I
nte
rna
t
io
na
l J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
pu
t
er
E
ng
ineering
(
I
J
E
CE
)
Vo
l.
11
,
No
.
6
,
Dec
em
b
er
2
0
2
1
,
p
p
.
4
9
2
2
~
4
9
3
1
I
SS
N:
2
0
8
8
-
8
7
0
8
,
DOI
: 1
0
.
1
1
5
9
1
/
ijece
.
v
1
1
i
6
.
pp
4
9
2
2
-
4
9
3
1
4922
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
ec
e.
ia
esco
r
e.
co
m
So
lv
ing
hy
brid
-
v
ehicle routi
ng
pro
blem using
mo
difi
ed
sim
ula
ted
a
nnea
li
ng
No
ur
Als
um
a
ira
t
,
M
a
hm
o
ud
Alre
f
a
ei
De
p
a
rtme
n
t
o
f
M
a
t
h
e
m
a
ti
c
s a
n
d
S
tatisti
c
s,
Jo
rd
a
n
Un
i
v
e
rsity
o
f
S
c
ien
c
e
a
n
d
Tec
h
n
o
l
o
g
y
,
Ir
b
id
,
Jo
r
d
a
n
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
J
an
1
,
2
0
2
1
R
ev
is
ed
Ma
y
1
8
,
2
0
2
1
Acc
ep
ted
Ju
n
1
,
2
0
2
1
In
t
h
is
p
a
p
e
r,
we
c
o
n
si
d
e
r
t
h
e
h
y
b
ri
d
v
e
h
icle
ro
u
ti
n
g
p
ro
b
lem
(
HV
RP
)
a
t
wh
ich
th
e
v
e
h
icle
c
o
n
su
m
e
s two
ty
p
e
s o
f
p
o
we
r:
fu
e
l
a
n
d
e
lec
tri
c
it
y
.
Th
e
a
im
o
f
th
is
p
ro
b
lem
is
to
m
i
n
imiz
e
th
e
to
tal
c
o
st
o
f
trav
e
ll
i
n
g
b
e
twe
e
n
c
u
sto
m
e
rs,
p
ro
v
id
e
d
t
h
a
t
e
a
c
h
c
u
sto
m
e
r
is
v
isit
e
d
o
n
l
y
o
n
c
e
.
Th
e
v
e
h
icle
d
e
p
a
rts
fro
m
th
e
d
e
p
o
t
a
n
d
re
tu
r
n
s
a
fter
c
o
m
p
letin
g
th
e
wh
o
le
ro
u
te.
T
h
is
o
p
ti
m
iza
ti
o
n
p
ro
b
lem
is
so
lv
e
d
u
si
n
g
a
m
o
d
ifi
e
d
s
imu
late
d
a
n
n
e
a
li
n
g
(S
A
)
h
e
u
rist
ic
p
ro
c
e
d
u
re
wit
h
c
o
n
sta
n
t
tem
p
e
r
a
tu
re
.
Th
is
a
p
p
r
o
a
c
h
is
imp
lem
e
n
ted
o
n
a
n
u
m
e
rica
l
e
x
a
m
p
le
a
n
d
th
e
re
su
lt
s
a
re
c
o
m
p
a
re
d
with
th
e
S
A
a
lg
o
rit
h
m
wit
h
d
e
c
re
a
sin
g
tem
p
e
ra
tu
re
.
Th
e
o
b
t
a
in
e
d
re
su
lt
s
sh
o
w
th
a
t
u
sin
g
th
e
S
A
with
c
o
n
s
tan
t
tem
p
e
ra
tu
re
o
v
e
rri
d
e
s
th
e
S
A
wit
h
d
e
c
re
a
sin
g
tem
p
e
ra
tu
re
.
Th
e
re
su
lt
s
in
d
ica
te
t
h
a
t
S
A
with
d
e
c
r
e
a
sin
g
tem
p
e
ra
tu
re
n
e
e
d
s
twice
t
h
e
n
u
m
b
e
r
o
f
it
e
ra
ti
o
n
s
n
e
e
d
e
d
b
y
th
e
S
A
with
c
o
n
sta
n
t
tem
p
e
ra
tu
re
to
re
a
c
h
a
n
e
a
r
o
p
ti
m
u
m
s
o
lu
ti
o
n
.
K
ey
w
o
r
d
s
:
Hy
b
r
id
v
e
h
i
cle
R
o
u
tin
g
p
r
o
b
lem
Simu
lated
an
n
ea
lin
g
T
r
an
s
p
o
r
tatio
n
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Ma
h
m
o
u
d
Alr
ef
ae
i
Dep
ar
tm
en
t o
f
Ma
th
em
atics a
n
d
Statis
tics
J
o
r
d
an
Un
iv
e
r
s
ity
o
f
Scien
ce
a
n
d
T
ec
h
n
o
lo
g
y
I
r
b
id
2
2
1
1
0
,
J
o
r
d
an
E
m
ail:
alr
ef
ae
i@
ju
s
t.e
d
u
.
jo
1.
I
NT
RO
D
UCT
I
O
N
Veh
icle
r
o
u
tin
g
p
r
o
b
lem
(
VR
P)
was
f
ir
s
t
i
n
tr
o
d
u
ce
d
b
y
Dan
tzig
[
1
]
,
wh
er
e
t
h
e
o
p
tim
u
m
r
o
u
tin
g
was
co
n
s
id
er
ed
f
o
r
a
f
leet
o
f
g
aso
lin
e
-
d
eliv
er
y
tr
u
c
k
s
tr
av
elin
g
b
etwe
en
a
d
e
p
o
t
an
d
ter
m
i
n
al
c
u
s
to
m
er
s
an
d
s
o
m
e
s
er
v
ice
s
tatio
n
s
.
T
h
ey
p
r
o
p
o
s
ed
th
e
f
ir
s
t
m
ath
em
atica
l
li
n
ea
r
p
r
o
g
r
a
m
m
in
g
f
o
r
m
u
latio
n
an
d
alg
o
r
ith
m
ic
ap
p
r
o
ac
h
.
C
ao
[
2
]
lis
ted
eig
h
t p
o
in
ts
to
class
if
y
th
e
VR
P
ac
co
r
d
in
g
t
o
;
n
u
m
b
e
r
o
f
d
is
tr
ib
u
ti
o
n
ce
n
ter
s
,
ty
p
e
o
f
v
eh
icle,
ch
a
r
ac
ter
is
tics
o
f
th
e
task
,
tim
e
co
n
s
tr
ain
ts
,
v
eh
icl
e
lo
ad
in
g
,
o
p
tim
izatio
n
o
f
th
e
n
u
m
b
er
o
f
g
o
als,
o
wn
er
s
h
ip
o
f
th
e
p
o
in
ts
,
an
d
m
aster
in
g
th
e
in
f
o
r
m
atio
n
o
f
c
er
tain
ty
.
Veh
icles
ca
p
ac
ity
p
lay
s
a
v
er
y
b
ig
r
o
le
in
th
e
VR
P;
t
h
er
ef
o
r
e
,
r
esear
ch
er
s
ad
d
th
e
ca
p
ac
ity
co
n
s
tr
ain
ts
to
th
e
o
r
i
g
in
al
p
r
o
b
lem
to
alig
n
with
r
ea
l
wo
r
ld
ca
s
e
wh
ich
is
k
n
o
wn
as
ca
p
ac
itated
v
eh
icle
r
o
u
tin
g
p
r
o
b
le
m
(
C
VR
P).
Fo
r
ex
am
p
le,
Fau
lin
et
a
l.
[
3
]
h
a
v
e
u
s
ed
alg
o
r
ith
m
s
with
en
v
ir
o
n
m
en
tal
cr
iter
ia
to
s
o
lv
e
th
e
C
VR
P,
wh
er
e
en
v
ir
o
n
m
en
tal
co
s
ts
wer
e
co
n
s
id
er
ed
to
g
eth
er
with
co
s
t,
d
is
tan
ce
,
n
u
m
b
er
o
f
v
eh
icles
an
d
p
r
o
f
it.
Ma
h
v
ash
et
a
l.
[
4
]
p
r
o
p
o
s
ed
th
e
C
VR
P
with
n
ew
co
n
s
tr
ain
ts
f
o
r
th
r
ee
-
d
i
m
en
s
io
n
al
s
h
ap
ed
p
r
o
d
u
cts,
wh
er
e
th
ey
h
av
e
u
s
ed
a
co
lu
m
n
g
e
n
er
atio
n
(
C
G)
tech
n
iq
u
e
-
b
ased
h
e
u
r
is
tic.
On
th
e
o
th
er
h
an
d
,
in
v
e
h
icle
r
o
u
tin
g
p
r
o
b
lem
with
tim
e
win
d
o
ws
(
VR
PT
W
)
;
th
e
s
er
v
ice
tim
e
at
ea
ch
cu
s
to
m
er
is
with
in
a
s
p
ec
if
ic
tim
e
win
d
o
w,
a
two
s
t
ag
e
alg
o
r
it
h
m
is
p
r
o
p
o
s
ed
b
y
L
im
[
5
]
to
s
o
lv
e
VR
PT
W
;
in
th
e
f
ir
s
t
s
tag
e
th
e
alg
o
r
ith
m
m
in
im
izes
th
e
n
u
m
b
er
o
f
v
eh
icles
with
a
n
ej
ec
tio
n
p
o
o
l,
th
e
n
it
m
in
im
izes
th
e
to
tal
tr
av
el
d
is
tan
ce
u
s
in
g
a
m
u
lti
-
s
tar
t
iter
ate
d
h
ill
-
clim
b
in
g
alg
o
r
ith
m
.
