D z i l s v t(So y l) Gziá vter% pnàmy 3càpncg

H Ì l NH 1.2: x a) k M® v t i ví g d p n 3 cho CVRP, v t e ro p n c g p đó hì p nh i v h uô p n c g y là o kho hà p n c g, hì p nh v t e rò p n y là

o khá 3 ch hà p n c g, l so c gh z i g dưó z i l mő z i o khá 3 ch hà p n c g y là p nh h u 3 c x a h u v tươ p n c g ú p n c g; @ b) k M® v t y lò z i c g z i x a z i

ho s p y l¾

lNcgưòzi vtxa pđã 3chúpncg lmzipnh pđưo3c, okzieelm vterxa ylzi¾hu lm®vt ylòzi cgzixazi hosp yl¾ 3có vtozi ưhu hxamy

ylósp @bàzi vtoápn lNP-okhó (lNP-hxaergd) (Tovth xapngd Vzicgo2002)

1.4 Cá3c @bzieepn vthee 3chuxa CVRP

kMpn3c pnàmy cgziózi vthzi¾hu lm®vt lso @bzieepn vthee spho @bzieepn okhá3c 3chuxa CVRP

Tù @bàzi vtoápn CVRP, vtxa 3có vthee vthhu pđưo3c lm®vt @bzieepn vthee lmózi @bxapncg 3cá3ch vthxamy pđozi @bàzi

So ylưopncg pxee 3cxapn gdùpncg pđee sphpn3c ivpn vtxavt 3cxa okhá3ch hàpncg ylà 3càpncg ívt 3càpncg vtovt lNeehu

(Beepnvt xapngd Vxapn Heepnvteepnermy3cok2004)

1.4.3 Thêlm 3cá3c eràpncg @bhu®3c 3cho 3cá3c vthumyeepn pxee

Bxapncg 3cá3ch vthêlm lm®vt lso eràpncg @bhu®3c, lm®vt lso @bzieepn vthee 3có vthee vthhu pđưo3c pđó ylà:

• é Đ% p nh v t h u m y e e p n p x e e i vé z i o kho x a p n c g v thè z i c g z i x a p n c g z i x ao hà p n c g (C x a s p x a 3 c z i v t x a v t e e g d V e eh z i 3 c y l e e

Ro h u v t z i p n c g P e ro @ b y l e e l m w z i v th T z i l m e e W z i p n g dow l s).

kMőzi pđ%xa pđzieelm, okho hàpncg ivà okhá3ch hàpncg, lsee 3có lm®vt okhoxapncg vthòzi cgzixapn “hoxavt

pđ®pncg” 3chuxa pnó Cxapn cgzixao hàpncg 3cho okhá3ch hàpncg vteropncg okhoxapncg vthòzi cgzixapn “hoxavt

pđ®pncg” 3chuxa okhá3ch hàpncg pđó Xee 3cho hàpncg 3có vthee pđeepn lsólm hơpn ivà pđozi 3cho vtózi

Chươpncg 2

Cá3c 3côpncg vterìpnh pncghziêpn 3cÉhu ylziêpn qhuxapn

Teropncg 3chươpncg pnàmy 3cá3c sphươpncg sphásp cgzixazi @bàzi vtoápn VRP pđã pđưo3c 3côpncg @bo lsee pđưo3c pđee

@bàzi vtoápn 3có okí3ch vthưó3c pnho ho¾3c ivùxa

• Thh u¾ v t v toá p n h e e h u e r z i l s v t z i 3 c.

Heehuerzilsvtzi3c 3có vthee hzieehu ylà lm®vt pđ%pnh hưópncg vtìlm okzieelm ylòzi cgzixazi Cá3c vthhu¾vt vtoápn

heehuerzilsvtzi3c vthưòpncg 3cho erxa pđưo3c ylòzi cgzixazi hosp yl¾ ivózi 3chxavt ylưopncg 3chxasp pnh¾pn pđưo3c

Vózi okí3ch vthưó3c gdhu ylzi¾hu vthpn3c 3cho @bàzi vtoápn VRP pncgàmy 3càpncg vtero pnêpn pncgàmy lm®vt ylópn

hơpn, 3cá3c vthhu¾vt vtoápn heehuerzilsvtzi3c ivà lmeevtxaheehuerzilsvtzi3c spho @bzieepn hơpn lso ivózi vthhu¾vt vtoápn

3chípnh pxá3c éĐ¾3c @bzi¾vt, lmeevtxaheehuerzilsvtzi3c pđxapncg ylà pxhu hưópncg pncghziêpn 3cúhu 3chípnh

2.1 Thhu¾vt vtoápn 3chípnh pxá3c

kMpn3c pnàmy cgziózi vthzi¾hu lm®vt lso vthhu¾vt vtoápn 3chípnh pxá3c vthưòpncg gdùpncg ásp gdpnpncg 3cho @bàzi vtoápnVRP

• l Nhá p nh 3 câ m y i và c g z ié z i h x a p n y lè z i c g z i x a z i - B&B (B e r x a p n 3 ch x a p n g d Bo h u p n g d).

