KHOA H O C - C O N G N G H e
- S o 6.,
Nghien cihi bai toan tim tuyen dtfofng di toi ifli ve tieu thu nhien Ueu va phat thai khi gitta hai diem trong mang lifdfi dtfofng giao thong
• KS. N C S . PHAM DlJfC THANH Hgc viin Ky thugt Quin stf
• TS. NGUYIN V I | T PHUONG
• PGS. T S . NGUYEN QUANG D A O Trtfdng Dgi hgc Xay dtfng
T o m tat: Bii bio trinh biy ngi dung bai todn tim tuyen dudng di gida hai diem bat ky trong mang ludi dudng giao thdng theo myc tieu tdi uu ve phit thai khi va tieu thy nhien ligu.
Tir khda: Quy hogch giao thing dd thi, khi thai vd nhien ligu.
Abstract: This paper presents the content problem of road connection in the theoretic plan of road network In order to get the smallest total emissions and fuel consumption to reduce the climate change.
Keyword s: Urban transport planning, emissions and fuel.
1 . D$t van de
Gidm thidu khi thdi giao thdng vd sQ dgng nhien lidu hieu qud Id van de vd eung quan trong, gdp p h i n gidm thieu bien ddi khf hdu cung nhu phuc vg phat then GTVT ben vQnp. Trong_cdng tdc quy hogch mgng ludi dudng, tdc gid da trinh bay cdc bai todn quy hoaeh mang ludi dudng ly t h u y l t theo tieu ehi tdi Uu v l nhien lieu tieu thu vd phdt thdi khi d T g p ehf Cdu dudng [ i ,2] vd d bdo cao tham gia hdi thdo Ha ting giao thdng Viet Nam vdi phat trien ben vdng [3]. Song ddi vdi mgng ludi dudng cd sdn, vdi gid thdnh nhieu lieu (xdng, dau) ngdy cdng dat dd thi mpt vd'n de dat ra ddi vdi ngudi tham gia giao thdng Id c l n xdc dmh tuyen dudng di trong mang ludi sao cho tieu thg nhidn l i d u v d phdt thai khi ft nhdt. Mgc tidu nay cung gdp phan gidm chi p h i d i igi, gidm tieu hao nhien lieu, gidm khf thdi cua ede phUdng tien giao thdng, qua dd gdp phan gidm nhg b i l n ddi khi hdu eung n h u phgc vg mgc tieu giao thdng v d n tai ben vQng.
2. Gidi thigu bai todn tim dUdng di ngan nhd't trong ly t h u y l t do thj
2.1. Ndi dung bii toin
Cho d d thi G (V,E) Id dd thi cd trpng s d a vd z Id 2 dfnh eija dd thi. Hay tim dudng di ed tdng trpng s d nhd n h i t iQ a d i n z.
2.2. Y ttfdng ehung cda cae thuat toin tim dudng di ngan nhit
Cac giai t h u a l dupc phdt trien de gldi bdi todn dgng nay tidu b i l u la cdc thudt todn: Dijkstra, Bellman-Ford
- Dd tim bdng each di qua cdc diem trung gian;
- Neu phdt hien dUdng di qua cde diem trung gian n g i n hdn dudng di hign tai thi se cap nhdt dudng di mdi, ddng thdi chfnh sQa ede thdng tin lien quan;
- SQ dung 2 mdng de luu trQ tgm thdi:
+ Mdng D[v]: LUu trQ dd dai dQdng di ngdn nhat hidn tgi tQ diem a den diem y;
+ Mdng T[v]:^ LUu trQ diem nam trUde didm v tren dudng di ngdn nhd't hien tai.
2.3. Thuat toin Bellman-Ford [6]
Gldi bdi todn ngudn ddn trong trudng hdp trpng sd canh cd the ed gid trj d m . Ap dgng dgpc ciio mpi trudng hpp, lUdng tfnh loan Idn.
2.4. Thugt toin Dijkstra [7]
Gidi bdi todn ngudn ddn neu td't cd cdc trgng s d canh deu khdng d m . Do khdng ed eanh d m ndn tai mdi budc se cd mdt diem ma thdng tin v l nd se khdng ddi v l sau. Tgi mdi bude, ta khdng can phdi kiem tra qua td't ca cdc diem trung gian ma chf thgc hien chpn mdt diem u cd gid i n D[u]
nhd nhd't, chpn u Idm diem trung gian de xdc dmh cac budc ke tiep.
Theo C d quan Nang lupng qudc te [4], khi phdt thai vd nhien lieu tieu thg cua cde phuong tien giao thdng cd C]uan he ty Id thudn n e n ed the sii dgng tieu chi toi uu v l tong khi thdi v d nhien lieu tieu thg lam hdm muc tieu. Mat khde, do nhien lieu tieu thg v a khf thdi eua phUdng tidn giao thdng di ehuyen giQa cdc diem id cdc s d khdng a m ndn thudt loan Dijkstra phu hdp de gldi quyet bdi todn vdi hdm mgc tieu id tdi uu v l tidu thg nhien lieu va phdt thdi khi.