Yu
l
iza
et
a
l.
[
6
]
s
o
lv
e
d
an
o
p
en
ca
p
ac
itated
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
f
o
r
waste
tr
an
s
p
o
r
tin
g
p
r
o
b
lem
s
,
with
u
n
ce
r
t
ain
am
o
u
n
t o
f
waste
an
d
tr
av
el
tim
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8
7
0
8
S
o
lvin
g
h
yb
r
id
-
ve
h
icle
r
o
u
tin
g
p
r
o
b
lem
u
s
in
g
mo
d
ified
s
imu
la
ted
a
n
n
ea
lin
g
(
N
o
u
r
A
ls
u
ma
ir
a
t
)
4923
VR
P
s
ca
n
b
e
s
o
lv
ed
u
s
in
g
d
if
f
er
en
t
ap
p
r
o
ac
h
es,
in
clu
d
in
g
th
e
ex
ac
t
ap
p
r
o
ac
h
;
E
l
-
Sh
er
b
en
y
[
7
]
class
if
ied
th
e
ex
ac
t
m
eth
o
d
f
o
r
th
e
VR
PTW
in
to
th
r
ee
ca
teg
o
r
ies:
L
ag
r
an
g
e
r
elax
at
i
o
n
-
b
ased
m
et
h
o
d
s
,
co
lu
m
n
g
en
er
atio
n
,
an
d
d
y
n
a
m
ic
p
r
o
g
r
am
m
in
g
.
I
o
r
i
et
a
l.
[
8
]
p
r
o
p
o
s
ed
an
ex
ac
t
ap
p
r
o
ac
h
b
ased
o
n
a
b
r
an
ch
-
an
d
-
cu
t
al
g
o
r
ith
m
f
o
r
th
e
ca
p
ac
itated
VR
P.
T
h
e
p
r
o
b
lem
was
co
n
s
id
er
ed
with
two
-
d
im
en
s
io
n
al
ad
d
itio
n
al
lo
ad
in
g
c
o
n
s
tr
ain
ts
.
B
ald
ac
ci
et
a
l.
[
9
]
u
s
ed
an
e
x
ac
t
m
eth
o
d
th
at
d
ec
o
m
p
o
s
es
th
e
two
-
ec
h
elo
n
ca
p
ac
itate
d
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
s
(
2
E
-
C
VR
P)
in
to
a
lim
ited
s
et
o
f
m
u
lti
d
ep
o
t
ca
p
ac
itated
v
eh
icl
e
r
o
u
tin
g
p
r
o
b
lem
s
with
s
id
e
co
n
s
tr
ain
ts
.
Heu
r
is
tic
alg
o
r
ith
m
s
h
av
e
b
ee
n
u
s
ed
to
r
ep
lace
t
h
e
d
ec
is
io
n
cr
iter
ia
o
f
th
e
ex
ac
t
a
p
p
r
o
ac
h
alg
o
r
ith
m
to
ef
f
ec
tiv
ely
n
ar
r
o
w
th
e
s
ea
r
ch
s
p
ac
e
wh
ich
is
k
n
o
wn
as
in
tellig
en
t
h
eu
r
is
tic
alg
o
r
ith
m
.
Fo
r
ex
am
p
le,
T
av
ak
o
li
[
1
0
]
u
s
ed
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
to
s
o
lv
e
th
e
C
V
R
P,
th
ey
r
ef
er
r
ed
to
ea
ch
f
o
u
n
d
so
lu
tio
n
as
a
p
o
in
t
in
n
-
d
im
en
s
io
n
al
s
p
ac
e
th
at
h
as
an
i
n
itial
v
elo
city
,
wh
ile
p
ar
ticle
s
(
s
o
lu
tio
n
s
)
wer
e
ev
alu
ated
ac
co
r
d
in
g
to
s
o
m
e
f
itn
ess
cr
iter
ia.
Ho
wev
er
,
PS
O
m
ig
h
t
b
e
s
tu
ck
in
to
lo
ca
l
o
p
tim
a;
th
er
ef
o
r
e,
m
u
lti
-
s
war
m
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
MSPSO)
h
as
b
ee
n
u
s
ed
b
y
o
th
er
r
esear
ch
er
s
,
wh
er
e
th
e
s
war
m
is
d
iv
id
ed
in
to
s
u
b
-
s
war
m
s
,
an
d
th
e
m
o
v
em
en
t
p
r
o
ce
s
s
o
f
a
p
a
r
ticle
is
en
h
an
ce
d
with
a
p
r
o
b
ab
ilit
y
o
f
b
is
ec
tio
n
m
eth
o
d
,
s
ee
Alf
ar
is
y
et
a
l.
[
1
1
]
.
Pu
s
p
ita
et
a
l.
[
1
2
]
,
[
1
3
]
h
a
v
e
m
o
d
eled
an
o
p
tim
izatio
n
wast
e
tr
an
s
p
o
r
t
as
a
C
VR
P a
n
d
s
o
lv
ed
it u
s
in
g
b
r
a
n
ch
an
d
b
o
u
n
d
m
eth
o
d
with
th
e
aid
o
f
L
I
NGO
1
3
.
0
.
On
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
m
e
th
o
d
s
th
at
ca
n
b
e
u
s
ed
f
o
r
s
o
l
v
in
g
VR
P
is
s
im
u
lated
an
n
ea
lin
g
wh
ich
is
a
co
m
m
o
n
lo
ca
l
s
ea
r
ch
m
eta
-
h
eu
r
is
tic
u
s
ed
to
ad
d
r
e
s
s
d
is
cr
ete,
an
d
to
a
les
s
er
ex
ten
t,
co
n
tin
u
o
u
s
o
p
tim
izatio
n
p
r
o
b
lem
s
.
An
n
e
alin
g
is
r
ef
e
r
r
ed
to
,
as
tem
p
e
r
in
g
ce
r
tain
allo
y
s
o
f
m
etal,
g
lass
,
o
r
cr
y
s
tal
b
y
h
ea
tin
g
ab
o
v
e
its
m
eltin
g
p
o
in
t,
h
o
ld
in
g
its
tem
p
er
atu
r
e
,
an
d
th
en
co
o
lin
g
it
v
e
r
y
s
lo
wly
u
n
til
it
s
o
lid
if
ies
in
to
a
p
er
f
ec
t
cr
y
s
tallin
e
s
tr
u
ctu
r
e.
T
h
e
s
im
u
latio
n
o
f
th
is
p
r
o
ce
s
s
is
k
n
o
wn
as
s
im
u
lated
an
n
ea
lin
g
(
SA)
,
th
e
b
asic
id
ea
is
to
f
in
d
a
g
lo
b
al
m
in
i
m
u
m
am
o
u
n
t
o
f
en
e
r
g
y
t
o
p
r
o
d
u
ce
a
d
ef
ec
t
-
f
r
ee
cr
y
s
tal
m
ater
ial.
T
h
e
f
ir
s
t
ap
p
ea
r
an
ce
o
f
s
im
u
lated
an
n
e
alin
g
was
in
1
9
5
3
b
y
Me
tr
o
p
o
lis
et
a
l.
[
1
4
]
.
I
n
Kir
k
p
atr
ick
e
t
a
l.
[
1
5
]
d
ev
elo
p
ed
th
e
s
im
ilar
ities
b
etwe
en
th
e
s
t
atis
tical
m
ec
h
an
ics an
d
co
m
b
in
ato
r
ial
o
p
tim
izatio
n
.
T
h
e
k
ey
alg
o
r
ith
m
ic
f
ea
tu
r
e
o
f
s
im
u
lated
an
n
ea
lin
g
is
th
at
it
p
r
o
v
id
es
a
m
ea
n
to
escap
e
lo
ca
l
o
p
tim
u
m
b
y
allo
win
g
h
ill
-
clim
b
in
g
m
o
v
es
(
i.e
.
,
m
o
v
es
wh
ich
wo
r
s
en
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
v
alu
e)
,
as
th
e
tem
p
er
atu
r
e
p
a
r
am
e
ter
d
ec
r
ea
s
es,
th
e
p
r
o
b
a
b
ilit
y
o
f
ac
ce
p
tin
g
a
wo
r
s
e
o
b
jectiv
e
f
u
n
ctio
n
will a
ls
o
d
ec
r
ea
s
e.
T
h
e
SA
alg
o
r
ith
m
s
tar
ts
with
an
in
itial
s
o
lu
tio
n
,
Szab
o
[
1
6
]
test
ed
th
e
ef
f
ec
tiv
e
n
ess
o
f
c
h
o
o
s
in
g
th
e
in
itial
s
o
lu
tio
n
in
SA
f
o
r
a
f
lo
w
s
h
o
p
p
r
o
b
lem
.
T
h
e
n
,
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
ev
alu
ate
d
,
af
ter
th
at
a
n
ew
(
n
eig
h
b
o
r
h
o
o
d
)
s
o
lu
tio
n
is
g
en
er
ated
,
C
r
u
z
-
C
h
av
ez
[
1
7
]
p
r
esen
ted
a
m
ec
h
an
is
m
t
o
g
en
er
ate
a
n
ew
n
eig
h
b
o
r
h
o
o
d
s
o
lu
tio
n
f
o
r
th
e
jo
b
s
h
o
p
s
ch
ed
u
lin
g
p
r
o
b
lem
(
J
SS
P).
I
n
itial
tem
p
er
at
u
r
e
p
lay
s
an
im
p
o
r
tan
t
r
o
le
in
SA
s
in
ce
th
e
ac
ce
p
tan
ce
r
atio
s
tr
o
n
g
ly
d
ep
en
d
s
o
n
th
e
tem
p
er
atu
r
e,
Sh
ak
o
u
r
i
et
a
l
.