B&B ylà lm®vt vteropncg pnhhupncg vtzieesp 3c¾pn pđxahu vtziêpn pđee cgzixazi ylósp @bàzi vtoápn VRP B&B

3có vthee pđưo3c vtólm vtxavt pnhư lsxahu T¾sp hosp 3cá3c ylòzi cgzixazi lsee pđưo3c @bzieehu gdzieepn @bozi

cgzixazi Lòzi cgzixazi vtozi ưhu pnhxavt pđưo3c vtìlm okzieelm @bxapncg 3cá3ch gdhumy¾vt vterêpn 3câmy pnàmy Vózi

• Qh u m y ho x a 3 ch p đ® p n c g (D m y p n x a l m z i 3 c s p e ro c g e r x a l m l m z i p n c g).

Qhumy hoxa3ch pđ®pncg ylà sphươpncg sphásp cgzixazi 3cá3c @bàzi vtoápn sphú3c vtxasp @bxapncg 3cá3ch 3chzixa

cgzixazi @bàzi vtoápn @bxapn pđxahu Phươpncg sphásp pnàmy pđưo3c sphávt vterzieepn @bozi Rzi3chxaergd

Beeylyllmxapn ivào pnhhupncg pnălm 1950 ivà pđã pđưo3c úpncg gdpnpncg vteropncg pnhzieehu ylĩpnh ivpn3c

• Lh uo p n c g v t e rê p n l m x a p n c g ( l N e e v two e r o k F y low).

Phươpncg sphásp pnàmy sphávt @bzieehu @bàzi vtoápn CVRP gdưózi lmô hìpnh 3chuxa @bàzi vtoápn ylhuopncg

Dưózi pđâmy ylà lm®vt lso heehuerzilsvtzi3c pxâmy gdpnpncg 3cho @bàzi vtoápn VRP.

• Thh u¾ v t v toá p n v t z i e e v t o k z i¾ l m.

Thhu¾vt vtoápn vtzieevt okzi¾lm (lsxaivzipncg xaylcgoerzivthlm) (Cylxaerokee xapngd Werzicghvt1964) ylà

heehuerzilsvtzi3c pnozi vtzieepncg ivà ylâhu pđòzi pnhxavt Thhu¾vt vtoápn pnàmy erxavt hxamy pđưo3c gdùpncg pđee vtìlm

đưoc vói nhau

(vtú3c lsxahu okhzi pnozi ivxapn vthoxa lmãpn ivee pđzieehu okzi¾pn vtopncg pnhhu 3cxahu okhôpncg qhuá gdhupncg

pxee) vthì pnozi 3chúpncg ylxazi vtxao vthàpnh vthumyeepn pxee lmózi e r = e r1 × e r2 Lòzi cgzixazi pđưo3c 3c¾sp

pnh¾vt @bxapncg 3cá3ch yloxazi @bo e r1, e r2 ivà vthêlm lmózi e r: So y l = So y l \{ e r1 , e r2} ∪{ e r}.

Thhu¾vt vtoápn okeevt vthú3c okhzi okhôpncg vthee vthxamy pđozi ylòzi cgzixazi pđưo3c pnhuxa

Lưhu ý, ylòzi cgzixazi vthhu pđưo3c vtù vthhu¾vt vtoápn pnàmy okhôpncg pđxalm @bxao ylà hosp yl¾, ivì lso

• Thh u¾ v t v toá p n q h ué v t c gó 3 c.

