设为首页
加入收藏
期刊导航
网站地图
首页
期刊
数学与物理
地球与环境
信息通讯
经济与管理
生命科学
工程技术
医药卫生
人文社科
化学与材料
会议
合作
新闻
我们
招聘
千人智库
我要投稿
办刊
期刊菜单
●领域
●编委
●投稿须知
●最新文章
●检索
●投稿
文章导航
●Abstract
●Full-Text PDF
●Full-Text HTML
●Full-Text ePUB
●Linked References
●How to Cite this Article
AdvancesinAppliedMathematics
A^
ê
Æ
?
Ð
,2022,11(9),6192-6198
PublishedOnlineSeptember2022inHans.http://www.hanspub.org/journal/aam
https://doi.org/10.12677/aam.2022.119653
ä
l
N
þ
å
Ï
þ
ï
6
Ž
{
ï
Ä
±±±
ŒŒŒ
-
Ÿ
¢
½
…
’
Æ
§
-
Ÿ
Â
v
F
Ï
µ
2022
c
8
1
F
¶
¹
^
F
Ï
µ
2022
c
8
30
F
¶
u
Ù
F
Ï
µ
2022
c
9
6
F
Á
‡
©
3
0
Wardrop
²
;
Ï
þ
ï
n
Ä
:
þ
§
-
:
0
ä
l
N
þ
å
Ï
þ
ï
n
§
¿
|
^
Beckmann
ú
ª
§
r
ä
l
N
þ
å
Ï
þ
ï
6
O
Ž
¯
K
=
z
¤
ê
Æ
5
y
¯
K
§
3
d
Ä
:
þ
E
ä
l
N
þ
å
Ï
þ
ï
6
Ž
{
§
Ó
ž
Þ
~
é
Ž
{
?
1
?
˜
Ú
`
²
"
'
…
c
ä
l
N
þ
å
§
Ú
´
»
§
Beckmann
ú
ª
§
Ž
{
§
þ
ï
6
ResearchontheAlgorithmofTraffic
EquilibriumFlowwithArcCapacity
Constraint
DaqiongZhou
ChongqingCityVocationalCollege,Chongqing
Received:Aug.1
st
,2022;accepted:Aug.30
th
,2022;published:Sep.6
th
,2022
Abstract
BasedontheintroductionofWardropsclassicaltrafficequilibriumprinciple,this
©
Ù
Ú
^
:
±
Œ
.
ä
l
N
þ
å
Ï
þ
ï
6
Ž
{
ï
Ä
[J].
A^
ê
Æ
?
Ð
,2022,11(9):6192-6198.
DOI:10.12677/aam.2022.119653
±
Œ
paperfocusesontheprinciple oftrafficequilibriumflowwitharccapacityconstraint,
andmakesuseofBeckmannformula,thecalculationproblemoftrafficequilibrium
flowwitharccapacityconstraintistransformedintoamathematicalprogramming
problem,andthealgorithmoftrafficequilibriumflowwitharccapacityconstraintis
constructed.
Keywords
ArcCapacityConstraint,SaturatedPath,BeckmannFormula,Algorithm,
EquilibriumFlow
Copyright
c
2022byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution InternationalLicense(CCBY4.0).
http://creativecommons.org/licenses/by/4.0/
1.
Ú
ó
C
c
5
§
du
¬
ˆ
•
¡
¯
„
u
Ð
§
´
×
l
¯
K
3
¢
½
F
ª
î
-
§
•
)û
¢
½
´
Ï
×
l
¯
K
§
~
f
•
<
Ñ
1
¤
§
Ò
I
‡
k
ê
Æ
.
â
U
)û
¯
K
"
²
;
Wardrop[1]
Ï
þ
ï
.
Ì
‡
^
5
)û
p
„
ú
´
×
l
¯
K
§
é
)û
¢
½
´
Ï
×
l
¯
K
k
˜
½
Û
•
5
§
Ï
d
“
<
r
Wardrop
Ï
þ
ï
.
?
1
U
?
§
3
.
¥
\
\
´
»
9
l
ï
Ä
§
r
.
í
2
ä
l
N
þ
å
Ï
þ
ï
.
[3,4]
¿
?
1
ï
Ä
§
'
u
Ï
þ
ï
¯
K
Ù
¦
ï
Ä
„
[5–8]
"
•
)û
Ï
þ
ï
6
O
Ž
¯
K
§
Beckmann
<
r
Wardrop
Ï
þ
ï
¯
K
†
ê
Æ
5
y
¯
K
é
X
å
5
[2]
§
^
ê
Æ
5
y
.
