TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3515 ~ 35
2
0
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.3535
3515
Re
cei
v
ed
Jun
e
17, 2013; Revi
sed
De
ce
m
ber 10, 201
3; Acce
pted
De
cem
ber 3
1
,
2013
Resear
ch on Real-Time Optimal Path Algorithm of
Urban Transport
Jie Zhang, Ji
anchun Li, Xiao
y
a
n Fan*, Zhuo Den
g
Schoo
l of Com
puter Scie
nce
and C
o
mmun
i
c
a
tion En
gi
neer
i
ng, Z
hengz
ho
u
Universit
y
of L
i
ght Industr
y,
Z
hengZ
h
ou, 45
000
2, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: fanxiao
y
a
n
1
8
@
12
6.com
A
b
st
r
a
ct
Based o
n
the ant colo
ny alg
o
rith
m, urba
n real
-ti
m
e traffic opti
m
a
l
path al
gorith
m
w
a
s desig
n
e
d
through restrict
ing s
earc
h
area and
search
direction of ant
colony system
, making the real
-tim
e traffic
and
distanc
e as th
e opti
m
a
l
path
w
e
ights and r
egar
din
g
in
ters
ection turn
in
g as the i
m
pact
of w
e
ight valu
e
combi
ned w
i
th
Chin
ese situ
ation. T
he al
g
o
rith
m c
oul
d calcul
ate
the opti
m
a
l
path throu
gh al
gor
ithm
complexity test
. We obtained
a traffi
c o
p
ti
ma
l p
a
th w
i
th ti
melin
ess
an
d pr
actical
val
u
e
c
o
mbi
ned
w
i
th
ant
colo
ny al
gorith
m
co
nsid
erin
g
mult
i
p
l
e
par
a
m
eters.T
h
e ob
taine
d
path
en
abl
ed us
er to reach d
e
stin
ati
o
n
w
i
thin a short time a
nd w
i
th the least fuel thr
oug
h ac
tua
l
traffic test. It w
a
s
regar
ded
as the opti
m
a
l
path.
Ke
y
w
ords
: intelli
ge
nt transpo
rtation, the opti
m
a
l
pat
h, rea
l
-time traffic, ant colo
ny alg
o
rith
m
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The daily number of regis
t
er
ed vehic
l
e
has
grown more than 800
vehic
l
es
in Zhengz
hou
in 2012. The
city owned
2 million veh
i
cle
s
till
August 201
2. Ca
r use
r
s are f
a
ce
d with great
difficulty [1] b
y
consi
deri
n
g
the current st
atus.
Except accel
e
rating u
r
ba
n
road con
s
tru
c
tion, path gu
idan
ce and o
p
timization i
s
anothe
r
necessa
ry way to solve
traffic p
r
ob
lems
and
h
e
lp car
use
r
s
get to th
eir d
e
stin
ations
conve
n
iently.
Dijkstra
al
gori
t
hm [2], A* al
gorithm
, gen
e
t
ic
alg
o
rithm
and ant col
o
n
y
algo
rithm [3],
etc are co
m
m
on path o
p
timization
a
l
gorithm
s [4
]. They are
simulated u
n
d
e
r stati
c
pat
h
con
d
ition
s
an
d the wei
ght
value consi
d
ered i
s
o
n
ly the length
of the path.
Except dista
n
ce, path
para
m
eters a
r
e affecte
d
b
y
real-time traffic [3]
and intersectio
n
tu
rning
numb
e
r in urba
n traf
fic.
Turni
ng limita
t
ions, turnin
g time and the delay time ca
n rea
c
h 17%
-35% of total time.
A problem n
e
ed to be solv
ed is ho
w to combi
ne the three p
a
ramet
e
rs: real-tim
e
traffic,
distan
ce
and
intersectio
n
. Since ea
ch p
a
th
ha
s
its co
rre
sp
ondi
ng
real-time
traffic, we
can
re
g
a
rd
each pa
rt of real
-time traffic as a
part
of the
weight
values an
d
each interse
c
tion turning i
s
rep
r
e
s
ente
d
by paramete
r
s [5-8], then
we
can
obt
ai
n a traffic opt
imal path
wit
h
timeline
s
s
and
pra
c
tical val
u
e in combin
a
t
ion with a
n
t colo
ny algo
rithm [9] and t
h
rou
gh
con
s
i
der the
multi
p
le
para
m
eters a
ffecting vehicl
e so a
s
.
