leading charac of the polygon
generator is n spatial dissect
density in the setting points.
There are W. and Gu
traditional one p3……pn} in
Ti={x|dx, pi distance. The w
providing that plane, an
λ
λ 、λ 、 d p, pi λj
⁄ , i the weight of t
2 Multi-ga
matching Accordin
the road netw diagram and r
stack. We can the overlap lay
the polygon constructed by
the zone whe gathering poin
selecting some
Accordin road evacuati
thickness and established by
multi-settling
Tab.1 is the s relationship o
points, we ca has four adjac
three adjacent adjacent point
cter is that the d n composing by
nearest. We u tion concerning
gathering poin e many ways to
Ch. L., 2000; e is provided
n the plane, s dx, pj p
weighted one is t n discrete po
nd n λ … … , Vn
j , divided t the point.
athering points g
ng to the coordi ork structure, w
oad network cl analyses the sp
yer. As shown proximity rela
y every point. In ere there is a
nt and the admi e setting points
Figure 1. O ng to the road
ion capacity a d the weighte
y the spatial loc points, we can
Table 1. Spa space adjacency
of the multi-ga an see from the
ent points here points here:
s here: T4, T distance betwee
y some points se weighted V
g the populati nts and the adm
o generate Voro ; Zhen Ch. H
that n discrete so the relevant
pi, pi pj}. d
s a little differe ints P={p1, p2
positive n Pi, λi
∩ the plane into
s and multi-se inates of the sim
we construct th lassified layer, a
patial point mat in the followin
ations in the n accordance w
a point, the p it population in
to every gather
Overlaying laye network layer
as a group of ed Voronoi d
ation of multi-g obtain the follo
ace adjacent tab y table about th
athering point e table that th
e: T10, T11, T1, T2, T
5, T6, T7; S en the internal
in the plane an Voronoi diagram
on and distrib mit population i
onoi diagram Z
H.et al. 2011 .
e points P={p1 t Voronoi dia
denotes Eucli ent from it. Like
2, p3……pn} in real num
P| d p, pi λi ⁄
n parts, λi den
ettling points s mulating points
he weighted Vo and then make
tching in the lig ng fig.1, we ca
radioactive re with road capac
population in e n every setting p
ring point.
rs which describe
f lines in diff iagram whic
gathering point owing table:
ble he space simul
s and multi-se he setting poin
T12, T13; S T3; S3
has S4 has four adj
point nd its
m as bution
in the Zhang
The 1, p2,
agram idean
ewise, n the
mbers i
notes space
s and ronoi
them ght of
n see egion
ity in every
point,
es the ferent
ch is ts and
lation ttling
nts S1 2 has
four acent
poin topo
and the T
base and
acco we c
S1 a T13
matc shou
popu free
betw the r
T12 can
poin the s
3.2 P
setti to se
rally part
cond obta
over seve
gath to M
one beca
to th over
max
et al 2000
gath eval
optim selec
poin secti
secti unde
we s nts here: T
ological relation the weights ab
Tab. 2 as below
Table Tab.2 is ultim
ed on the topolo the traffic
ommodation o can see that,
and the adopt ca which shou
ching setting po uld distribute t
ulation accept population acc
ween the origi remaining popu
, T11 has bee define the corr
nt and can get t setting points.
Path searching
To transfer th ng points, we h
elect the optima y points to settle
in constructing dition. Accord
ained based on rlay of road n
eral setting poin hering point, an
Multi-destinatio path as evacua
ause one path o he road transpo
rall evacuation ximum flow
on l.2009; Ch J. Ch
0, selecting
hering point t uation criteria
mal K path. T ction method is
nt to other setti ions. According
ions, we dete erstanding path
select the path T7, T8, T
nships of th bout the ability
w.