[
1
8
]
d
is
cu
s
s
ed
th
e
in
itial
tem
p
er
atu
r
e
an
d
p
r
o
p
o
s
ed
an
ap
p
r
o
ac
h
to
s
p
ee
d
u
p
th
e
alg
o
r
ith
m
o
f
SA
wh
ile
o
b
tain
in
g
ac
cu
r
ate
s
o
lu
tio
n
s
f
o
r
th
e
tr
av
elin
g
s
alesm
an
p
r
o
b
lem
(
T
SP
)
.
T
h
e
g
e
n
er
ated
s
o
lu
tio
n
is
co
m
p
ar
ed
to
th
e
o
ld
s
o
lu
tio
n
,
if
th
e
n
ew
s
o
lu
tio
n
h
as
b
e
tter
o
b
jectiv
e
f
u
n
ctio
n
v
al
u
e,
th
e
alg
o
r
ith
m
m
o
v
es
to
th
at
s
o
l
u
tio
n
,
o
th
e
r
wis
e
a
r
an
d
o
m
n
u
m
b
er
b
etwe
en
0
an
d
1
is
g
e
n
er
ated
an
d
co
m
p
ar
e
d
with
a
p
r
o
b
a
b
ilit
y
r
atio
th
at
d
ec
id
es
wh
eth
er
to
ac
ce
p
t o
r
r
ejec
t th
e
n
ew
s
o
lu
ti
o
n
.
B
aiza
l
et
a
l.
[
1
9
]
u
s
ed
th
e
s
im
u
lat
ed
an
n
ea
lin
g
f
o
r
s
o
lv
in
g
th
e
T
SP
an
d
h
av
e
s
h
o
wn
th
r
o
u
g
h
e
x
am
p
les
th
at
th
e
SA
m
u
ch
b
etter
t
h
an
s
o
m
e
o
th
er
c
o
m
p
eten
t
m
et
h
o
d
s
.
An
o
th
er
v
e
r
s
io
n
o
f
s
im
u
lated
an
n
ea
lin
g
th
at
u
s
es
co
n
s
tan
t
tem
p
er
atu
r
e
was
p
r
esen
ted
b
y
Alr
ef
ae
i
[
2
0
]
an
d
an
o
th
er
v
er
s
io
n
u
s
es
th
e
r
a
n
k
in
g
a
n
d
s
elec
tio
n
m
et
h
o
d
was
p
r
o
p
o
s
ed
b
y
Alr
ef
ae
i
[
2
1
]
.
Ar
iy
a
n
i
[
2
2
]
s
o
lv
e
d
th
e
VR
PT
W
u
s
in
g
a
h
y
b
r
id
GA
-
SA a
lg
o
r
ith
m
.
Yu
et
a
l.
[
2
3
]
h
av
e
u
s
ed
th
e
s
im
u
l
ated
an
n
ea
lin
g
to
s
o
lv
e
th
e
h
y
b
r
id
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
(
HVRP
)
.
T
h
e
HVRP
is
an
ex
ten
s
io
n
o
f
th
e
o
r
i
g
in
al
VR
P
with
th
e
ad
d
itio
n
o
f
t
h
e
ab
ilit
y
to
r
ec
h
ar
g
e
th
e
v
eh
icle
elec
tr
ically
.
M
o
r
e
ap
p
licatio
n
s
o
f
s
im
u
lated
an
n
ea
lin
g
o
n
m
u
lti
o
b
jectiv
e
o
p
tim
izatio
n
ca
n
b
e
f
o
u
n
d
in
[
2
4
]
-
[
2
9
]
.
Mo
r
e
r
ec
en
t
ap
p
licatio
n
s
o
f
t
h
e
s
im
u
l
ated
an
n
ea
lin
g
alg
o
r
ith
m
f
o
r
s
o
lv
in
g
e
n
g
in
ee
r
in
g
p
r
o
b
lem
s
ca
n
b
e
f
o
u
n
d
in
[
3
0
]
-
[
3
3
]
.
T
h
e
ad
v
a
n
tag
e
o
f
s
im
u
lated
a
n
n
ea
lin
g
alg
o
r
ith
m
is
th
at
it
r
e
d
u
ce
s
th
e
n
u
m
b
er
o
f
s
o
lu
tio
n
s
th
at
m
u
s
t
b
e
test
ed
to
f
in
d
th
e
o
p
tim
u
m
s
o
lu
tio
n
.
Mo
r
eo
v
e
r
,
th
e
s
tr
u
ctu
r
e
o
f
th
e
SA
alg
o
r
ith
m
is
co
n
s
is
ten
t
co
m
p
ar
ed
w
ith
o
th
er
h
eu
r
is
tic
alg
o
r
ith
m
s
.
An
n
ea
lin
g
at
co
n
s
tan
t
an
d
d
ec
r
ea
s
in
g
tem
p
er
atu
r
es
wer
e
u
s
ed
in
th
is
s
tu
d
y
.
T
h
e
u
s
e
o
f
co
n
s
tan
t
tem
p
er
atu
r
e
co
n
s
id
er
ed
h
e
r
e
g
iv
es
th
e
a
lg
o
r
ith
m
m
o
r
e
f
r
ee
d
o
m
to
m
o
v
e
ar
o
u
n
d
th
e
s
tate
s
p
ac
e
an
d
r
ap
id
ly
f
in
d
s
th
e
o
p
t
im
al
s
o
lu
tio
n
,
Alr
ef
ae
i a
n
d
An
d
r
ad
o
ttir
[
2
0
]
.
T
h
is
p
ap
e
r
is
o
r
g
an
ized
as f
o
llo
w;
in
s
ec
tio
n
2
,
we
f
o
r
m
u
late
th
e
VR
P
p
r
o
b
lem
,
in
s
ec
tio
n
3
,
we
p
r
esen
t
th
e
m
eth
o
d
o
lo
g
y
u
s
ed
to
s
o
lv
e
th
e
p
r
o
b
lem
,
in
s
ec
tio
n
4
,
a
n
u
m
er
ical
ex
am
p
le
is
g
iv
en
,
an
d
in
s
ec
tio
n
5
,
we
in
clu
d
e
th
e
r
esu
lts
f
o
llo
wed
b
y
co
n
clu
d
in
g
r
em
a
r
k
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
Veh
icle
r
o
u
tin
g
p
r
o
b
lem
(
VR
P)
is
u
s
u
ally
s
o
lv
e
d
u
s
in
g
t
h
e
tr
an
s
p
o
r
t
r
o
u
te
o
p
tim
izatio
n
.
T
h
e
m
ain
g
o
al
o
f
th
e
v
eh
icle
r
o
u
tin
g
o
p
tim
izatio
n
is
to
m
in
im
ize
th
e
to
tal
co
s
t
with
o
f
f
er
in
g
th
e
n
ee
d
ed
s
er
v
ice
f
o
r
ev
er
y
cu
s
to
m
e
r
.
T
h
is
s
tu
d
y
e
m
p
lo
y
s
p
ar
a
m
eter
s
b
ased
o
n
p
r
ev
io
u
s
r
esear
ch
,
Y
u
et
a
l.
[
2
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
9
2
2
-
4
9
3
1
4924
T
h
e
f
o
llo
win
g
n
o
tatio
n
s
ar
e
n
e
ed
ed
th
r
o
u
g
h
o
u
t th
is
p
a
p
er
:
0
: D
ep
o
t in
d
ex
.
: T
h
e
s
et
o
f
all
cu
s
to
m
er
s
.
: T
h
e
s
et
o
f
elec
tr
ic
s
tatio
n
s
.
: T
h
e
s
et
o
f
f
u
el
s
tatio
n
s
.
: T
h
e
s
et
o
f
all
elec
tr
ic
an
d
f
u
e
l statio
n
s
to
g
eth
er
with
th
e
d
e
p
o
t.
: T
h
e
s
et
o
f
all
s
tatio
n
s
an
d
all
cu
s
to
m
er
s
to
g
eth
er
with
t
h
e
d
e
p
o
t.
: T
h
e
r
em
ain
in
g
d
is
tan
ce
th
at
t
h
e
v
eh
icle
ca
n
co
v
er
u
s
in
g
ele
ctr
icity
.
: T
h
e
r
em
ain
in
g
d
is
tan
ce
th
at
t
h
e
v
eh
icle
ca
n
co
v
er
u
s
in
g
f
u
e
l.
: M
a
x
im
u
m
tim
e
th
at
th
e
v
eh
i
cle
is
n
o
t a
llo
wed
to
ex
ce
e
d
p
e
r
r
o
u
n
d
.
i
,
j
: Bi
n
ar
y
v
ar
iab
le
eq
u
al
to
o
n
e
if
th
e
v
eh
icle
tr
a
v
eled
f
r
o
m
v
e
r
tex
to
v
er
tex
an
d
ze
r
o
,
o
th
e
r
wis
e.
i
,
j
: T
h
e
tim
e
n
ee
d
e
d
to
tr
a
v
el
f
o
r
m
v
er
tex
to
v
er
te
x
.
i
,
j
: T
h
e
d
is
ta
n
ce
f
r
o
m
v
er
te
x
to
v
er
tex
th
at
is
co
v
er
ed
u
s
in
g
el
ec
tr
icity
.
i
,
j
: T
h
e
d
is
tan
ce
f
r
o
m
v
er
te
x
to
v
er
tex
th
at
is
co
v
er
ed
u
s
in
g
f
u
el.