2. The Estab
lishment of
Road
Ne
t
w
o
r
k Model
2.1. The Esta
blishment of Urban
Road
s Model
The
compl
e
x urba
n road
traffic net
work ma
ke
s the st
ru
cture
of topologi
ca
l relatio
n
network diagram. Plane i
n
tersection
will be the
analysis
object
of system. T
he urban traf
fic
netwo
rk i
s
a
n
a
lyzed
to pl
a
ne inte
rse
c
tio
n
a
s
sp
lit
poin
t, then the
ro
ad traffic n
e
twork ha
s
be
come
point and lin
e topology n
e
twork
stru
cture. The
stru
cture
rep
r
e
s
e
n
ts a plan
e intersectio
n
a
s
a
point and a
road a
s
a line.
The wh
ole n
e
twork mo
del
can b
e
de
scribed through
grap
h G =
(V, D,
W, A) as i
s
shown in Figu
re 1. V is the
set of
urb
a
n
road n
ode
s;
D is the
wei
ght values from
node Vi to Vj
. W indi
cate
s the delay ti
me when
pa
ssing
nod
e Vj
from Vi to Vk. The pa
ram
e
ter
has di
re
ctivity. A stands for road
line
seg
m
ents an
d ha
s dire
ctivity.
The ro
ad traffic dire
ction a
nd city road
netwo
rk m
o
d
e
l of the interse
c
tion was
built. The
probl
em for real-time p
a
th
is equale
d
to find the
sm
allest weight values b
e
twe
en two nod
es in
the diagram
G (V, D, W, A), which sim
p
l
i
fies the solvi
ng pro
c
e
s
s of path.
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TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3515 – 35
20
3516
2.2. Speed-flo
w
M
odel Se
lection
This sp
eed
-fl
o
w
m
odel
is con
s
i
s
tent wi
th
the
United
States BPR functio
n
an
d
sp
eed
-
flow mo
del
suited for Chi
na traffic is
obtaine
d
fro
m
Chi
n
e
s
e
Ministry T
r
a
n
s
po
rtation
project
named "
H
igh
w
ay Ca
pa
city rese
arch", su
ch a
s
Equatio
n (1).
3
10
23
,/
1(
/
)
V
VU
C
UC
(1)
In Equation (1), V is actua
l
spee
d, and
V0 is
stan
dard spe
ed. U is
the actual vehicl
e
s
and C is the
maximum vehicl
es with
stand by road
.
α
1,
α
2,
α
3
is the regre
ssi
on pa
ram
e
ter
who
s
e val
ue
varies with
di
fferent road
grad
e.
Assu
ming L
is th
e
roa
d
len
g
th,
and
ro
ad tra
v
el
time can be
show in Equ
a
tion (2
):
0
1
)
/
(
V
C
U
L
L
V
L
T
(2)
We
sh
ould
u
pdate
re
al-ti
m
e traffic flo
w
U in
∆
t. The
∆
t
can
dif
f
er a
c
cording
to a
c
tual
situation.
Ge
nerally, the
value i
s
1
0
mi
n. Ro
ad
net
work i
s
refre
s
he
d o
n
ce
∆
t
whi
c
h ca
n kee
p
system out of
continuo
us refres
hing
state and en
sure
a small error. Combine
d
with ant colo
ny
algorith
m
, it
wa
s ado
pted
to study on
urban re
al-time
traffic optimal
path.
2.3. Intersec
tion Dela
y
Model Design
Before
ea
ch
se
ction
s
d
o
wn
stre
am i
n
tersectio
n
ago, the
ve
hicle
line
d
u
p
in
the
downstream
se
ction
s
of column
s and
extends b
a
ck con
s
tantly when the light
turns red. The
vehicle
queue length decreases
cons
tantly when the red li
ght turn
ed off. This is called
scattered
wave fo
rmati
on an
d di
sa
p
pearan
ce. Se
tting the s
pee
d of vehi
cle
q
ueue l
ength
chang
e is fast
er
than wave
sp
eed ba
ck the light turns g
r
e
en,
namely the queu
e ca
n compl
e
tely disap
pea
r.