)û
Ï
þ
ï
6
O
Ž
¯
K
§
ù
•
•
Ï
þ
ï
6
O
Ž
J
ø
n
Ø
Ä
:
"
3
©
¥
§
·
‚
Ï
L
ê
Æ
5
y
E
ä
l
N
þ
å
Ï
þ
ï
6
Ž
{
§
¿
Þ
~
é
Ž
{
?
1
`
²
§
'
u
Ï
þ
ï
6
Ù
¦Ž
{
ï
Ä
„
[9–11]
"
2.
ý
•
£
3
Ï
ä
¥
§
V
•
!
:
8
Ü
§
E
•
k
•
l
8
Ü
§
W
•
OD
:é
£
å
:
/
ª
:
¤
8
Ü
§
é
?
Û
ω
∈
W
§
P
ω
•
OD
:é
ω
´
»
8
Ü
§
P
K
=
∪
ω
∈
W
P
ω
,m
=
|
K
|
"
D
=(
d
ω
)
ω
∈
W
•
I
¦
•
þ
§
Ù
¥
d
ω
(
>
0)
•
OD
:é
ω
Ï
I
¦
þ
§
é
?
Û
l
a
∈
E
§
x
a
∈
R
+
=
{
z
∈
R
:
z
≥
0
}
•
l
þ
6
þ
"
é
?
Û
ω
∈
W
§
k
∈
P
ω
§
^
x
k
(
≥
0)
k
•
´
»
þ
Ï
6
þ
"
¡
x
=(
x
k
)
T
k
∈
K
∈
R
m
+
=
{
(
z
1
,z
2
,
···
,z
m
)
∈
R
m
:
z
i
≥
0
,i
=1
,
2
,
···
,m
}
•
´
»
6
(
{
¡
6
)
"
´
•
§
é
l
a
∈
E
§
x
a
=
P
ω
∈
W
P
k
∈
P
ω
δ
ak
x
k
§
l
a
á
u
´
»
k
ž
§
δ
ak
= 1
§
l
a
Ø
á
u
´
»
k
ž
§
δ
ak
= 0
"
^
C
=
DOI:10.12677/aam.2022.1196536193
A^
ê
Æ
?
Ð
±
Œ
(
c
a
)
a
∈
E
L
«
N
þ
•
þ
§
Ù
¥
c
a
(
>
0)
L
«
l
a
þ
Ï
6
N
þ
"
é
?
Û
l
a
∈
E
§
3
l
a
þ
6
þ
I
÷
v
e
¡
N
þ
å
^
‡
:
c
a
≥
x
a
≥
0
§
Ó
ž
§
é
?
Û
OD
:
é
ω
∈
W
§
6
x
I
‡
÷
v
e
¡
I
¦
å
^
‡
:
P
k
∈
P
ω
x
k
=
d
ω
"
r
Ó
ž
÷
v
I
¦
å
^
‡
Ú
N
þ
å
^
‡
6
x
¡
•
Œ
1
´
»
6
(
{
¡
Œ
1
6
)
"
Œ
1
6
8
Ü
^
A
=
{
x
∈
R
m
+
:
∀
ω
∈
W,
P
k
∈
P
ω
x
k
=
d
ω
and
∀
a
∈
E,c
a
≥
x
a
≥
0
}
L
«
"
3
©
¥
§
é
?
Û
ω
∈
W
§
b
Ï
I
¦
d
ω
´
ØC
§
¿
…
A
6
=
∅
"
´
•
§
8
Ü
A
´
˜
‡
;
à
8
"
é
a
∈
E
§
^
t
a
=
t
a
(
x
a
) =
t
a
(
x
)
∈
R
+
L
«
l
a
þ
¤
§
é
?
Û
ω
∈
W,k
∈
P
w
§
b
½
´
»
k
þ
¤
t
k
´
´
»
þ
¤
k
l
¤
ƒ
Ú
§
=
t
k
(
x
) =
P
a
∈
E
δ
ak
t
a
(
x
)
"
Ï
ä
˜
„
L
«
•
ℵ
=
{
V,E,W,D,C
}
"
3.
Ï
þ
ï
K
9
Beckmann
ú
ª
3
Ï
þ
ï
6
O
Ž
¥
§
du
z
‡
<
Ñ
1
8
IØ
Ó
§
é
•
þ
Ï
þ
ï
6
O
Ž
ï
Ä
L
u
E
,
§
Ï
d
·
‚
•
é
I
þ
Ï
þ
ï
6
O
Ž
?