: T
h
e
m
ax
im
u
m
d
is
tan
ce
th
at
ca
n
b
e
tr
av
ele
d
wh
en
t
h
e
v
eh
i
cle
is
elec
tr
ically
f
u
lly
ch
ar
g
e
d
.
:
T
h
e
m
ax
im
u
m
d
is
tan
ce
th
at
ca
n
b
e
tr
av
ele
d
wh
en
t
h
e
v
eh
i
cle
is
f
u
lly
f
illed
with
f
u
el.
i
,
j
: T
h
e
elec
tr
icity
co
s
t to
tr
av
el
f
r
o
m
v
er
tex
to
v
er
tex
.
i
,
j
: T
h
e
f
u
el
c
o
s
t to
tr
av
el
f
r
o
m
v
er
tex
to
v
er
tex
.
i
,
j
: T
h
e
d
is
tan
ce
b
etwe
en
v
er
tex
an
d
v
er
te
x
.
: T
h
e
elec
tr
icity
co
n
s
u
m
p
tio
n
r
ate.
: T
h
e
elec
tr
icity
co
s
t p
er
k
wh
.
: T
h
e
f
u
el
c
o
n
s
u
m
p
tio
n
r
ate.
: T
h
e
f
u
el
c
o
s
t p
er
g
allo
n
.
T
h
e
HVRP
is
d
ef
in
ed
as
a
d
ir
ec
ted
g
r
a
p
h
=
(
,
)
,
wh
er
e
t
h
e
v
e
r
tex
s
et
A
is
a
co
m
b
in
atio
n
o
f
th
e
d
ep
o
t
0
,
th
e
elec
tr
ic
s
tatio
n
s
s
et,
th
e
f
u
el
s
tatio
n
s
s
et,
an
d
th
e
cu
s
to
m
er
s
s
et.
T
h
e
s
et
is
th
e
d
ep
o
t
to
g
eth
er
with
th
e
elec
tr
ic
s
tat
io
n
s
an
d
f
u
el
s
tatio
n
s
.
T
h
e
s
et
o
f
ed
g
es
=
{
(
,
)
:
,
is
th
e
in
d
ex
f
o
r
th
e
v
is
ited
cu
s
to
m
er
o
r
s
tatio
n
}.
E
ac
h
p
ai
r
in
is
ass
o
ciate
d
w
ith
tr
av
el
tim
e,
d
is
tan
ce
,
an
d
to
tal
co
s
t
till
th
at
p
o
in
t.
As
an
ex
am
p
le,
d
en
o
te
th
e
d
ep
o
t
b
y
0
,
th
e
elec
tr
ic
s
tat
io
n
s
s
et
b
y
=
{
1
,
2
}
,
th
e
f
u
el
s
tatio
n
s
s
et
by
=
{
3
,
4
}
an
d
th
e
c
u
s
to
m
er
s
s
et
b
y
=
{
5
,
6
,
7
,
8
,
9
,
10
,
11
,
12
}
,
th
en
th
e
s
et
A
=
{
0
,
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
,
10
,
11
,
12
}
an
d
=
{
(
,
)
:
,
∈
,
j
≠
i
}
.
T
h
e
m
ath
em
at
ical
f
o
r
m
u
latio
n
o
f
HVRP
is
as
(
1
)
:
min
∑
(
Ec
i
,
j
+
Fc
i
,
j
)
i
,
j
∈
A
(
1
)
Su
b
ject
to
∑
x
i
,
j
j
∈
A
j
≠
i
=
1
,
∀
i
∈
V
(
2
)
0
<
∑
x
i
,
j
,
,
∈
<
(
3
)
0
<
Rf
i
,
j
+
Re
i
,
j
≤
Re
+
Rf
,
,
∈
A
(
4
)
,
=
,
∗
∗
(
5
)
,
=
,
∗
∗
(
6
)
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
is
g
iv
e
n
in
(
1
)
w
h
ich
is
th
e
to
tal
co
s
t
in
clu
d
in
g
elec
tr
icity
co
s
t
as
well
as
f
u
el
co
s
t
th
at
ca
n
b
e
ev
alu
ated
u
s
in
g
f
o
r
m
u
las
(
5
)
an
d
(
6
)
.
T
h
e
f
ir
s
t
co
n
s
tr
ain
t
is
to
m
ak
e
s
u
r
e
th
at
all
cu
s
to
m
er
s
wer
e
v
is
ite
d
o
n
ly
o
n
ce
is
g
iv
en
b
y
(
2
)
.
T
h
e
s
ec
o
n
d
c
o
n
s
tr
a
in
t
is
to
k
ee
p
th
e
to
tal
tim
e
f
o
r
ev
er
y
r
o
u
n
d
less
th
an
th
e
m
ax
im
u
m
tim
e
th
at
t
h
e
v
eh
icle
is
n
o
t
allo
wed
to
e
x
ce
ed
(
3
)
.
T
h
e
th
i
r
d
co
n
s
tr
ain
t
is
to
en
s
u
r
es
th
at
an
y
m
o
v
em
en
t
f
r
o
m
v
e
r
tex
to
v
er
tex
ca
n
b
e
c
o
v
er
ed
at
m
o
s
t
b
y
th
e
elec
tr
icity
an
d
f
u
el
s
to
r
ag
e
(
4
)
.
T
h
e
v
eh
icle
ca
n
b
e
r
ec
h
a
r
g
ed
at
th
e
d
ep
o
t
as
well
as
th
e
elec
tr
ic
s
tatio
n
s
.
T
h
e
v
eh
icle
ca
n
b
e
r
e
f
u
eled
at
th
e
d
ep
o
t
as we
ll a
s
f
u
el
s
tatio
n
s
.
Hy
b
r
id
v
eh
icle
r
o
u
ti
n
g
p
r
o
b
l
em
(
HVRP
)
is
an
ex
ten
s
io
n
o
f
th
e
g
r
ee
n
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
(
GVRP
)
.
I
n
GVRP
,
th
e
v
eh
icl
e
is
p
u
r
e
elec
tr
ic.
Ho
wev
e
r
,
i
n
HVRP
,
th
e
v
eh
icle
r
u
n
s
o
n
elec
tr
icity
an
d
f
u
el
wh
ich
ex
ten
d
s
th
e
d
is
tan
ce
tr
av
elled
.
T
h
e
r
ef
o
r
e
,
h
y
b
r
id
v
e
h
icle
ca
n
s
er
v
e
m
o
r
e
cu
s
to
m
e
r
s
.
Ma
th
em
atica
lly
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8
7
0
8
S
o
lvin
g
h
yb
r
id
-
ve
h
icle
r
o
u
tin
g
p
r
o
b
lem
u
s
in
g
mo
d
ified
s
imu
la
ted
a
n
n
ea
lin
g
(
N
o
u
r
A
ls
u
ma
ir
a
t
)
4925
th
e
p
r
o
b
lem
is
to
m
in
im
ize
th
e
to
tal
co
s
t
o
v
er
th
e
s
et
o
f
f
e
asib
le
s
o
lu
tio
n
s
S.
Hy
b
r
id
v
eh
icle
ca
n
u
s
e
b
o
th
elec
tr
ic
an
d
f
u
el
s
to
r
ag
e,
in
o
u
r
s
tu
d
y
,
we
g
iv
e
th
e
p
r
io
r
ity
to
co
n
s
u
m
e
elec
tr
ic,
s
in
ce
it
c
o
s
ts
less
ac
co
r
d
in
g
t
o
th
e
u
s
ed
v
e
h
icle
s
p
ec
if
icatio
n
s
.
Fig
u
r
e
1
s
h
o
ws an
ex
am
p
le
o
f
HVRP
.
Fig
u
r
e
1.
E
x
am
p
le
o
f
a
v
e
h
icle
n
ee
d
th
r
ee
r
o
u
n
d
s
to
c
o
m
p
le
te
th
e
tr
ip
I
n
HVRP
,
th
e
v
eh
icle
d
ep
ar
ts
f
r
o
m
th
e
d
ep
o
t
an
d
s
er
v
es
as
m
an
y
c
u
s
to
m
er
s
as
it
ca
n
.
At
ea
ch
s
tep
,
elec
tr
icity
an
d
f
u
el
le
v
els,
r
em
ain
in
g
tim
e
to
r
ea
ch
n
ex
t
c
o
s
tu
m
er
,
a
n
d
clo
s
en
ess
to
elec
tr
ic
ity
o
r
f
u
el
r
ec
h
ar
g
e
s
tatio
n
n
ee
d
to
b
e
ch
ec
k
ed
.
I
f
th
e
elec
tr
ici
ty
o
r
f
u
el
lev
el
is
n
o
t
en
o
u
g
h
to
r
ea
ch
th
e
n
ea
r
est
cu
s
to
m
er
;
a
ch
ec
k
o
n
th
e
n
ea
r
est
s
tatio
n
n
ee
d
to
b
e
m
ad
e.
I
f
th
e
elec
tr
icity
an
d
f
u
el
lev
els
ar
e
n
o
t
e
n
o
u
g
h
t
o
r
ea
ch
a
r
ec
h
ar
g
e
s
tatio
n
,
th
e
v
eh
icle
g
o
es
b
ac
k
to
th
e
d
ep
o
t,
r
ef
ills
f
u
el
a
n
d
elec
tr
icity
,
a
n
d
s
tar
ts
a
n
ew
r
o
u
n
d
.
T
h
e
tr
ip
en
d
s
wh
en
all
cu
s
to
m
er
s
ar
e
s
er
v
ed
.
T
h
er
e
a
r
e
n
o
co
n
s
tr
ain
ts
o
n
t
h
e
n
u
m
b
er
o
f
r
o
u
n
d
s
(
d
e
p
ar
tu
r
e
f
r
o
m
an
d
r
etu
r
n
to
th
e
d
ep
o
t is co
n
s
id
er
ed
as
o
n
e
r
o
u
n
d
)
.