e 2. Spatial poin mate space-point
ogical relationsh c capacity
of population o according to
apacity of each ld consider f
oint of S1 are: the population
tance of poin eptance of T1
nal population ulation after the
en completed . responding sett
the number of
g
he disaster vict have several rou
al path to make e safely and eff
g emergency ev ding to the s
n the weighted etwork layer,
nts that is con nd that is the pa
ons. Usually it’ ation route from
ften causes the ort pressure, an
time. We use t the premise of
h. et al. 2007; A the optimum
o single setti of road transp
The basic thou s that there are s
ing points, and g to the discre
ermine the o h from gathering
of least resistan T9, T10.Acco
he various gat
of the road traf
nt matching tabl t matching pro
hips of the two of road netw
of each point . F the simulated
setting points: firstly, we ca
T11, T12, T13 to the best pl
nt T12, T11 13 is the diffe
n acceptance o e transmission
According to ting points of
the population
ims from gath utes to choose f
e the disaster vi ficiently is the m
vacuation model spatial point m
d Voronoi figu we get some
sidered prefere ath searching o
’s impractical m a rally point
short time cong nd directly caus
the K optimal f global optimu
Ahuja R K and m several path
ing point acc portation ability
ught of the op several roads fr
d each road is etion of the imp
overall impeda g points to setti
nce as optimal ording to
the thering points
ffic, we can get
le gram which is
kind of points work and
the From the table
population of T10, T11, T12,
an define the 3, Because we
lace, when the is full, the
erence number of T13 and
between S1 to the method we
each gathering distribution of
ering points to from. And how
ictims from the most important
l under disaster matching way
ure and layers information of
entially in each of single Origin
if only choose to another site,
gestion, adding se the delay of
paths based on um
Kou W. H. Magnanti T L,
hs from single ording to the
y, namely, the ptimal K path
rom a gathering made by some
pedance of the ance of each
ing points, then path, which in
e s
t
s ,
e e
f ,
e e
e e
r d
o e
g f
o w
e t
r y
s f
h n
e ,
g f
n .
, e
e e
h g
e e
h n
n
XXII ISPRS Congress, 25 August – 01 September 2012, Melbourne, Australia
197
turn to the se again until K o
3.2.1 Multi-pa
constraints: T
section is base flow, road dam
realize the Rea process of eva
path method b of increasing t
caused by sh population dis
node, as below
Figure 2． The secti
of the impeda transportation
the weight o population on
Based on available to ev
point. Three p 2, 4, 7, 9}; {1
nodes is alread relationship am
people in the f
Road sectio Road tran
ability Distributed
population
Based on following form
people of each Calculation o
nodes: calculation law
econd best sele optimal path.
aths problem
he assessment ed on the inform
mage degree an al-time optimal
acuation under based on the ma
traffic flow and hort term perso
stribution inform
w.
．Population di ions weight in f
ance of those r capacity, the a
of each section the section from
n the above fig vacuate people
paths, respective 1, 2, 5, 8, 9}; {
dy available in mong road sec
figure, the follo
ons 1-2 nsportation
a1
Table 3 n the ideas o
mula to calcula h path:
of the popula
;
the po
;
the po
;
th w, the populatio
ection, the opt
m under the
t of traffic ca mation of real-t
d static road co l quality of sele
r disaster, we a aximum flow t
d affecting overa onnel congestio
mation of each
istribution base figure is assess
roads which is a1, a2, a3......s
n. indica
m link node 1 t gure, starting th
from the gathe ely, go through
1, 3, 6, 9}, roa data of road ne
ctions, nodes an owing table is ob
1-3 2-4
a2 a3
. Information ta f maximum f
ate the final num ation flow be
pulation flow b opulation flow
he population ; then
on on each road timal path sele
e maximum
apacity of sel time dynamic tr
onditions. In ord ected road durin
adopt the K op o solve the pro
all evacuation s on. We recode
h section in the
ed on max-flow ed by the recip
s to be assessed eparately stand
ates the distrib o node 2.
here are three p ering point to se
different nodes ad sections with
twork. Accordi nd the high flo
btained:
4 2-5 …
a4 …
…
able flow, we adop
mber of distrib etween 1-2 n
between 1-3 n between 2-4 n
flow between according to
d section is obta ection
flow
ected raffic
der to ng the
ptimal oblem
speed e the
links
procal d the
ds for buted
paths etting
s: {1, h link
ing to ow of
…
…
…
t the bution
nodes: odes:
odes: n 2-5
the ained.