The
analy
s
is of q
ueue
ve
hicle
s
dissip
a
t
e rate
in t
h
e
interse
c
tion
(by the
jam
to flow)
sho
w
s that th
e delay i
s
rel
a
ted to n
u
mb
er of q
ueui
ng
vehicle
an
d
queu
e di
ssi
p
a
tion rate. Qu
eue
dissipatio
n ra
te is the inte
rse
c
tion
ca
p
a
city C(
t
)
wh
en interse
c
ti
on is
con
g
e
s
ted. The rate
is
inflow rate of
traffic if there is no qu
euin
g
.
Assu
ming do
wn
strea
m
intersectio
n
on
Red ti
me r, the numb
e
r o
f
queuing ve
hicle
s
at
time t se
ction
s
<Vi, Vj >i
s
N an
d the t
r
a
ffic sp
eed
on
the ro
ad
<Vi,Vj> at time t i
s
the flo
w
V,
we
c
an get intersec
tion delay within the time interval
∆
t .The res
u
lt is
s
h
own in Equation (3):
C
t
t
V
r
t
V
r
t
C
t
Q
t
w
2
)
(
)
(
)
(
)
(
)
(
(3)
3. The Optim
a
l Path Ba
se
d on Impro
v
ed An
t Colo
n
y
Algorithm
3.1. Algorith
m
Model-bui
lding
The mo
re
ant
s pa
ss o
n
a
p
a
th and
it ca
n
affe
ct choi
ce
of othe
r ant
s. An optimal
path is
formed
thro
u
gh iterative. The ant
col
ony
algo
rith
m i
s
robu
st and
ea
sy to pa
ram
e
ters.
The
path
is
determi
ned th
roug
h wei
ght, includi
ng dist
ance, real
-time traffic and d
e
lay.
Assu
ming th
ere a
r
e
m a
n
ts at sta
r
tin
g
poi
nt. Th
e
path is
<Vi,
Vj>. Wei
ght i
s
d.
τ
is
pheromo
ne o
n
the p
a
th.
η
is p
a
th visibili
ty or expe
ctat
ions to
choo
se <Vi,Vj> wit
h
a valu
e of
1 /
dij. Allowed
k
is the next selecte
d
set of
node
s.
α
is
stimulating
p
hero
m
on
e factor.
β
is
de
sir
e
d
inspi
r
ation fa
ctor. The
n
an
ts cho
o
se a p
a
th to
Vj. The proba
bility can be sho
w
n
in Equation (4).
else
allowed
j
p
k
allowed
j
ij
ij
ij
ij
ij
k
0
(4)
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TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Real
-Tim
e Optim
a
l Path Algorithm
of Urban Tran
spo
r
t (Jie Zha
ng)
3517
This p
a
th ph
erom
one
will be upd
ated a
fter an ant ch
ooses a p
a
th
. It can be sh
own in
Equation (5).
1
(1
)
1
(
)
,
(
)
f
r
ij
ij
ij
ij
ij
r
Q
tt
d
(5)
In Equation
(5), t is numb
e
r
of iteration
s
,
ρ
is phe
romo
ne evapo
ratio
n
coeffici
ent.
τ
ij(t+1)
rep
r
e
s
ent
s p
hero
m
on
e
ch
ange
s i
n
n
e
xt iteration
on
<vi,vj>.
∆τ
ij
i
s
in
crea
sed
pheromo
ne
whe
n
ants choo
se
<vi,vj>. Q is the quality factor of
pherom
one, whi
c
h i
s
a con
s
tant, often taken 1.
Optimal network
path is o
b
tained by combinin
g the
actual mod
e
l road n
e
twork
an
d
improvin
g the
basi
c
ant col
ony algorith
m
.
3.2. Optimization of Tim
e
liness
If we consi
d
er the wh
ole
city node
s, it
will
nee
d a long com
putati
on time. In real driving
situation, the
y
are limite
d
to so
me a
r
e
a
s
un
de
r
r
eal
f
a
ct
or
s su
ch a
s
t
i
me, fuel
consumption
a
nd
traffic. Ant colony algo
rithm
ca
n be
sim
p
l
i
fied if
the rea
s
on
able
se
arch
of
a rang
e
of area
can
be
sele
ct
ed.
Selection
of
sea
r
ch
are
a
i
s
sho
w
n
in
F
i
gure
2.