3. Lfng dgng thuat loan Dijkstra de gidi bai toan tim dUdng di t£ii Uu tieu thu nhien lieu va phdt thdi khi giQa 2 die'm trong mang ludi dudng giao thong
6 5
KHOA H O C - C O N G N G H I 3.1. Ngi dung bii toin
Mdt mgng ludi dudng cd n diem thudc tap V, b i l l ehieu ddi vd van tde trung binh khi di ehuyen tren tuyen dudng ndi giQa cdc diem trong mang ludi. Tim dudng di tU diem a d e n diem z trong mgng ludi dudng giao thdng d l phUdng tidn tham gia giao thdng tidu thy nhien lieu vd phdt sinh khf thai ft nhdt.
3.2. Cic btfdc cda thugt todn Dijkstra Theo Dijkstra [7], cdc bUde cua thudt todn Dijkstra nhU sau:
Gpi: L[u,vj - C h i l u ddi tuyen dudng ndi tQ diem u d i n diem v (km);
S[u,v] - Vdn tde trung binh khi di c h u y i n trdn tuyen dudng ndi iQ diem u d i n diem v (km/h).
O mdi diem v, thudt loan Dijkstra xde djnh 3 thdng tin: Chon^, D^ vd truoc,,.
Chon^ • Mang gid tri true hogc false de xde dinh trang thdi dupe chgn cua diem v.
Khdi tgo tat ed edc diem v chua dUdc c h g n , nghTa id: Chon^ = false, V^ e V.
D^ - Tdng nhien lieu lieu thg va k h i p h a t thai cho d i n thdi didm dang xet khi di tU diem a d i n diem v. Khdi tgo, D^ = •», V^eV\{a}, D = 0.
Truoc^- Diem trude etja diem i/lren dudng di tdi uu v l nhidn lieu vd khf ihdi khi di tQ a d i n z.
DQdng dl tdi Qu v l nhidn lieu vd khf thdi tU a d i n z cd dgng (a ,..., truoc^ v,..., z). Khdi tgo, truoc^ = null, V^ G V.
BUdc 1: Khdi tgo: Ddt chon;= false V e I/; D ;=
•», V ^ e l / l { a } , D;.=0.
Sudc 2 ; Chgn v l / s a o c h o e h o n ^ = false vd D^
= min {D, / fG V, chon, = false}.
N l u D^ = thi kit thdc, khdng tdn tgi dudng di tQ a d i n z.
Btfdc 3; Ddnh dau d i l m v, ehon^= true.
eude 4 ; Ndu v = z thi/(e/r/7uc vd D j a tdng khi thdi vd nhidn lieu tieu thg it nhd't khi di W a d i n z.
Ngupc lai, n l u v * z sang Bude 5.
BUdc 5: Vdi moi diem v k l vdi u md chon^ = false, kiem tra.
N e u D ^ > D „ + /.(u,i').[518,257-8,88657.S(u,v)+
0,059146 S(u.v)2]
thi D^= D^ + i.(U,i/).[518,257-8,88657.S(u,v)+
0,059146.S(u,v)2].
Ghi nhd d i l m i^ truoc;= u. Quay lai Budc 2.
Trong dd:
518,257 - 8,88657.V+ 0,059146.V2 la phUdng trinh tfnh tdng khf Ihdi vd tieu thg nhien lidu quy ddi sang CO^ (gCOj/km) cCia d td con theo md hinh tfnh khf thdi Copert III [5] khi xe di chuyen vdi v a n tdc V (km/h).
3.3. Cdi d$t thudt todn Dijkstra tim dudng di tdi uu vi nhiin liiu tiiu thy vi khi phit thai gida 2 diem trong mgng itfdi dtfdng giao thdng bang ngdn ngd lip trinh Pascal
DQ lieu dupc lay tQ t d p Dulieu.txt ed c a u true:
Sau khi l l y dQ lieu, chUdng trinh se xde dmh ed tdn lgi dudng di tdi Uu ve nhien lieu Hdu thg va phdt thdi khi hay khdng, n e u cd tdn tai thi tirn^dudng di dd ddng thdi tim d u d n g di ngdn nhat de so sanh ket q u d . Sau dd luu k i t q u d vdo tdp Ketqua.lxt cd cd'u trUe:
D d n g 1: KHONG C 6 T U Y E N D U C J N G Dl (ndu khdng tin tgi tuyin dtfdng di)
Ddng 1: T U Y E N DUCiNG TOI L/U VE NHIEN LIEU VA KHf T H A I (neu tin tgi)
Ddng 2: Tong phdt thdi khi va tieu thg nhien lieu la: F1(z) g
Ddng 3: T d n g chieu dai Id: D l (z) km Ddng 4: Di theo thQ tQ n h u sau: a => z, => z^
=> ... z => z
D d n g 5 : T U Y E N D U 6 N G N G A N N H A T D d n g 6: T d n g phdt thai khi vd tieu thu nhidn l i e u l a : F 2 ( z 2 ) c |
D d n g 7: T o n g c h i l u ddi Id: D2(z2) km Ddng 8: Di theo thU tU nhU sau: a => z, => z^
= > ... z^ => z 3.4. Vidy
Tim dudng di tU d i l m 1 d i n d i l m 7 sao cho nhien lidu tidu thg v a phdt thdi khi it nhd't, b i l t chieu dai, vdn tde trung binh, hUdng dl cdc cgnh ndi giQa cde didm cho n h u sd dd d Hinh 3.1.