A popu
certa Duri
we w the
flow reco
mini
3.2.2 effic
theo area
infor algo
desti well
typic node
by s foun
optim trave
searc data
are p vario
algo high
road evac
netw mod
princ
by t H={
and of ro
as:
w base
thres ζ
After the pop ulation needs to
ain settlement p ing the assignm
will record the node informati
w on a path, orded in all th
imum value as
2 Road search
ciency when pa ory to calculate
a 、 real time rmation road
orithms could ination point w
l if the question cal shortest pat
es of the shorte step search algo
nd from them to mal solution, b
ersal, so ineffic ching algorithm
a sets. To solve proposed
Xian ous networks, t
orithms are diffe hest efficiency t
d network and cuation model
work hierarchy del for path op
ciples are show
Fig All road netw
the ability of {H1,H2,H3,H4}
V means the se oad, W means th
Vi v
, w , w … … . ed on the abil
shold ,
pulation on ea o be identified
point on a cert ments process b
flow of people ion. In order t
you should co he nodes inclu
the final popula
hing in networ
ath searching p multiple optim
and includin network data.
find the optim while those alg
n is very compl th algorithm to
est path. Becaus orithm for each
o m shortest pat but because of
cient. That is t m suites to sma
this problem, s ng J. P. et al.20
the efficiencies ferent .And ther
to all kinds of n d the detailed
under the d searching is u
ptimizing searc wn in the figure
gure 3 .Road ne work data is div
road evacuatio }. The graph of
et of road node he set of weigh
v , v , v … … .The threshold
lity of road e value:
; ζ ach section is
from an assem tain accessible
based on the m e assigned to ro
to determine th ompare the po
uded in the p ation flow on th
rk hierarchy: I
processes based mal paths whic
ng POIpoint . Traditional p
mal path from gorithms could
licated. Dijkstra o calculate a no
se Dijkstra algo h vertex n rese
th to work, it c f its calculatio
to say, Dijkstr all data sets ra
some optimal ro 11; Qiao L. et
s of all optimal re is no algorith
networks. Based requirements
disaster condit used to establis
hing. The who below.
etwork layers vided into four
on which is re f road network
es, E means the ht of each sectio
; Ei e , e ,
value of each l evacuation. As
ζ ζ , ζ , ζ
, ; ζ
s figured out, mbly point to a
road transport. maximum flow,
oad sections in he final person
opulation flow ath, then take
he entire path. It will has low
d on max-flow h face to large
of interesting path searching
start point to dn’t figure out
a algorithm is a ode to all other
orithm is a step ervations so far
an arrive at the on of the node
a shortest path ather than large
oute algorithms al. 2011
.As to route planning
hm that has the d on the special
of emergency tion, the road
sh mathematics ole algorithmic
specific layers epresented as :
k G={V, E, W} set of sections
on of road, such e … … ; Wi
layer is defined ssume that the
, ζ .
, a
. ,
n n
w e
w w
e g
o t
a r
p r
e e
h e
s o
g e
l y
d s
c
s :
s h
d e
XXII ISPRS Congress, 25 August – 01 September 2012, Melbourne, Australia
198
, ；
ζ ；
. For each layer Hi∈ H,
we compare Wiv, e with threshold ζi and make sure the
current road data belongs to which layer. After all road data has compared with threshold, we will get four sets such as: Hi= {Vi,
Ei, Wi}, i=1, 2, 3, 4. Searching the K optimal paths from gathering point to setting point based on following steps:
Step1: Finding the nearest road to the current gathering point and compare the ability of road evacuation with threshold of
each layer; Step2: Looking for the other collinear points with current
gathering point and compare those points with threshold value to make sure they are located in which layer. Assume that the
set of road nodes of collinear road section be represented as: N={n|ni
∈ Ls, i , … ….}.
Step3: Taking one node from the set N to begin the next step of path searching.
Step4: If the current road node is located in the highest layer then search the next section of road which is collinear with it.
The end node of the current section of road as the current node, that is, to reuse the same method over and over again until the
current node is collinear with settling point. Step5: If we can’t find the collinear node with current node in
the current data layer, we need to find the mapping point of current node in the next layer and reuse Step 4 and Step 5 until
to find all the successful way from all gathering points to all setting points. The concrete methods are shown in the figure
below.
Figure 4. Detailed network
3.3 Vehicle Assignment