The
recta
ngul
ar I
is fo
rmed
ba
sed
on
diago
nal re
ct
angle of sta
r
t and en
d. The
recta
ngle
ca
n be used a
s
the smalle
st
area to
cal
c
ul
ate
optimal p
a
th, but
we
sh
ou
ld be
mag
n
ified the
sea
r
ch a
r
ea
be
cau
s
e
of the
re
striction
s
in
re
al
traffic. Extending the
diag
onal fo
r oute
r
of sta
r
t an
d end
point
s to take i
n
terse
c
t nod
es,
we
sho
u
ld scale
out
1
-
2 nod
e
s
on the diag
onal of
recta
ngle I. The search area is enlarg
ed fro
m
recta
ngul
ar I to recta
ngul
ar
II.
A vector is fo
rmed
from
be
ginnin
g
to e
n
d
, as
is sho
w
n in Fi
gu
re
3. Algorithm
co
mputing
spe
ed can b
e
accele
rate
d and the
complexity ca
n be re
du
ce
d throu
gh m
a
kin
g
the se
arch
dire
ction alm
o
st acco
rd wit
h
vector du
rin
g
the pro
c
e
s
s.
Value of
η
ij controls
direction.
η
ij re
prese
n
ts exp
e
ctations
that
a
n
ts choo
se
the pat
h
<vi,vj>. The
pa
ramet
r
ic
dje, dje
represe
n
ts
li
nea
r dista
n
ce from vj to ta
rget
point, a
n
d
para
m
eters d
j
e aims to st
rengt
he
n the sea
r
ch directi
on.
λ
1 a
nd
λ
2 rep
r
e
s
ent t
he scale fa
ct
or .It
can b
e
sh
own in Equation
(6).
12
12
1
1/
,
(
1
)
ij
ij
ij
j
e
d
dd
(6)
Ant colo
ny al
gorithm
is re
stricted
from
sear
ch area a
nd
di
re
ction, and
th
e com
p
lexity
of
the algorithm is greatly reduced. It
will be proved by following instances.
3.3. Obtainm
e
nt of
the O
p
tim
a
l Path Weigh
t
The o
p
timal p
a
th in sy
stem
is ba
se
d o
n
time, namely t
he optim
al pa
th is the
path
whi
c
h
tak
e
s
the
s
h
ortes
t
time. I
n
order to mak
e
the
cal
c
ulation of the
optimal path
timely, real-t
ime
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02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3515 – 35
20
3518
Speed
-flow a
nd interse
c
tion delay time sho
u
ld be
rega
rde
d
a
s
part
s
of the weig
ht value.
Namely, the model of valu
e is esta
blish
ed throu
gh th
ese two facto
r
s.
Assu
ming
th
e path
length
is
L. S is th
e av
erage
ve
hicle
length,
r represents
red li
ght
time of intersection. The
re
sults a
r
e
sho
w
n in Equatio
n (7).
r
t
V
CS
t
t
V
t
V
LC
t
QCV
ij
)]
(
)][
(
)
(
[
2
)
(
2
(7)
12
12
2(
)
,(
1
)
{
2
[
(
)
(
)][
(
)
]
}
2
(
)
ij
je
CV
t
L
C
Vt
Vt
t
C
S
V
t
r
C
V
t
d
(8)
Whe
n
ant col
ony algo
rithm
values
cha
n
ge,
η
ij and
∆τ
ij will ch
ang
e. Then valu
e of pij is
affected
, and finally we sh
ould sele
ct the optimal pat
h.
4. Applicatio
n Experimen
t
The timeli
ne
ss a
n
d
effectiv
ene
ss ba
se
d
on im
pr
ove
d
ant colony
al
gorithm
is verified by
an example, takin
g
part in
Zheng
zh
ou City. The map is sh
own in Figure 4.
The m
a
p
is a
b
stra
cted
a
s
a net
wo
rk mo
del
diag
ram with weig
ht. There are 21
node
s in
the diag
ram
and the
flow of path
s
i
s
measured
sh
own i
n
Fig
u
re 5. Di
re
ctio
n of the
arro
w i
s
pointed f
r
om
vi to vj. Times of e
a
ch inte
rse
c
tion
traffi
c light
s h
a
ve
been te
sted
to obtain
the
d
a
ta
in advan
ce. If steerin
g is p
r
ohibited, the time of traffic lights is infinit
e
(
∞
).
We ta
ke
α
= 1,
β
= 2, Q
= 1,
λ
1
= 0.4,
λ
2 =
0.3,
λ
3
=
0.3,
α
1 = 1
.