T
o
s
o
lv
e
th
e
HVRP
,
a
m
o
d
if
ied
v
er
s
io
n
o
f
th
e
s
im
u
la
ted
an
n
ea
lin
g
tech
n
i
q
u
e
with
co
n
s
tan
t
tem
p
er
atu
r
e
is
u
s
ed
to
f
i
n
d
th
e
o
p
tim
u
m
s
o
lu
tio
n
.
Ma
n
y
l
o
ca
l
o
p
tim
izer
s
ca
n
b
e
h
a
n
d
led
u
s
in
g
th
is
m
eth
o
d
s
in
ce
it
h
as
th
e
h
ill
clim
b
in
g
f
ea
tu
r
e
as
th
e
o
r
ig
in
al
s
im
u
lated
an
n
ea
lin
g
alg
o
r
ith
m
.
A
t
th
e
b
eg
in
n
in
g
,
a
f
ea
s
ib
le
in
itial
s
o
lu
tio
n
f
o
r
t
h
e
p
r
o
b
lem
is
u
s
ed
,
th
en
,
th
e
o
b
jectiv
e
f
u
n
ctio
n
(
to
tal
tr
a
v
el
co
s
t)
(
)
is
co
m
p
u
ted
b
ased
o
n
th
e
in
itial
s
o
lu
tio
n
,
af
ter
th
at,
a
ca
n
d
id
at
e
s
o
lu
tio
n
is
g
en
er
ated
b
ased
o
n
r
e
p
lacin
g
o
n
e
cu
s
to
m
er
with
an
o
th
er
o
n
e
r
a
n
d
o
m
ly
.
T
h
en
,
t
h
e
to
tal
tr
av
el
co
s
t
(
)
is
co
m
p
u
ted
at
,
if
(
)
<
(
)
,
th
en
th
e
alg
o
r
ith
m
ac
ce
p
ts
th
e
m
o
v
e
to
th
e
ca
n
d
id
ate
s
o
lu
tio
n
.
Ho
wev
er
,
if
(
)
≥
(
)
,
th
en
th
er
e
is
p
o
s
s
ib
ilit
y
th
at
a
b
etter
s
o
lu
tio
n
is
h
id
d
e
n
b
eh
in
d
th
e
ca
n
d
id
ate
s
o
lu
ti
o
n
,
s
o
th
e
ca
n
d
i
d
ate
s
o
lu
tio
n
will
b
e
ac
ce
p
ted
with
p
r
o
b
ab
ilit
y
(
,
)
th
at
d
ep
en
d
s
o
n
th
e
d
if
f
er
en
ce
b
etwe
e
n
th
e
two
o
b
jectiv
e
f
u
n
ctio
n
v
alu
es
∆
=
[
(
)
−
(
)
]
.
T
h
e
ac
ce
p
tan
c
e
p
r
o
b
ab
ilit
y
(
,
)
is
g
iv
en
b
y
:
(
,
)
=
{
−
(
∆
)
if
(
)
≥
(
)
1
othe
r
wi
s
e
wh
er
e
is
a
co
n
t
r
o
ller
p
ar
am
e
ter
;
ca
lled
th
e
tem
p
er
atu
r
e.
I
n
im
p
lem
en
tatio
n
,
a
u
n
if
o
r
m
r
an
d
o
m
n
u
m
b
er
b
etwe
en
0
an
d
1
is
g
en
er
ated
an
d
co
m
p
ar
e
d
with
(
,
)
,
if
≤
(
,
)
,
th
e
m
o
v
e
is
ac
ce
p
ted
,
o
th
er
wis
e
a
n
ew
s
o
lu
tio
n
is
g
en
er
ated
f
r
o
m
th
e
n
eig
h
b
o
r
h
o
o
d
o
f
,
an
d
th
e
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
a
s
to
p
p
in
g
r
u
le
is
r
ea
ch
ed
.
T
h
e
s
im
u
lated
an
n
ea
lin
g
p
r
o
ce
d
u
r
e
is
p
r
esen
ted
in
th
e
f
l
o
w
ch
ar
t
in
Fig
u
r
e
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
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m
p
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g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
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9
2
2
-
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9
3
1
4926
Fig
u
r
e
2
.
Simu
lated
a
n
n
ea
lin
g
p
r
o
ce
d
u
r
e
with
c
o
n
s
tan
t
tem
p
er
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3.
NUM
E
RIC
AL
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M
P
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E
C
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n
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th
e
HVRP
p
r
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0
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tr
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s
tatio
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s
{
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s
{
3
,
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,
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d
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en
cu
s
to
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er
s
{
5
,
6
,
7
,
8
,
9
,
10
,
11
,
12
}
.
T
h
e
v
eh
icle
s
p
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if
icatio
n
s
ar
e
g
i
v
en
in
T
ab
le
1
.
T
h
e
v
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s
h
o
u
l
d
v
is
it
all
c
u
s
to
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er
s
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tar
tin
g
f
r
o
m
th
e
d
ep
o
t
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d
r
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r
n
to
it
,
th
e
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d
e
s
cr
ib
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in
(
1
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-
(
6
)
is
s
o
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u
s
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g
SA
alg
o
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ith
m
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h
e
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im
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u
s
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i
s
co
m
p
ar
ed
with
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d
ec
r
ea
s
in
g
tem
p
e
r
atu
r
e
as
s
u
g
g
ested
b
y
[
9
]
.
W
e
u
s
e
th
r
e
e
d
if
f
er
e
n
t
v
alu
es
f
o
r
th
e
c
o
n
s
tan
t
tem
p
er
atu
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e
=
1
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=
5
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d
=
10
.
W
e
u
s
e
th
e
s
o
lu
tio
n
th
at
h
as
th
e
m
in
im
u
m
v
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e
s
o
f
a
r
as
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e
o
p
tim
al
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o
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tio
n
as
in
th
e
alg
o
r
ith
m
o
f
Alr
e
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ae
i
a
n
d
An
d
r
ad
ó
ttir
[
2
0
]
.
T
h
e
ca
n
d
id
ate
s
o
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tio
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is
g
e
n
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ated
b
y
r
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lacin
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a
r
an
d
o
m
cu
s
to
m
er
with
an
o
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er
r
a
n
d
o
m
o
n
e.
W
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u
s
ed
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ty
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th
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ith
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T
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2
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1
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Veh
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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C
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4.
RE
SU
L
T
S
A
ND
D
I
SCU
SS
I
O
N
T
o
f
in
d
th
e
o
p
tim
u
m
s
o
lu
tio
n
,
we
f
ir
s
t g
en
er
ate
an
in
itial so
lu
tio
n
.
Star
tin
g
f
r
o
m
th
e
d
e
p
o
t,
ch
ec
k
th
e
ab
ilit
y
to
s
er
v
e
th
e
n
ea
r
est
cu
s
to
m
er
b
y
ch
e
ck
in
g
th
e
tim
e
as
well
as
th
e
elec
tr
icity
a
n
d
f
u
e
l
s
to
r
ag
e.
Fin
d
th
e
n
ea
r
est
cu
s
to
m
er
an
d
ch
ec
k
i
f
it
ca
n
b
e
r
ea
ch
ed
an
d
ch
ec
k
th
e
n
ea
r
est
s
tatio
n
to
th
e
n
ea
r
est
cu
s
to
m
er
,
if
it
ca
n
n
o
t
b
e
r
ea
ch
ed
,
th
en
m
o
v
e
to
th
e
n
ea
r
est
s
tatio
n
o
f
t
h
e
cu
r
r
en
t
n
o
d
e.
I
f
th
e
tim
e
is
n
o
t
e
n
o
u
g
h
to
r
ea
c
h
an
y
o
f
th
e
m
e
n
tio
n
ed
n
o
d
es
it
wil
l
r
etu
r
n
to
th
e
d
ep
o
t
a
n
d
s
tar
ts
a
n
ew
r
o
u
n
d
.
I
f
th
e
r
em
ai
n
in
g
tim
e
o
r
p
o
wer
is
n
o
t
en
o
u
g
h
to
r
et
u
r
n
to
t
h
e
d
ep
o
t,
th
e
alg
o
r
ith
m
will
r
ev
ea
l
an
in
f
ea
s
ib
le
s
o
lu
tio
n
.
T
h
e
t
o
t
a
l
c
o
s
t
w
i
l
l
b
e
c
a
l
c
u
l
a
t
e
d
b
a
s
e
d
o
n
t
h
e
d
i
s
t
a
n
c
e
t
r
a
v
e
l
l
e
d
,
t
h
e
p
o
w
e
r
(
e
l
e
c
t
r
i
c
i
t
y
a
n
d
f
u
e
l
)
c
o
n
s
u
m
p
t
i
o
n
r
a
t
e
,
a
n
d
t
h
e
p
o
wer
co
s
t.
T
ab
le
3
s
h
o
ws
th
e
g
en
er
ated
in
itial
s
o
lu
tio
n
f
o
r
v
is
itin
g
all
cu
s
to
m
er
s
wh
er
e
th
e
f
in
al
to
tal
co
s
t
i
s
$
9
4
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5
8
.
I
n
t
h
is
s
o
lu
tio
n
,
th
e
v
e
h
icle
v
is
ited
o
n
e
elec
tr
ic
s
tatio
n
,
wh
ich
h
as in
d
ex
2
,
an
d
o
n
e
f
u
el
s
tatio
n
,
wh
ich
h
as
in
d
ex
3
.