D o n g l
Dong 2 Donni
1 (soitiimj 1 Diemdnu
Idimiiu DxinniD
>,
i liliim^uoi, ' O u r a d a i l k m )
L, U
Vanl w ( k m l i ) ,
!
\,
Hinh 3.1: Sd do minh hoa m^ng ludi dudng giao thdng
File dOii^u dSu vao: (Dulieu.txt) 10 1 7
1 2 1 50 1 5 3 8 0 1 9 3 2 0 1 10 2 60 2 3 4 50 2 5 1 4 0 5 3 2 60 3 4 1 50 6 3 2 60 4 7 6 50 4 8 3 8 0 5 6 5 6 0 5 9 5 8 0 4 6 1 70 6 7 3 20 8 7 4 50 9 6 5 5 0 9 8 3 30 10 9 6 60 0
File kef qui: (Ketqua.tjaj
• T U Y E N BLfONG TOI UU VE N H I E N LIEU V A K H I T H A I :
66
KHOA H O C - C O N G NGHg
- T d n g phdt thdi khf vd tidu thg nhien lieu Id:
2206 g C O ,
- T d n g chieu ddi Id: 10,0km
- Di thep IhUtU nhu sau: 1 = > 2 = > 5 = > 3 = > 4 = > 7
" T U Y E N D U 5 N G D I N G A N N H A T : - T d n g phdt thdi khf vd tieu thu nhien lidu Id:
2376 g C O j
- T d n g chieu ddi Id: 9,0km
- Dl theo thQ t u nhQ sau: 1 =>2=o5=>3=;>4=>6=>7 4. V l d p bai t o a n thUc td'
V i dg cho k i t qud nghien cQu bdi loan nay, tde gid l l y T P . H d Ndi de mmh hga. Bai l o a n : Tim tuyen dUdng tieu thg nhien lidu va phat thai khf ft nhd't di tU Trudng Dgi hgc Didn Lgc (235 Hodng Qude VidL Ha Ndi) de'n Trudng Dai hpe Xdy d g n g (55 Gidi Phdng, Hd Ndi).
Tien hanh khdo sdt vd xdy dgng ed sd dQ lieu cdc t u y I n dudng gdm 2 thdng s d : Chieu dai (km) vd van td'c trung binh d td di ehuyen tren tuyen dudng trong gid eao diem (km/h).
K i t hpp phan mem Google Map ta tim dUpc eae phUdng dn khd thi eho d td di IQ Trudng Dai hpe Didn lgc den TrUdng Dgi hpe Xdy dung H d Ndi ta cd k i t qud nhU sau:
T U Y E N D U 6 N G D I NGAN NHAT - T d n g chieu ddi Id: 9,7km
- T d n g khf thdi vd nhidn lidu tidu t h g : 3419g - D i theo 16 trinh:
Trgdng Dai hgc Didn lgc
=> Hoang Qud'c Viet
=> Phgm Van Ddng
=> Hodng Qudc Viet_
=> Nguyen Phong Sdc
=> Tran D d n g Ninh
=> Cdu Gid'y
=> La Thanh
=> Hodng C l u
=> Xd D a n
=> Gidi Phdng
=> Trudng Ogi hpe Xdy dUng
* T U Y E N D U O N G T O I U U VE NHIEN LIEU VA K H I J H A I :
- T d n g chieu ddi Id: 12,7km
- T d n g khi thdi vd nhidn lidu tidu t h g : 3367g - Dl theo Id trinh:
Trudng Dgi hpe Didn Ipc
=> Hodng Qudc Viet
=> Phgm Vdn Ddng
=> Phgm Hung
=> Dudng trdn cao
=> Nguydn Trai
=> Trudng Chinh
=> Gidi Phdng
=> Trudng Dgi hpe Xdy dgng_
Nhgn xit: Tuyen dUdng ngan nhdt (9,7km) ngdn hdn tuyen dudng tdi uu ve khf thdi vd nhidn lidu (12,7km) tdi 3km nhung Igi phdt thdi vd tidu thp nhidn lidu n h i l u hdn.