Thhu¾vt vtoápn qhuévt cgó3c (lsweeeesp xaylcgoerzivthlm) (Reepnxahugd xapngd Bo3cvtoer2002) @bxao cgolm

hxazi cgzixazi pđoxapn éĐxahu vtziêpn ylà sphâpn 3cpnlm (3cylhulsvteeer), 3cá3c okhá3ch hàpncg vthhu®3c 3cùpncg

lm®vt vthumyeepn pxee lsee vthhu®3c 3cùpncg lm®vt 3cpnlm Tzieesp vtheeo, ásp gdpnpncg @bàzi vtoápn TSP 3cho

H Ì l NH 2.2: Th h u¾ v t v toá p n q h ué v t c gó 3 c

Gzixazi pđoxapn sphâpn 3cpnlm pnhư lsxahu Gzixa lshu 3cá3c iv% vterí 3chuxa okhá3ch hàpncg ivà pnhà okho 3có

vthzi¾pn ylòzi cgzixazi hzi¾pn vtxazi @bxapncg 3cá3ch vthxamy pđozi lm®vt lso vthàpnh sphxapn 3chuxa ylòzi cgzixazi 3cũ Lòzi

3cá3ch vthxamy pđozi lm®vt lso vthàpnh sphxapn pđưo3c C GQ Z I ylà okee pnhxahu, hxamy ylà ylápncg cgzieepncg ivózi ylòzi

cgzixazi 3cũ Do pđó vtxa 3có vtêpn C GQ Z I vtìlm okzieelm pđ%xa sphươpncg

Cá3c 3cá3ch vthú3c 3cxazi vthzi¾pn ylòzi cgzixazi vthưòpncg ylà vthxamy pđozi vthàpnh sphxapn vteropncg lm®vt vthumyeepn

pxee ho¾3c vteráo pđozi/vthxamy pđozi 3cá3c vthàpnh sphxapn vteropncg lm®vt 3c¾sp vthumyeepn pxee Ví gdpn, lm®vt

okhá3ch hàpncg 3có vthee @b% 3chhumyeepn lsxapncg vthumyeepn pxee okhá3c, hxazi okhá3ch hàpncg o hxazi vthumyeepn pxee

3có vthee @b% vteráo pđozi, hxamy vthú vtpn vthălm okhá3ch hàpncg vterêpn lm®vt vthumyeepn pxee @b% vthxamy pđozi,

3cxazi vthzi¾pn pnhuxa Lòzi cgzixazi vthhu pđưo3c ylà lm®vt ylòzi cgzixazi vtozi ưhu 3cpn3c @b®

2.3 kMeevtxaheehuerzilsvtzi3c

2.3.1 Tìlm okzieelm Txa@bhu

Thhu¾vt vtoápn vtìlm okzieelm Txa@bhu pđưo3c pđee pxhuxavt @bozi Gyloiveeer ivào pnălm 1989 (Gyloiveeer1989)

Tìlm okzieelm Txa@bhu pđưo3c vthzieevt okee pđee cgziúsp vtìlm okzieelm pđ%xa sphươpncg vthoávt okhozi ivùpncg vtozi ưhu

Teropncg vthhu¾vt vtoápn vtìlm okzieelm pđ%xa sphươpncg, okhzi okhôpncg vtopn vtxazi lm®vt ylápncg cgzieepncg pnào vtovt

hơpn hzi¾pn vtxazi, vthhu¾vt vtoápn lsee okeevt vthú3c Thumy pnhziêpn o vtìlm okzieelm Txa@bhu, okhzi pđzieehu pđó pxxamy

ưhu 3cpn3c @b® See 3có lm®vt gdxapnh lsá3ch ylưhu 3cá3c ylòzi cgzixazi pđã pđưo3c vthălm cgxapn pđâmy pnhxavt 3cùpncg

ivózi lm®vt gdxapnh lsá3ch 3cá3c ylhu¾vt 3cxalm pđ%pnh pncghĩxa @bozi pncgưòzi gdùpncg Lòzi cgzixazi ylápncg cgzieepncg pđã

pđưo3c vthălm cgxapn pđâmy ho¾3c ivzi sphxalm sphxazi ylhu¾vt 3cxalm vthì lsee okhôpncg pđưo3c vthălm ylxazi pnhuxa

Dxapnh lsá3ch 3cá3c ylhu¾vt 3cxalm pđưo3c C GQ Z I ylà gdxapnh lsá3ch vtxa@bhu (vtxa@bhu 3có pncghĩxa ylà okhôpncg vthee

pnhxavt (lNeexaereelsvt lNeezicgh@boerhoogd Seexaer3ch) pđưo3c cgziózi vthzi¾hu @bozi (Dhu xapngd Hee2012) 3có vthee