1ï
Ä
§
Ï
d
e
¡
Ï
þ
ï
K
þ
•
I
þ
Ï
þ
ï
K
"
½
Â
3.1.(Wardrop
Ï
þ
ï
K
).
[1]
Œ
1
6
x
∈
A
1
¡
•
þ
ï
6
§
•
‡
÷
v
∀
ω
∈
W,
∀
k,j
∈
P
ω
,t
k
(
x
)
−
t
j
(
x
)
>
0
⇒
x
k
= 0
.
þ
ï
6
x
¡
•
Ï
þ
ï
¯
K
˜
‡
)
"
d u
²
;
Ï
þ
ï
.
Û
•
5
§
Ï
d
“
<
3
ï
Ä
¥
O
\
é
´
»
9
l
ï
Ä
§
r
²
;
Ï
þ
ï
.
í
2
ä
l
N
þ
å
Ï
þ
ï
.
"
„
e
¡
½
Â
[4]
"
½
Â
3.2.
é
Œ
1
6
x
∈
A,a
∈
E
,
i)
X
J
x
a
=
c
a
§
K
a
´
x
˜
^
Ú
l
§
Ä
K
§
a
´
x
˜
^
š
Ú
l
;
ii)
é
OD
:é
ω
∈
W
§
´
»
k
∈
P
ω
§
X
x
˜
^
Ú
l
á
u
´
»
k
§
K
´
»
k
¡
•
x
˜
^
Ú
´
»
§
Ä
K
¡
´
»
k
•
x
˜
^
š
Ú
´
»
"
½
Â
3.3.(
ä
l
N
þ
å
Ï
þ
ï
K
).
6
x
∈
A
¡
•
ä
l
N
þ
å
Ï
þ
ï
6
§
•
‡
÷
v
X
e
^
‡
µ
∀
ω
∈
W,
∀
k,j
∈
P
ω
,t
k
(
x
)
−
t
j
(
x
)
>
0
⇒
x
k
= 0
½
ö
j
´´´
666
x
˜˜˜
^^^
ÚÚÚ
´´´
»»»
.
r
6
x
•
¡
•
ä
l
N
þ
å
Ï
þ
ï
¯
K
)
"
˜
„
œ
¹
e
·
‚
^
Γ =
{ℵ
,A,t
}
L
«
ä
l
N
þ
å
Ï
þ
ï
¯
K
)
"
é
u
ä
l
N
þ
å
Ï
þ
ï
¯
K
Γ=
{ℵ
,A,t
}
§
Ï
L
E
X
e
ê
Æ
5
y
¯
K
Q
5
O
Ž
Ï
þ
ï
6
:
DOI:10.12677/aam.2022.1196536194
A^
ê
Æ
?
Ð
±
Œ
Minz
(
x
) = Σ
a
∈
E
R
x
a
0
t
a
(
x
)
dx
s.t.
P
k
x
k
=
d
ω
,
∀
ω
∈
W,k
∈
P
ω
x
a
=
P
ω
P
k
x
k
δ
ak
≤
c
a
,
∀
a
∈
E,ω
∈
W,k
∈
P
ω
x
k
≥
0
,
∀
ω
∈
W,k
∈
P
ω
.
þ
ª
¡
•
2
Â
Beckmann
ú
ª
"
e
¡
(
Ø
„
[9]
"
|
^
Beckmann
ú
ª
O
Ž
Ï
þ
ï
6
§
I
y
²
ê
Æ
5
y
¯
K
)Ò
´
Ï
þ
ï
6
§
Ï
d
Ú
^
±
e
(
Ø
"
Ú
n
3.1.[9]
é
ä
l
N
þ
å
Ï
þ
ï
¯
K
{ℵ
,A,t
}
§
X
J
é
?
Û
a
∈
E
§
t
a
(
x
)
3
R
m
+
þ
ë
Y
§
¿
…
x
∈
A
´ê
Æ
5
y
Q
)
§
@
o
§
x
´
Ï
þ
ï
6
"
^
P
s
ω
L
«
Œ
1
6
x
'
u
OD
:é
ω
¤
k
Ú
´
»
8
Ü
§
P
T
ω
= max
k
∈
P
ω
{
t
k
:
x
k
>
0
}
,
e
T
ω
=
(
T
ω
,
XXX
JJJ
P
s
ω
=
P
ω
min
k
∈
P
ω
\
P
s
ω
{
t
k
}
,
XXX
JJJ
P
s
ω
6
=
P
ω
.