T
h
e
alg
o
r
ith
m
s
tar
ts
f
r
o
m
cu
s
to
m
er
6
th
en
v
is
its
cu
s
to
m
er
9
th
en
5
an
d
th
e
n
8
.
Af
ter
th
at,
th
e
v
eh
icle
is
r
u
n
o
u
t
o
f
en
o
u
g
h
el
ec
tr
icity
an
d
f
u
el,
th
e
r
ef
o
r
e
th
e
alg
o
r
ith
m
lo
o
k
s
f
o
r
th
e
n
ea
r
est
s
tatio
n
,
wh
ich
is
n
o
d
e
3
,
a
f
ter
r
e
f
u
elin
g
,
th
e
v
e
h
icle
m
o
v
es
t
o
cu
s
to
m
e
r
1
0
th
en
cu
s
to
m
er
7
an
d
th
en
cu
s
to
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1
2
,
th
en
it
n
ee
d
s
to
r
ec
h
ar
g
e
a
g
ain
f
r
o
m
s
tatio
n
2
,
a
n
d
s
in
ce
it
co
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l
d
n
’
t
g
o
t
o
o
th
er
c
u
s
to
m
er
b
ec
a
u
s
e
th
e
r
e
m
ain
in
g
tim
e
is
n
o
t
en
o
u
g
h
,
it
r
e
tu
r
n
s
to
th
e
d
ep
o
t
to
s
tar
t
a
n
ew
r
o
u
n
d
to
co
n
tin
u
e
s
er
v
i
n
g
th
e
r
est
cu
s
to
m
er
s
.
T
h
en
a
ca
n
d
id
at
e
s
o
lu
tio
n
is
g
en
er
ated
,
b
y
ch
an
g
in
g
th
e
o
r
d
e
r
o
f
cu
s
to
m
er
s
to
b
e
s
er
v
ed
an
d
th
e
to
tal
co
s
t
is
co
m
p
u
ted
.
Af
ter
th
at,
we
co
m
p
ar
e
th
e
c
u
r
r
en
t
v
alu
e
o
f
t
h
e
to
tal
c
o
s
t
with
th
e
n
ew
o
n
e.
W
e
f
ir
s
t
c
o
n
s
id
er
a
co
n
s
tan
t
tem
p
er
atu
r
e
with
th
r
ee
d
if
f
e
r
en
t
v
alu
es
f
o
r
,
=
1
,
5
a
n
d
10
an
d
t
h
en
u
s
e
a
d
ec
r
ea
s
in
g
tem
p
e
r
atu
r
e
0
=
20
,
+
1
=
0
.
8
∗
.
T
h
e
f
o
u
r
ca
s
es a
r
e
d
escr
ib
e
d
b
elo
w.
4
.
1
.
T
he
ca
s
e
when
=
Fig
u
r
e
3
s
h
o
ws
th
e
SA
p
er
f
o
r
m
an
ce
wh
en
=
1
.
W
h
er
e
th
e
d
o
tted
lin
e
(
r
ed
)
s
h
o
ws
th
e
o
b
ject
iv
e
f
u
n
ctio
n
o
f
th
e
ca
n
d
id
ate
s
o
l
u
tio
n
s
an
d
th
e
s
tr
ict
lin
e
s
h
o
ws
th
e
cu
r
r
en
t
o
b
jectiv
e
f
u
n
c
tio
n
o
f
th
e
c
u
r
r
e
n
t
s
o
lu
tio
n
s
.
I
f
th
e
s
tr
ict
lin
e
m
o
v
es
u
p
war
d
,
th
en
a
wo
r
s
e
s
o
lu
tio
n
is
ac
c
ep
ted
,
th
is
is
b
ec
au
s
e
a
b
etter
s
o
lu
tio
n
m
ay
b
e
h
i
d
d
en
b
eh
in
d
th
is
s
o
lu
tio
n
.
No
te
th
at
th
e
p
r
o
b
ab
ilit
y
o
f
ac
ce
p
tin
g
an
y
wo
r
s
e
o
b
jectiv
e
f
u
n
ctio
n
v
alu
e
is
v
er
y
s
m
all,
as
s
h
o
wn
in
Fig
u
r
e
3
,
it
alm
o
s
t
d
o
es
n
o
t
a
cc
ep
t
an
y
wo
r
s
e
f
u
n
ctio
n
v
al
u
e,
th
is
m
ea
n
s
th
at
alg
o
r
ith
m
s
tu
ck
i
n
a
lo
ca
l
m
in
im
u
m
s
o
lu
tio
n
.
I
t
n
ee
d
s
6
0
iter
atio
n
s
to
r
ea
c
h
th
e
o
p
tim
u
m
v
alu
e,
wh
ich
in
d
icate
s
th
at
it
k
ee
p
s
p
e
r
f
o
r
m
in
g
g
o
o
d
b
u
t
a
p
p
r
o
ac
h
es
th
e
o
p
tim
u
m
s
lo
wly
.
Acc
o
r
d
i
n
g
to
t
h
e
f
ir
s
t
s
to
p
p
in
g
r
u
le
wh
ich
is
to
h
av
e
f
iv
e
iter
atio
n
s
with
o
u
t
i
m
p
r
o
v
em
en
t
i
n
th
e
o
b
jectiv
e
f
u
n
ctio
n
v
alu
e
;
th
e
o
p
tim
u
m
v
alu
e
was
$
6
3
.
9
4
r
esu
lted
af
te
r
1
2
it
er
atio
n
s
,
wh
ich
is
a
g
o
o
d
s
o
lu
tio
n
,
b
u
t
is
n
o
t
th
e
m
in
im
u
m
.
T
h
e
m
in
im
u
m
was
o
b
tain
ed
at
iter
atio
n
6
5
with
a
v
alu
e
o
f
$
5
9
.
1
1
.
T
ab
le
3
.
T
h
e
in
itial so
lu
tio
n
F
r
o
m
To
El
e
c
t
r
i
c
i
t
y
c
o
st
F
u
e
l
C
o
s
t
To
t
a
l
C
o
st
0
6
=
0
.
55
=
0
.
00
=
0
.
55
6
9
=
0
.
09
=
15
.
25
=
15
.
89
9
5
=
0
.
00
=
2
.
89
=
18
.
78
5
8
=
0
.
00
=
4
.
27
=
23
.
05
8
3
=
0
.
00
=
5
.
39
=
28
.
44
3
10
=
0
.
00
=
7
.
72
=
36
.
17
10
7
=
0
.
00
=
8
.
42
=
44
.
59
7
12
=
0
.
00
=
6
.
78
=
51
.
38
12
2
=
0
.
00
=
10
.
06
=
61
.
45
2
0
=
0
.
43
=
10
.
06
=
61
.
88
0
11
=
0
.
63
=
13
.
57
=
76
.
09
11
0
=
0
.
00
=
18
.
49
=
94
.
58
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
9
2
2
-
4
9
3
1
4928
Fig
u
r
e
3
.
C
u
r
r
e
n
t v
er
s
u
s
n
ew
s
o
lu
tio
n
wh
e
n
T
=
1
4
.
2
.
T
he
ca
s
e
when
=
No
w
we
ap
p
ly
th
e
SA
alg
o
r
it
h
m
with
a
co
n
s
tan
t
tem
p
er
atu
r
e
v
alu
e
T
=
5
.
I
n
th
is
ca
s
e,
t
h
e
p
r
o
b
a
b
ilit
y
o
f
ac
ce
p
tin
g
an
y
wo
r
s
e
o
b
jec
tiv
e
f
u
n
ctio
n
v
alu
e
is
s
till
s
m
all
b
u
t
it
is
b
etter
th
an
th
e
ca
s
e
wh
er
e
T
=1
.
T
h
e
r
esu
lts
ar
e
d
ep
icted
in
Fig
u
r
e
4
.
Fig
u
r
e
4
.
C
u
r
r
e
n
t v
er
s
u
s
n
ew
s
o
lu
tio
n
wh
e
n
T
=
5
4
.
3
.
T
he
ca
s
e
whe
n
=
T
h
e
SA
alg
o
r
ith
m
with
a
co
n
s
tan
t
v
alu
e
T
=1
0
.
I
n
th
is
ca
s
e,
th
e
p
r
o
b
ab
ilit
y
o
f
ac
ce
p
tin
g
an
y
wo
r
s
e
o
b
jectiv
e
f
u
n
ctio
n
v
alu
e
is
lar
g
er
th
an
th
e
p
r
ev
io
u
s
two
ca
s
es.
T
h
er
ef
o
r
e,
th
e
cu
r
r
e
n
t
s
o
l
u
tio
n
v
a
r
ies
f
o
r
all
iter
atio
n
s
,
an
d
it r
ea
c
h
ed
th
e
m
in
im
u
m
(
$
5
9
.
1
1
)
at
iter
atio
n
1
2
,
as sh
o
wn
i
n
Fig
u
r
e
5
.
Fig
u
r
e
5
.
C
u
r
r
e
n
t v
er
s
u
s
n
ew
s
o
lu
tio
n
wh
e
n
T
=
10
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8
7
0
8
S
o
lvin
g
h
yb
r
id
-
ve
h
icle
r
o
u
tin
g
p
r
o
b
lem
u
s
in
g
mo
d
ified
s
imu
la
ted
a
n
n
ea
lin
g
(
N
o
u
r
A
ls
u
ma
ir
a
t
)
4929
4
.
4
.
T
he
ca
s
e
whe
n
=
+
=
.
∗
No
w
to
c
o
m
p
ar
e
th
e
r
esu
lts
I
n
th
e
SA
alg
o
r
ith
m
with
a
d
ec
r
ea
s
in
g
v
alu
e
s
tar
tin
g
at
T
=2
0
a
n
d
d
ec
r
ea
s
es
with
r
atio
o
f
0
.