00,
α
2 = 1.8
8
,
α
3 =
7.00. The
pro
c
e
ss i
s
im
ple
m
ented
by using MATLAB
7.
0. It is verifi
ed by
sele
ctin
g the
same
time
for thre
e con
s
e
c
utive day
s in different
st
arting
a
nd e
n
d
ing for
auth
enticatio
n: Experim
ent A: A1
-
A2; Experime
n
t B: B1-B2;
Experiment C: C1-C2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Real
-Tim
e Optim
a
l Path Algorithm
of Urban Tran
spo
r
t (Jie Zha
ng)
3519
The b
a
si
c a
n
t
colony al
go
rithm and th
e
improve
d
ant
colo
ny algo
ri
thm we
re
co
mpared
in timeliness
and a
c
tual jo
urney time.
4.1. Algorithm Simulatio
n
Test
Test
s a
r
e
written by
Usi
ng MATLAB.
The tim
e
lin
ess of th
e
algorith
m
i
s
made
a
c
o
mparis
on firs
tly.
As can b
e
se
en from
Figu
re 6, It can
be
see
n
that the
improve
d
ant
colo
ny algo
ri
thm on
the co
nverge
nce
rate i
s
better tha
n
basi
c
a
n
t co
lony algo
rith
m in term
s
of timeline
s
s or
optimizatio
n capabilitie
s.
As can b
e
se
en from Expe
riment A, the two
cu
rves a
r
e not su
bsta
ntially chan
g
ed after
50 iteration
s
.
However, the improve
d
ant colony
alg
o
rithm ha
s g
o
t its optimal value after 28
iteration
s
. It
can be
see
n
that the imp
r
oved ant
col
ony algorith
m
on the co
nverge
nce ra
te is
signifi
cantly b
e
tter than
ba
sic ant
colo
n
y
algor
ith
m
.As
can
be
se
e
n
from
Experi
m
ent B, opti
m
al
path wei
ghts obtained fro
m
improved
ant colo
ny al
gorithm i
s
lower tha
n
tha
t
from basi
c
ant
colo
ny alg
o
rithm, so
the cal
c
ulati
on
spe
ed of im
proved
alg
o
rithm in
crease
signifi
cantly.Experime
n
t C proved o
n
ce again the
con
c
lu
sion
s of A and B.
4.2. Actu
al Trav
el Time T
est
For different
algo
rithm
s
, we m
ade
a
c
tual travel
time text. As sa
me weight v
a
lue i
s
obtaine
d from
A, two different algorithm
s
in B and C wil
l
be tested.
Experiment
B ,ant colon
y
algo
rithm
p
a
th is
:
B1-v1
9
-v14
-v8-v7
-v6-B2. It
cont
ains five
intersectio
n
s,
v19-v14 and
v8-v7 road a
r
e co
nge
st
ed
to delay travel time. Improved ant colo
ny
algorith
m
pat
h is: B1-v19-v
18-v15
-
v16
-
v6-B
2. Five intersectio
n
s a
r
e contai
ned.
Experiment
C, ant
col
ony algo
rith
m pat
h is
:
C
1
-
v
2-
v9-
v
8-
v7-
v
6-
v16-C
2
. Six
intersectio
n
s are contai
n
ed. v8-v7 is conge
st
ed t
o
delay travel time. Improved ant col
ony
algorith
m
pat
h is: C1
-v2- v
3
-v4-v5
-v6-v1
6-C2, six
inte
rse
c
tion
s a
r
e
contain
ed, while the path
is
smooth.
The
im
proved
ant col
ony algorith
m
can
re
du
ce
th
e u
s
er's path
tra
v
el time a
c
co
rding
t
o
Table 1. The
results a
r
e sh
own in Ta
ble
1.
Table 1. Co
m
pari
s
on of Act
ual Travel Ti
me
Algorithm
Basic ant colony
algorithm
Improved Ant Co
lon
y
Algorithm
(B)
(B)41
mi
n
(B)30mi
n
(C)
(C)32
mi
n
(C)25mi
n
In summa
ry, improve
d
ant
colony alg
o
ri
thm is
su
pe
rior to ba
sic a
n
t colony alg
o
rithm i
n
timeliness an
d sele
ction of
optimal path, and user
s ca
n quickly find the optimal p
a
th to drive.