VRP 3có okí3ch vthưó3c ylópn Thhu¾vt vtoápn pnàmy pđưo3c 3chzixa ylàlm hxazi cgzixazi pđoxapn Gzixazi pđoxapn

pđoxapn vthú hxazi ásp gdpnpncg vtìlm okzieelm Txa@bhu

kM®vt lso pncghziêpn 3cúhu okhá3c pđã ásp gdpnpncg vtìlm okzieelm Txa@bhu 3cho @bàzi vtoápn CVRP ivà 3cá3c @bzieepn

vthee ylà (kM Geepngdereexahu eevt xayl.1999), (Berxapngdão2009), (lNcghueeiveehu, Perzipnls, xapngd Cxaylivo2009), (Lzihu, Xziee, xapngd Gxaerxazipx2014) éĐee vtìlm hzieehu vthêlm, 3có vthee P ĐQ 3 C @bàzi okhxao lsávt ivee vthhu¾vt

vtoápn Txa@bhu úpncg gdpnpncg 3cho @bàzi vtoápn VRP 3chuxa (Bxalshu2012)

2.3.2 Thhu¾vt vtoápn ylhumy¾pn okzilm

Thhu¾vt vtoápn ylhumy¾pn okzilm, pnhư vtêpn C GQ Z I, lmô sphopncg qhuá vterìpnh ylhumy¾pn okzilm yloxazi vteropncg pđó

okzilm yloxazi @bxapn pđxahu pđưo3c pnhupncg o pnhzi¾vt pđ® 3cxao erozi lsxahu pđó pđưo3c ylàlm ylxapnh gdxapn Thhu¾vt

Thhu¾vt vtoápn ylhumy¾pn okzilm 3có lm®vt vthxalm lso pnhzi¾vt pđ® vthxamy pđozi vtheeo vthòzi cgzixapn T Bxapn pđxahu

T ylópn, lsxahu pđó lsee gdxapn gdxapn cgzixalm ivee 0 Khzi pđxapncg o ylòzi cgzixazi l s, ylòzi cgzixazi ylápncg cgzieepncg l s Jlsee

pđưo3c 3cHQ P N pđee gdzi 3chhumyeepn vtózi ivózi lm®vt pxá3c lshuxavt Chxavt ylưopncg 3chuxa l s J 3càpncg vtovt vthì pxá3c

lshuxavt pnàmy 3càpncg 3cxao Hàlm pxá3c lshuxavt sphpn vthhu®3c ivào T Khzi T 3càpncg pnho, 3càpncg vtzieepn ivee 0

hzi¾pn vtxazi l s lsee 3càpncg ivee pnho, 3càpncg ivee 0 lNózi 3cá3ch okhá3c, @bxapn pđxahu vthhu¾vt vtoápn 3cho sphésp

gdzi 3chhumyeepn vtózi pnhhupncg ylòzi cgzixazi 3có 3chxavt ylưopncg vthxasp pđee okhxazi sphá pđưo3c pnhzieehu okhôpncg

Thhu¾vt vtoápn ylhumy¾pn okzilm pđã pđưo3c ásp gdpnpncg 3cho @bàzi vtoápn VRP vtù pnhhupncg pnălm 1990, iví

gdpn pnhư ylà (Olslmxapn1993) ivà (Chzixapncg xapngd Rhulslseeylyl1996) (Txaivxaokokoylzi-kMocghxagdgdxalm eevt

okhoxapncg vthòzi cgzixapn cgzixao hàpncg VRPTW (Veehzi3cylee Rohuvtzipncg Pero@byleelm Tzilmee Wzipngdowls)

Cũpncg cgzixazi @bàzi vtoápn VRPTW, (Bxapn˜Ols eevt xayl.2013) pđee pxhuxavt lm®vt vthhu¾vt vtoápn 3cũpncg gdpnxa

2.3.3 Gzixazi vthhu¾vt gdzi vterhumyeepn

Gzixazi vthhu¾vt gdzi vterhumyeepn (cgeepneevtzi3c xaylcgoerzivthlm) ylà lm®vt vthhu¾vt vtoápn lmô sphopncg qhuá vterìpnh

3cHQ P N Y LQ 3 C vtpn pnhziêpn 3chuxa 3cá3c qhuxapn vthee lszipnh iv¾vt Hoylylxapngd cgziózi vthzi¾hu vthhu¾vt vtoápn gdzi vterhumyeepnvào năm 1960 dna vào thuyet tien hóa cua Darwin, sau đó HQ C trò cua ông là

Dxaivzigd E Goylgd@beeercg lmo er®pncg pnó ivào pnălm 1989 (J Sxagdeecghzi, S Sxagdeecghzi, xapngd

lNzixaokzi2014)