5. Kd't tudn
Qua c u n g mdt vi dg sd lieu dau vao nhu trdn nhung khi tim Id trinh tuydn dddng ta thd'y ed s g khac nhau giQa tuydn dQdng ngdn n h a l vd t u y I n dudng cd khi thdi tidu thg vd phat thdi khf ft nhdt.
(0,4km; 25km/h) (0,02km; 20km/h) (0,95km; 25km/h) (0,66km; 20km/h) (0,8km; 20km/h) (1,15km; 15km/h) (2,7km; 15km/h) (0,56km; 35km/h) (1,7km;30km/h) (0,73km; 30km/h)
(0,4km; 25km/h) (0,7km; 20km/h) (0,9km; 40km/h) (5,4km; 70km/h (2,2km; 25km/h) (2,3km; 25km/h) (0,8km; 30km/h)
So 6/2015
Nhu vdy, cd the thay ket qud eua vide tim tuyen dudng di ngdn nhdt chua chac da dam bdo di theo Id trinh dd thi nhien lidu tidu thg vd phdt thai khf Id ft nhdt.
Neu thay ddi sd iieu dau vdo sao cho trdn cac tuyen dudng ngdn cho phep di ehuyen vdi vgn tdc eao hdn v a n tde d cac tuyen dUdng ddi thi ke't qud eua bdi todn tim t u y I n dudng ncjdn nhd't se trung vdi ke't qud vdi bdi todn tim tuydn dudng idi uu vd nhien lieu tieu thg va phat thdi khf.
Cde hdng cung cap cdc phan m e m vd djch vp ban dd s d ed the dp dgng y tudng bdi todn tim tuyen dudng tdi uu ve nhidn lidu tieu thg vd phdt thai khi vdo trong sdn pham ei^a hang minh de phgc vg ngudi sQ dgng dupe tdt hdn. Ddc biet, cdc cdng ty van tai ndn ddc biet luu y tdi bdi todn ndy nham gidm bdt chi phf van tdi va tang ipi nhuan cho doanh nghidp.
Do tuydn dudng di tdi uu ve khi thdi vd nhidn lidu tieu thu se thay doi theo tinh trang lUu thdng (td'c dd) cua t u y I n dudng nen de cd the cap nhdt lien Ige t g y i n dudng tdi Uu ve khf thai vd lieu thg nhien lidu thi tde gid k i l n nghj can nghien eUu xdy dgng hd thdng theo ddi llnh trgng giao thdng c u a ede tuyen phd theo thdi gian thpc. Trdn cd sd dQ lidu thdi gian thgc, cac hang cung edp djch vg ban dd sd cd the lien tgc cdp nhdt tinh trgng iLiu thdng tren ede tuyen dUdng de ed thd tim ra luyen dudng di tdi uu ve nhidn lieu va khi thdi Q
Tdi lidu t h a m k h d o
[1]. Pham DUc Thanh, Nguydn Quang Dgo (5/2013), Nghien cdu bai toan dddng ndi trong quy hoach mang ludi dddng ly thuyet nham gidm thieu BDKH, Tgp chi Cau dUdng.
[2]. Phgm DUe Thanh, Nguydn Quang Dao (9/2013), Nghidn cdu bai todn Itfdi dudng co quan hd vdn tdi gom nhiSu diem trong quy hoach mang ludi dudng ly thuyet nhdm giim thieu BDKH, T a p chi Cau dudng.
[3]. Phgm DUe Thanh, Nguyen Quang D g o , Phgm Cao Thang (17/8/2013), Nghien cdu giam thieu khi nha kinh vd sd dung ndng lUdng hieu qui phuc vu m^ic tieu GTVT ben vdng, Hdi thdo qude gia Hg tang giao thdng Viet Nam vdi phdt tnen b i n vQng, D d Nang, NXB. Xdy dUng, ISBN 978- 604-82-0019-0.
[4] International Energy Agency (2012), CO^
Emissions from fuel combustion highlights.
[5]. European Environment Agency (2000), COPERT III Computer programme to calculate emissions from road transport.
[6]. Bellman, Richard ( 1 9 5 8 ^ On a routing problem. Quarterly of Applied Mathematics, roi.
16, pp. 87-90.
[7]. Dijkslra.E (1959), A note on two problems In connection with graphs, Humensche Mathemalik, V o l . 1 .
N g a y n h g n b a i : 4/5/2015 N g a y c h ^ p n h g n d a n g : 20/5/2015 NgUdi p h d n b i ^ n : PGS. T S . V u Hoai Nam
TS. H o a n g Quo'c L o n g