5. Conclusio
n
The o
p
timal p
a
th algo
rithm
of urb
an
real
-time traffic i
s
based o
n
a
n
t
colo
ny algo
rit
h
m for
recta
ngul
ar
restri
ction
s
an
d limit
ations dire
ction,
det
ermin
ed weig
hts by the
re
al-time traffi
c
and
distan
ce, an
d
con
s
ide
r
ing i
n
tersectio
n
. Throu
gh the a
c
tual test, con
c
lu
sion
s are as follo
ws:
(1) We can cal
c
ulate
th
e optimal
path
i
n
a
short tim
e
throu
gh
re
ctangle rest
rict
ion an
d
dire
ction restriction for the
ant colo
ny algorithm,
(2)
The
opti
m
al path,
whose
weig
ht value
i
s
de
termine
d
by
real
-time t
r
affic an
d
distan
ce
an
d
is
add
ed
b
y
the inte
rse
c
tion tu
rnin
g
facto
r
s,
ca
n
help
the
users g
e
t to th
eir
destin
a
tion wi
thin a sho
r
t time and with l
e
ss fuel.
(3) If there is emerg
e
n
c
y situation and t
he user
want
s to re-sel
ect
the optimal p
a
th, the
algorith
m
will
re
-sele
c
t the
optimal
path
ba
sed
on
re
gardi
ng th
e l
o
catio
n
of
user
as a
sta
r
ting
point.
In co
nclu
sio
n
, the optim
al path
algo
rithm of re
al-time traffic
h
a
s
high vali
dity and
practicability for car
users i
n
the city.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3515 – 35
20
3520
Referen
ces
[1]
YANG Li. An Optimist
ic P
a
th Alg
o
rithm
for Lo
gistics
T
r
ansportatio
n
Base
d o
n
D
y
namic
T
r
affi
c
Information.
Pa
ckagi
ng En
gin
eeri
n
g
. 20
10; 3
1
(23): 10
2-1
0
4
.
[2]
GE Li. Stu
d
y
on
Pla
n
n
i
ng
Method
of Op
timum Ro
ute
i
n
Mu
lti-scal
e
Roa
d
N
e
t
w
ork
s
Base
d
on
Dijksrac
a’s Algorithm.
Journ
a
l
of Hubei U
n
iv
ersity for Natio
naliti
e
s.
20
12; 30(3): 27
8-2
8
0
.
[3]
CHEN L
i
an
g, HE W
e
i, HAN Liq
un. Stud
y o
n
an ur
ban tra
n
sportati
on o
p
timal p
a
th al
go
rithm.
CAA
I
T
r
ansactio
n
s o
n
Intelli
ge
nt Systems
. 20
12; 7
(
2): 167-1
73.
[4]
W
A
N W
e
i, LIU
Ye, LI L
i
-ho
ng.
Rese
arch
on
optim
a
l
p
a
th s
e
arch
alg
o
rithm
ado
ptin
g u
n
io
n
optimiz
atio
n
method.
Co
mp
uter Engi
ne
erin
g and Ap
pl
icati
ons
. 200
7; 43(
30): 97- 10
0.
[5]
W
A
NG W
e
i.Hi
gh
w
a
y Sp
ee
d-
F
l
o
w
practica
l
relati
onsh
i
p
m
ode
l.
Jo
urna
l
o
f
South
east U
n
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. 2
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25(7): 48
7-4
9
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.
[6]
WANG
Yaw
e
n
，，
W
A
NG Xili
CAO Han. Sh
ortest route-p
l
ann
i
ng al
gorith
m
w
i
t
h
in d
y
n
a
m
ic
restricted
search-i
ng ar
e
a
.
Applic
atio
n Rese
arch of C
o
mputer.
20
07;
24(7): 89-9
1
．
[7]
Hossei
n
Miar
Naimi, Nim
a T
aher
ine
j
a
d
. Ne
w
r
obust a
nd
efficient a
n
t co
lon
y
a
l
g
o
rithm
s
: Using n
e
w
interpr
e
tatio
n
o
f
local up
dati
n
g
process
. Expe
rt Systems w
i
th Applic
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. 2
009; 36(
1): 481
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[8]
BAI Chen.T
he Selectio
n of
t
he Ro
uteW
eight for Optim
u
m Path
Alg
o
r
ithmin the T
r
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rtatio
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Net
w
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Ch
in
a Mana
ge
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Informati
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200
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[9]
W
A
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R
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on W
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rel
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ss
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r
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11; 28(6): 1
21-
124.
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