4.
ä
l
N
þ
å
Ï
þ
ï
6
Ž
{
þ
¡
·
‚
0
Beckmann
ú
ª
í
2
ª
§
ù
Ò
•
Ï
þ
ï
6
O
Ž
J
ø
n
Ø
Ä
:
§
Ï
d
·
‚
3
O
Ž
Ï
þ
ï
6
L
§
¥
§
|
^
d
ú
ª
§
,
^
Lingo
^
‡O
Ž
Ñ
Ï
þ
ï
6
"
du
ä
l
N
þ
å
Ï
þ
ï
¯
K
·
A
5
2
§
k
éÐ
ï
Ä
d
Š
§
Ï
d
3
d
ú
ª
Ä
:
þ
§
E
ä
l
N
þ
å
Ï
þ
ï
6
Beckmann
ú
ª
í
2
ª
Ž
{
§
¿
^
ä
N
~
f
\
±
`
²
"
3
O
Ž
ä
l
N
þ
å
Ï
þ
ï
6
L
§
¥
§
·
‚
k
X
e
b
µ
é
?
Û
α
∈
E
§
t
α
(
·
)
3
R
r
+
þ
´
ë
Y
§
d
ž
§
é
?
Û
α
∈
E
§
k
∈
P
ω
§
´
»
¤
¼
ê
t
α
(
·
)
3
R
r
+
þ
´
ë
Y
§
Ï
d
§
Ï
þ
ï
6
•
3
"
P
K
=
∪
ω
∈
W
,W
=
{
ω
1
,ω
2
,
···
,ω
v
}
.
Ù
¥
§
v
•
ê
"
5.
Ï
þ
ï
6
Ž
{
Þ
~
3
Ï
þ
ï
6
O
Ž
¥
§
é
÷
v
N
þ
å
Ú
I
¦
å
ä
l
N
þ
å
Ï
þ
ï
6
O
Ž
¯
K
§
A^
±
þ
Beckmann
ú
ª
í
2
ª
§
E
Beckmann
ú
ª
Ž
{
§
©
±
e
n
‡
Ú
½
¤
µ
1
˜
Ú
µ
é
Ø
Ó
:é
§
r
¤
k
l
O
:
D
:
´
»
é
Ñ
5
§
¿
r
¤
k
:é
´
»
L
«
Ñ
5
"
1
Ú
µ
é
¤
k
:é
¤
k
´
»
§
Ž
Ñ
z
^
l
þ
¤
k
´
»²
L
´
»
6
§
=
r
l
þ
¤
k
´
»
²
L
´
»
6
ƒ
\
"
DOI:10.12677/aam.2022.1196536195
A^
ê
Æ
?
Ð
±
Œ
1
n
Ú
µ
E
±
e
ê
Æ
5
y
¯
K
(
MP
2
)
§
|
^
Lingo
^
‡
¦
Ñ
ä
l
N
þ
å
Ï
þ
ï
6
"
Minz
(
x
) =
P
a
∈
E
R
x
a
0
t
a
(
x
)
dx
s.t.
P
k
x
k
=
d
ω
,
∀
ω
∈
W,k
∈
P
ω
x
a
=
P
ω
P
k
x
k
δ
ak
≤
c
a
,
∀
a
∈
E,ω
∈
W,k
∈
P
ω
x
k
≥
0
.
∀
ω
∈
W,k
∈
P
ω
e
¡
Þ
~
§
^
Beckmann
ú
ª
í
2
ª
O
Ž
Ï
þ
ï
6
"
~
µ
•
Ä
ä
l
N
þ
å
Ï
þ
ï
¯
K
£
„
ã
1
¤§
Figure1.
Thefigureoftrafficnetwork
ã
1.
Ï
ä
ã
Ù
¥
V
=
{
1
,
2
,
3
,
4
,
5
,
}
§
E
=
{
e
1
,e
2
,e
3
,e
4
,e
5
,e
6
,e
7
,e
8
}
,
C
=
{
5
,
6
,
5
,
8
,
7
,
9
,
8
,
6
}
,
W
=
{
ω
1
,ω
2
}
=
{
(1
,
5)
,
(2
,
4)
}
,D
= (
d
ω
1
,d
ω
2
) = (11
,
10)
.