8
.
T
h
e
al
g
o
r
ith
m
ac
ce
p
ts
wo
r
s
e
f
u
n
ctio
n
v
alu
e
with
h
ig
h
p
r
o
b
ab
ilit
y
at
th
e
b
eg
in
n
in
g
,
h
o
wev
er
,
it
d
id
n
o
t
ac
ce
p
t
an
y
w
o
r
s
e
v
alu
e
f
o
r
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
f
r
o
m
ite
r
atio
n
9
to
iter
atio
n
2
9
.
I
t r
ea
ch
ed
t
h
e
m
in
im
u
m
(
$
5
9
.
1
1
)
at
iter
atio
n
2
2
,
as sh
o
w
n
in
Fig
u
r
e
6
.
Fig
u
r
e
7
p
r
esen
ts
th
e
av
er
ag
e
p
er
f
o
r
m
an
ce
o
f
th
e
alg
o
r
ith
m
o
v
er
1
0
r
ep
licat
io
n
s
u
s
in
g
th
e
ab
o
v
e
f
o
u
r
ca
s
es
o
f
th
e
tem
p
er
at
u
r
e
T
.
I
t
is
clea
r
th
at,
u
s
in
g
a
co
n
s
ta
n
t
tem
p
er
atu
r
e
=
10
,
allo
ws
th
e
alg
o
r
ith
m
to
ex
p
lo
r
e
t
h
e
s
tate
s
p
ac
e
f
r
ee
l
y
an
d
th
e
n
lo
ca
te
t
h
e
o
p
tim
al
s
o
lu
tio
n
f
aster
.
H
o
wev
er
,
u
s
in
g
a
s
m
all
tem
p
er
atu
r
e
=
1
o
r
=
5
,
th
e
alg
o
r
ith
m
d
o
es
n
o
t
m
o
v
e
f
r
ee
ly
s
o
it
s
tick
in
a
l
o
ca
l
o
p
tim
al
s
o
l
u
tio
n
.
Mo
r
eo
v
er
,
u
s
in
g
a
d
ec
r
ea
s
in
g
tem
p
e
r
atu
r
e
e
n
d
s
i
n
lo
ca
tin
g
a
lo
ca
l
o
p
tim
al
s
o
lu
tio
n
also
,
wh
ich
r
eq
u
i
r
es
r
estar
tin
g
th
e
al
g
o
r
ith
m
to
ex
p
lo
r
e
th
e
s
tate
s
p
ac
e.
T
a
b
le
4
s
h
o
ws
a
co
m
p
ar
is
o
n
b
e
twee
n
th
e
o
p
tim
u
m
f
u
n
ctio
n
v
alu
e
f
o
r
th
e
f
o
u
r
ca
s
es o
f
th
e
tem
p
er
atu
r
e
v
alu
e
u
s
in
g
th
e
two
s
to
p
p
in
g
r
u
les o
v
er
1
0
r
ep
licatio
n
s
.
Fig
u
r
e
6
.
Cu
r
r
e
n
t v
er
s
u
s
n
ew
s
o
lu
tio
n
at
T
=
2
0
an
d
d
ec
ea
s
in
g
at
+
1
=
0
.
8
∗
Fig
u
r
e
7
.
T
h
e
av
er
a
g
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
SA o
v
er
1
0
r
e
p
licatio
n
s
u
s
in
g
f
o
u
r
d
if
f
er
en
t
v
alu
es o
f
th
e
tem
p
er
atu
r
e
T
ab
le
4
.
A
co
m
p
ar
is
o
n
b
etwe
en
th
e
f
o
u
r
ca
s
es o
f
th
e
tem
p
er
a
tu
r
e
v
alu
e
Te
mp
e
r
a
t
u
r
e
v
a
l
u
e
Th
e
f
i
r
st
st
o
p
p
i
n
g
r
u
l
e
Th
e
se
c
o
n
d
st
o
p
p
i
n
g
r
u
l
e
A
v
e
r
a
g
e
n
u
m
b
e
r
o
f
i
t
e
r
a
t
i
o
n
s
T=
1
6
6
.
3
4
3
6
3
.
1
7
8
23
T=
5
6
4
.
9
5
9
6
1
.
9
4
5
22
T=
1
0
6
2
.
8
0
9
6
0
.
8
2
6
22
+
1
=
0
.
8
∗
,
0
=
20
6
5
.
3
3
9
6
1
.
9
4
5
19
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
11
,
No
.
6
,
Dec
em
b
e
r
2
0
2
1
:
4
9
2
2
-
4
9
3
1
4930
5.
CO
NCLU
SI
O
N
I
n
th
is
p
ap
er
,
we
h
av
e
s
tu
d
ie
d
th
e
h
y
b
r
id
v
e
h
icle
r
o
u
tin
g
p
r
o
b
lem
(
HVRP
)
at
wh
ic
h
a
v
eh
icle
is
p
lan
n
ed
to
v
is
it
all
cu
s
to
m
er
s
o
n
ly
o
n
ce
an
d
r
etu
r
n
to
th
e
d
ep
o
t,
th
e
s
im
u
lated
an
n
ea
lin
g
alg
o
r
ith
m
with
co
n
s
tan
t
tem
p
er
atu
r
e
was
u
s
e
d
to
s
o
lv
e
th
e
HVRP
,
th
is
al
lo
ws
th
e
alg
o
r
ith
m
to
ex
p
lo
r
e
th
e
s
tate
s
p
ac
e
f
r
ee
ly
,
esp
ec
ially
f
o
r
lar
g
e
v
alu
es
o
f
T
.
T
h
e
r
esu
lts
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
a
r
e
co
m
p
ar
ed
wit
h
th
e
SA
alg
o
r
ith
m
u
s
in
g
d
ec
r
ea
s
in
g
tem
p
e
r
atu
r
e.
T
h
e
r
esu
lts
in
d
icate
th
at
th
e
av
er
ag
e
p
e
r
f
o
r
m
an
ce
o
f
t
h
e
a
lg
o
r
ith
m
u
s
in
g
SA
with
co
n
s
tan
t te
m
p
er
atu
r
e
g
iv
es b
etter
s
o
lu
tio
n
an
d
less
av
er
ag
e
n
u
m
b
er
o
f
iter
atio
n
s
.
ACK
NO
WL
E
DG
E
M
E
NT
S
T
h
e
a
u
t
h
o
r
s
w
o
u
l
d
l
i
k
e
t
o
t
h
a
n
k
J
o
r
d
a
n
U
n
i
v
e
r
s
i
t
y
o
f
S
c
i
e
n
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
f
o
r
s
u
p
p
o
r
t
i
n
g
t
h
i
s
wo
r
k
.
RE
F
E
R
E
NC
E
S
[1
]
G
.
B.
Da
n
tzig
a
n
d
J
.
H.
Ra
m
se
r,
“
Th
e
Tr
u
c
k
Dis
p
a
tch
in
g
P
r
o
b
lem
,
”
M
a
n
a
g
e
me
n
t
S
c
ien
c
e
,
v
o
l.
1
,
n
o
.
6
,
p
p
.
8
0
-
9
1
,
1
9
5
9
,
d
o
i:
1
0
.
1
2
8
7
/m
n
sc
.
6
.
1
.
8
0
.
[2
]
W.
Ca
o
a
n
d
W.
Ya
n
g
,
“
A
S
u
r
v
e
y
o
f
Ve
h
icle
Ro
u
ti
n
g
P
r
o
b
lem
,
”
Pro
c
e
e
d
in
g
s
o
f
th
e
1
3
t
h
Glo
b
a
l
Co
n
g
re
ss
o
n
M
a
n
u
f
a
c
tu
ri
n
g
a
n
d
M
a
n
a
g
e
me
n
t
(GCM
M
),
n
o
.
6
,
2
0
1
6
,
p
p
.
1
-
6
,
d
o
i:
1
0
.
1
0
5
1
/ma
tec
c
o
n
f/2
0
1
7
1
0
0
0
1
0
0
6
.
[3
]
J.
F
a
u
li
n
,
A.
J
u
a
n
,
E.
Lera
a
n
d
S
.
G
ra
sm
a
n
,
“
S
o
lv
i
n
g
t
h
e
Ca
p
a
c
it
a
t
e
d
Ve
h
icle
Ro
u
ti
n
g
P
r
o
b
lem
wit
h
En
v
iro
n
m
e
n
tal
Crit
e
ria
Ba
se
d
o
n
Re
a
l
Esti
m
a
ti
o
n
s
in
R
o
a
d
Tran
s
p
o
rtati
o
n
:
A
Ca
se
S
tu
d
y
,
”
Pro
c
e
d
ia
S
o
c
ia
l
a
n
d
Beh
a
v
io
ra
l
S
c
ien
c
e
s
,
v
o
l
.
2
0
,
n
o
.
1
,
p
p
.
3
2
3
-
3
3
4
,
2
0
1
1
,
d
o
i:
1
0
.
1
0
1
6
/j
.
s
b
sp
ro
.
2
0
1
1
.
0
8
.
0
3
8
.
[4
]
B.
M
a
h
v
a
sh
,
S
.
C
h
a
u
h
a
n
a
n
d
A
.
Aw
a
sth
i,
“
A
C
o
lu
m
n
G
e
n
e
ra
ti
o
n
Ba
se
d
He
u
risti
c
fo
r
th
e
Ca
p
a
c
it
a
ted
Ve
h
icle
Ro
u
ti
n
g
P
r
o
b
lem
wit
h
T
h
re
e
-
Dim
e
n
sio
n
a
l
L
o
a
d
i
n
g
Co
n
stra
in
ts,”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Pr
o
d
u
c
ti
o
n
Res
e
a
rc
h
,
v
o
l.