¿
…
k
t
e
1
(
x
e
1
)=20
x
2
e
1
+12,
t
e
2
(
x
e
2
)=2
x
2
e
2
+80,
t
e
3
(
x
e
3
)=3
x
2
e
3
+25,
t
e
4
(
x
e
4
)=3
x
2
e
4
+15
§
t
e
5
(
x
e
5
)=
x
2
e
5
+60
§
t
e
6
(
x
e
6
)=4
x
2
e
6
+30
§
t
e
7
(
x
e
7
)=3
x
2
e
7
+113
§
t
e
8
(
x
e
8
)=6
x
e
8
"
d
ã
•
1
˜
Ú
µ
é
O/D
:é
ω
1=(1,5)
§
P
ω
1
•
¹
´
»
l
1
=
{
e
1
}
§
l
2
=
{
e
5
e
6
}
,
§
l
3
=
{
e
5
e
4
e
7
}
¶
é
O/D
:é
ω
2=(2,4)
§
P
ω
2
•
¹
´
»
l
4
=
{
e
6
e
2
}
,
§
l
5
=
{
e
4
e
3
}
§
l
6
=
{
e
4
e
7
e
2
}
"
DOI:10.12677/aam.2022.1196536196
A^
ê
Æ
?
Ð
±
Œ
1
Ú
µ
P
x
= (
x
1
,x
2
,x
3
,x
4
,x
5
,x
6
)
T
∈
R
6
+
.
Ù
¥
x
j
L
«
´
»
l
j
þ
6
þ
(
j
= 1
,
2
,
···
,
6)
§
Ï
d
§
k
x
e
1
=
x
1
§
x
e
2
=
x
4
+
x
6
§
x
e
3
=
x
5
§
x
e
4
=
x
3
+
x
e
5
+
x
e
6
§
x
e
5
=
x
2
+
x
e
3
§
x
e
6
=
x
2
+
x
4
§
x
e
7
=
x
3
+
x
6
§
x
e
8
= 0
§
Œ
•
R
x
e
1
0
t
e
1
(
x
)
dx
=
R
x
e
1
0
(20
x
2
+12)
dx
=
20
3
x
3
e
1
+12
x
e
1
=
20
3
(
x
1
)
3
+12
x
1
)
,
R
x
e
2
0
t
e
2
(
x
)
dx
=
R
x
e
2
0
(2
x
2
+80)
dx
=
2
3
x
3
e
2
+80
x
e
2
=
2
3
(
x
4
+
x
6
)
3
+80(
x
4
+
x
6
)
,
R
x
e
3
0
t
e
3
(
x
)
dx
=
R
x
e
3
0
(3
x
2
+25)
dx
=
x
3
e
3
+25
x
e
3
=
x
3
5
+25
x
5
,
R
x
e
4
0
t
e
4
(
x
)
dx
=
R
x
e
4
0
(3
x
2
+15)
dx
=
x
3
e
4
+15
x
e
4
= (
x
3
+
x
5
+
x
6
)
3
+15(
x
3
+
x
5
+
x
6
)
,
R
x
e
5
0
t
e
5
(
x
)
dx
=
R
x
e
5
0
(
x
2
+60)
dx
=
1
3
x
3
e
5
+60
x
e
5
=
1
3
(
x
2
+
x
3
)
3
+15(
x
2
+
x
3
)
,
R
x
e
6
0
t
e
6
(
x
)
dx
=
R
x
e
6
0
(4
x
2
+30)
dx
=
4
3
x
3
e
6
+30
x
e
6
=
4
3
(
x
2
+
x
4
)
3
+30(
x
2
+
x
4
)
,
R
x
e
7
0
t
e
7
(
x
)
dx
=
R
x
e
7
0
(3
x
2
+113)
dx
=
x
3
e
7
+113
x
e
7
= (
x
3
+
x
6
)
3
+113(
x
3
+
x
6
)
,
1
n
Ú
µ
Beckmann
ú
ª
í
2
ª
MP
3
X
e
Minz
(
x
) =
20
3
(
x
1
)
3
++12
x
1
+
2
3
(
x
4
+
x
6
)
3
+80(
x
4
+
x
6
)+
x
3
5
+25
x
5
+(
x
3
+
x
5
+
x
6
)
3
+15(
x
3
+
x
5
+
x
6
)+
1
3
(
x
2
+
x
3
)
3
+15(
x
2
+
x
3
)+
4
3
(
x
2
+
x
4
)
3
+30(
x
2
+
x
4
)+(
x
3
+
x
6
)
3
+113(
x
3
+
x
6
)
s.t
x
1
+
x
2
+
x
3
= 11
x
4
+
x
5
+
x
6
= 10
x
4
+
x
6
≤
6
,x
2
+
x
3
≤
7
x
2
+
x
4
≤
9
,x
3
+
x
6
≤
8
x
3
+
x
5
+
x
6
≤
8
,
0
≤
x
2
0
≤
x
5
≤
5
,
0
≤
x
1
≤
5
0
≤
x
3
,
0
≤
x
4
,
0
≤
x
6
^
Lingo
^
‡
§
Œ
±
Ž
Ñ
Ù
þ
ï
6
•
(A
•
Œ
1
6
8
Ü
)
x
= (4
.