5
5
,
n
o
.
6
,
p
p
.
1
7
3
0
-
1
7
4
7
,
2
0
1
7
,
d
o
i:
1
0
.
1
0
8
0
/0
0
2
0
7
5
4
3
.
2
0
1
6
.
1
2
3
1
9
4
0
.
[5
]
A.
Li
m
a
n
d
X.
Zh
a
n
g
,
“
A
Two
-
S
tag
e
He
u
risti
c
with
Ej
e
c
ti
o
n
P
o
o
ls
a
n
d
G
e
n
e
ra
li
z
e
d
Ej
e
c
ti
o
n
Ch
a
in
s
fo
r
t
h
e
Ve
h
icle
Ro
u
ti
n
g
P
ro
b
lem
wit
h
T
ime
Wi
n
d
o
ws
,
”
IN
FORM
S
J
o
u
r
n
a
l
o
n
Co
mp
u
ti
n
g
,
v
o
l
.
1
9
,
n
o
.
3
,
p
p
.
4
4
3
–
4
5
7
,
2
0
0
7
,
d
o
i:
1
0
.
1
2
8
7
/
ij
o
c
.
1
0
6
0
.
0
1
8
6
.
[6
]
E.
Yu
li
z
a
,
F
.
M
.
P
u
sp
it
a
a
n
d
S
.
S
.
S
u
p
a
d
i
,
“
Th
e
R
o
b
u
st
Co
u
n
terp
a
rt
Op
e
n
Ca
p
a
c
it
a
ted
Ve
h
icle
R
o
u
ti
n
g
P
ro
b
lem
with
Ti
m
e
Wi
n
d
o
ws
o
n
Was
te
Tran
sp
o
rt
P
ro
b
lem
s,”
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
In
fo
rm
a
ti
c
s
(BE
EI)
,
v
o
l.
9
,
n
o
.
5
,
p
p
.
2
0
7
4
-
2
0
8
1
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
5
9
1
/ee
i.
v
9
i5
.
2
4
3
9
.
[7
]
N.
El
-
S
h
e
rb
e
n
y
,
“
Ve
h
icle
R
o
u
t
i
n
g
wi
th
Ti
m
e
Wi
n
d
o
ws
:
An
O
v
e
rv
iew
o
f
E
x
a
c
t,
He
u
risti
c
a
n
d
M
e
tah
e
u
risti
c
M
e
th
o
d
s,”
J
o
u
rn
a
l
o
f
Ki
n
g
S
a
u
d
U
n
ive
rs
it
y
(S
c
ien
c
e
),
v
o
l.
2
2
,
n
o
.
3
,
p
p
.
1
2
3
-
1
3
1
,
2
0
1
0
,
d
o
i:
1
0
.
1
0
1
6
/j
.
j
k
su
s.
2
0
1
0
.
0
3
.
0
0
2
.
[8
]
M
.
Io
r
i,
J.
S
.
G
o
n
z
á
lez
a
n
d
D.
Vi
g
o
,
“
An
E
x
a
c
t
Ap
p
r
o
a
c
h
f
o
r
t
h
e
Ve
h
icle
Ro
u
ti
n
g
P
r
o
b
lem
with
T
wo
-
Dim
e
n
sio
n
a
l
Lo
a
d
i
n
g
C
o
n
stra
i
n
ts,”
T
ra
n
sp
o
rta
ti
o
n
S
c
ien
c
e
,
vol
.
4
1
,
n
o
.
2
,
p
p
.
2
5
3
-
2
6
4
,
2
0
0
7
,
DO
I:1
0
.
1
2
8
7
/t
rsc
.
1
0
6
0
.
0
1
6
5
.
[9
]
R.
Ba
ld
a
c
c
i,
A.
M
in
g
o
z
z
i,
R.
R
o
b
e
rti
a
n
d
R.
Walfl
e
r,
“
An
E
x
a
c
t
Alg
o
r
it
h
m
fo
r
t
h
e
Two
Ech
o
l
e
n
Ca
p
a
c
it
a
ted
Ve
h
icle
Ro
u
ti
n
g
P
ro
b
lem
,
”
Op
e
ra
ti
o
n
s R
e
se
a
rc
h
,
v
o
l
.
6
1
,
p
p
.
2
9
8
-
3
1
4
,
2
0
1
3
,
d
o
i:
1
0
.
1
2
8
7
/
o
p
re
.
1
1
2
0
.
1
1
5
3
.
[1
0
]
M
.
M
.
Tav
a
k
o
li
a
n
d
A.
S
a
m
i,
“
P
a
rti
c
le
S
wa
rm
Op
ti
m
iza
ti
o
n
in
S
o
lv
in
g
Ca
p
a
c
it
a
ted
Ve
h
icle
Ro
u
ti
n
g
P
ro
b
lem
,
”
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
En
g
in
e
e
rin
g
a
n
d
I
n
fo
rm
a
ti
c
s
(BE
EI)
,
v
o
l
.
2
,
n
o
.
4
,
p
p
.
2
5
2
-
2
5
7
,
2
0
1
3
,
d
o
i:
1
0
.
1
2
9
2
8
/ee
i.
v
2
i4
.
1
9
0
.
[1
1
]
G
.
Alfa
risy
,
W.
F
.
M
a
h
m
u
d
y
a
n
d
M
.
H.
Na
tsir,
“
Op
ti
m
izin
g
Lay
i
n
g
He
n
Die
t
u
sin
g
M
u
lt
i
-
S
wa
rm
P
a
rti
c
le
S
wa
rm
Op
ti
m
iza
ti
o
n
,
”
T
E
L
KOM
NIKA
(T
e
lec
o
mm
u
n
ica
ti
o
n
,
C
o
mp
u
ti
n
g
,
El
e
c
tro
n
ics
a
n
d
C
o
n
tr
o
l),
v
o
l.
1
6
,
n
o
.
4
,
p
p
.
1
7
1
2
-
1
7
2
3
,
2
0
1
8
,
d
o
i:
1
0
.
1
2
9
2
8
/t
e
l
k
o
m
n
i
k
a
.
v
1
6
i
4
.
7
7
6
5
.
[1
2
]
F
.
M
.
P
u
sp
it
a
,
Y.
Ha
rt
o
n
o
,
N.
Z.
S
y
a
p
u
tri
,
E.
Y
u
li
z
a
a
n
d
W
.
D.
P
ra
ti
wi,
“
Ro
b
u
st
Co
u
n
terp
a
rt
O
p
e
n
Ca
p
a
c
it
a
ted
Ve
h
icle
Ro
u
ti
n
g
(RC
-
OCV
RP
)
M
o
d
e
l
i
n
O
p
ti
m
iza
ti
o
n
o
f
G
a
rb
a
g
e
Tran
s
p
o
rtati
o
n
i
n
Distr
ict
S
a
k
o
a
n
d
S
u
k
a
ra
m
i,
P
a
lem
b
a
n
g
Cit
y
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(IJ
ECE
),
v
o
l.
8,
n
o
.
6
,
p
p
.
4
3
8
2
-
4
3
9
0
,
2
0
1
8
,
d
o
i:
10
.
1
1
5
9
1
/i
jec
e
.
v
8
i
6
.
p
p
4
3
8
2
-
4
3
9
0
.
[1
3
]
F
.
M
.
P
u
s
p
it
a
,
A
.
S
.
S
ima
n
ju
n
tak
,
R.
M
e
lati
a
n
d
S
.
Oc
tarin
a
,
“
De
m
a
n
d
r
o
b
u
st
c
o
u
n
terp
a
rt
o
p
e
n
c
a
p
a
c
it
a
ted
v
e
h
icle
ro
u
ti
n
g
p
ro
b
le
m
ti
m
e
win
d
o
ws
a
n
d
d
e
a
d
l
in
e
m
o
d
e
l
o
f
g
a
rb
a
g
e
tran
sp
o
rtati
o
n
with
LING
O
1
3
.
0
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
E
n
g
in
e
e
rin
g
(IJ
ECE
)
,
v
o
l.
1
0
,
n
o
.
6
,
p
p
.
6
3
8
0
-
6
3
8
8
,
2
0
2
0
,
d
o
i:
1
0
.
1
1
5
9
1
/
ij
e
c
e
.
v
1
0
i6
.
p
p
6
3
8
0
-
6
3
8
8
.
[1
4
]
N.
M
e
tro
p
o
li
s,
A.
W.
Ro
se
n
b
lu
t
h
,
M
.
N.
Ro
se
n
b
lu
t
h
a
n
d
A.
H.
Teller,
“
Eq
u
a
ti
o
n
o
f
S
tate
Ca
lcu
latio
n
s
b
y
F
a
st
Co
m
p
u
ti
n
g
M
a
c
h
in
e
s,”
T
h
e
J
o
u
rn
a
l
o
f
Ch
e
mic
a
l
Ph
y
sic
s
,
v
o
l.
2
1
,
n
o
.
6
,
p
p
.
1
0
8
7
-
1
0
9
2
,
2
0
1
8
,
d
o
i:
1
0
.
1
0
6
3
/1
.
1
6
9
9
1
1
4
.
[1
5
]
S
.
Kirk
p
a
tri
c
k
,
C
.
D.
G
e
latt
a
n
d
M
.
P
.
Ve
c
c
h
i,
“
Op
ti
m
iza
ti
o
n
b
y
S
imu
late
d
An
n
e
a
li
n
g
,
”
S
c
ien
c
e
,
v
o
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