58
,
6
.
09
,
0
.
33
,
2
.
58
,
5
.
00
,
2
.
42)
T
∈
A.
Ï
L
d
~
Œ
±
w
Ñ
§
3
ä
l
N
þ
å
Ï
þ
ï
6
O
Ž
¥
§
r
Ï
þ
ï
6
O
Ž
=
z
•
ê
Æ
5
y
¯
K
§
|
^
Beckmann
ú
ª
í
2
ª
E
Ž
{
§
´
˜
«
1
ƒ
k
•{
§
=
•
Ï
þ
ï
6
O
Ž
J
ø
n
Ø
Ä
:
§
q
U
A^u
¢
S
"
DOI:10.12677/aam.2022.1196536197
A^
ê
Æ
?
Ð
±
Œ
Ä
7
‘
8
-
Ÿ
¢
½
…
’
Æ
‰
ï
‘
8
(No.XJKJ202102004)
"
ë
•
©
z
[1]Wardrop,J.(1952)SomeTheoreticalAspectsofRoadTrafficResearch.
Proceedingsofthe
InstituteofCivilEngineers,PartII
,
1
,325-378.https://doi.org/10.1680/ipeds.1952.11259
[2]Beckmann, M.J.,McGuire,C.B. andWinsten,C.B.(1956) Studiesin theEconomics ofTrans-
portation.YaleUniversityPress,NewHaven.
[3]Lin,Z.(2010)TheStudyofTrafficEquilibriumProblemswithCapacityConstraintsofArcs.
NonlinearAnalysis:RealWorldApplications
,
11
,2280-2284.
https://doi.org/10.1016/j.nonrwa.2009.07.002
[4]Lin,Z.(2010)OnExistenceofVectorEquilibriumFlowswithCapacityConstraintsofArcs.
NonlinearAnalysis:Theory,MethodsandApplications
,
72
,2076-2079.
https://doi.org/10.1016/j.na.2009.10.007
[5]Chen, A., Zhou,Z. andXu, X.D.(2012)A Self-Adaptive GradientProjectionAlgorithm forthe
NonadditiveTrafficEquilibriumProblem.
ComputersandOperationsResearch
,
39
,127-138.
https://doi.org/10.1016/j.cor.2011.02.018
[6]Xu,Y.D. andLi,S.J. (2013) Optimality Conditions for Generalized Ky Fan Quasi-Inequalities
withApplications.
JournalofOptimizationTheoryandApplications
,
157
,663-684.
https://doi.org/10.1007/s10957-012-0242-z
[7]Xu,Y.D. and Li, S.J. (2014) Vector Network Equilibrium Problems with Capacity Constraints
ofArcsandNonlinearScalarizationMethods.
ApplicableAnalysis
,
93
,2199-2210.
https://doi.org/10.1080/00036811.2013.875160
[8]Luc,D.T. andPhuong, T.T.T. (2016) Equilibrium in Multi-Criteria Transportation Networks.
JournalofOptimizationTheoryApplications
,
169
,116-147.
https://doi.org/10.1007/s10957-016-0876-3
[9]Zhi,L.(2015)AnAlgorithmforTrafficEquilibriumFlowwithCapacityConstraintsofArcs.
JournalofTransportationTechnologies
,
5
,240-246.https://doi.org/10.4236/jtts.2015.54022
[10]Chiou,S.W. (2010) An Efficient Algorithm for Computing Traffic Equilibria Using TRANSYT
Model.
AppliedMathematicalModelling
,
34
,3390-3399.
https://doi.org/10.1016/j.apm.2010.02.028
[11]Xu,M.,Chen,A.,Qu,Y.andGao,Z.(2011)ASemismoothNewtonMethodforTraffic
EquilibriumProblemwithaGeneralNonadditiveRouteCost.
AppliedMathematicalModelling
,
35
,3048-3062.https://doi.org/10.1016/j.apm.2010.12.021
DOI:10.12677/aam.2022.1196536198
A^
ê
Æ
?
Ð