一直坚信我是神的孩子

shows a histogram of the mean percent
from optimal when the heuristic was restarted 128 times from each node and any node within 77%
of the greedy choice at each step is a potential candidate to add to the cluster. In this case, the
heuristic identi®ed the optimal solution 70% of the time and the mean percent from optimal was
3%.
7. 7 。 Producing risk maps using the CCM and GIS
Maps are often used in depicting risk which varies spatially, like ¯ood plains and seismic zones
subject to liquefaction. The designation of a ¯ood plain, for example, involves identifying which
areas will be ¯ooded with some annual frequency (eg once in 50 yr). A ¯ood plain map then
depicts those areas which are subject to a reasonable risk of ¯ooding (ie probability of an event
occurring on a given land unit). Such maps depict ``event risk occurrence'', but not the risk the
occupants face when an emergency evacuation is made. The most common map associated with
evacuation involves the depiction of evacuation routes and safe zones (like shelters). Such maps
depict an evacuation plan for a designated area, but not the risks. A critique of such maps can be
found in Dymon and Winter (1993).
What is proposed in this work and in Cova and Church (1997) is the development of risk maps
of potential evacuation di culty, which could be used in conjunction with event-risk maps to
develop better evacuation planning maps. The major objective would be to identify places of high
event-risk and high evacuation-risk. For example, hind-sight shows that the Oakland Hills area
was such an area. Advanced knowledge and public recognition could have possibly averted the
tragedy of 1991.
The CCM represents one possible model that can be used to estimate small neighborhood
evacuation risk di culty. The higher the bld or cte, the greater the possible problems that may be
encountered in an emergency evacuation. If each node of the network is used as a anchor node for
the CCM, it is then possible to label each node on the transport network with a risk measure like
bld or cte. Given a spatial depiction of node locations and risk values, it is possible to perform two
types of mapping functions: (1) interpolate lines of equal risk, like elevation contours, and develop
a risk contour map; or (2) classify each node according to its ``relative risk value'' and map nodes
and arcs using some type of color scheme or gray scale according to the risk.
To develop such a map would be realistically out of the question for a large area, unless many
of the functions were automated. It is only natural to select a GIS platform to supply much of this
functionality. For our project, we selected the ARC INFO GIS system, although other systems
332 RL Church, TJ Cova / Transportation Research Part C 8 (2000) 321±336
would support such an application as well. Essentially, data in the GIS was represented by a set of
coverages, including network and population information. An export function using the ARC
INFO macro language was developed which produced a forward star data structure for the associated
road network. This data structure was used by the MPS setup program and the heuristic.
All network data was stored within the GIS and was exported in the special form for a given
selected anchor node. The CCM model was then solved (using either heuristic or CPLEX general
purpose LP/IP software system) and the result was imported back into the GIS. The application
was automated so that each node was systematically selected as an anchor node and solved by the
Fig. 6. 6 。 An evacuation vulnerability map of Santa Barbara.
RL Church, TJ Cova / Transportation Research Part C 8 (2000) 321±336 333
heuristic. The risk values, eg bld, were then imported into the GIS and assigned as attributes to
the nodes. Each identi®ed critical cluster represented a set of nodes and a bld value. After solution
for a speci®ed anchor node was determined, each node within the critical cluster was tested to see
if the new bld value was higher than the current bld value in the data layer. If the new value was
higher, then the node attribute for the critical value was set at that new value. If the new value was
lower, then the node attribute for the critical value was left unchanged. Essentially, for each node
the critical value is the highest value found associated with all critical clusters found which included
that node.
After all nodes were considered as possible anchor nodes for solving a CCM, then several Arc
Macro Language (AML) routines were executed. These routines assigned the evacuation di culty
of each arc the higher of the nodal endpoint evacuation risk values (ie bld values). Then each
node and arc was categorized by the relative bld value. These categories were then assigned either
a color or a gray scale value, and a complete map was produced. Without the capabilities of the
GIS, this type of mapping exercise would be too time consuming.
An example evacuation risk map developed by the use of the CCM model coupled with ARC/
info is given in Fig. 6. 6 。 Fig. 6 depicts a risk map for the south coast region of Santa Barbara
County. The upper portion of Fig. 6 depicts the entire south coast region. This region is bounded
by the ocean to the south and a mountain range to the north. A gray scale was used to depict bulk
lane demand in ranges of 0±200; 201±300; 301±400; 401±500; >500 people per exit lane. Census
population data was used to estimate population values and a NavTech database was used to
depict transport network links.
In the lower part of Fig. 6, four separate areas are shown in greater detail. They are Mission
Canyon (upper left), Carpenteria (upper right), downtown Santa Barbara southwest of highway
101 (lower right), and Isla Vista (lower left). These depict four of the areas that appear as very
dark in the upper map. Because of the natural foliage and steep terrain the mission canyon area is
a region of very high ®re risk. If a ®re risk map were available, then it would be possible to identify
Mission Canyon as both high evacuation risk and high ®re risk. Most other Santa Barbara
foothill locations have lower evacuation risk, thus planning e€orts can be concentrated in such
special areas of high risk. As an aside, homeowners and ®re department o cials have been
convinced of the urgency of the problem by this map. Even a district supervisor called a planning
meeting based upon the results of this mapping exercise. Members of the homeowners association
are now suggesting the need for a detailed simulation and evacuation plan.
8. 8 。 Conclusion
We have presented a specialized network partition model called the critical cluster model. This
model can be used to identify small neighborhoods about a given node that have potentially risky
combinations of high population and low exit road capacity. The CCM can be used to identify a
contiguous nodal cluster that maximizes bulk lane demand or an estimate of network clearing
time. Both measures, while not exact, are assumed to be reasonable surrogate measures of
evacuation risk. Although it would be desirable to identify neighborhoods at risk by a micro
simulation model, such a process would require de®ning the neighborhood in advance. The CCM
model can be used to perform this task.
334 RL Church, TJ Cova / Transportation Research Part C 8 (2000) 321±336
We have presented details on the solution of the CCM using general purpose optimization
software. Although the model does take considerable time to solve optimally, optimal solutions
have been used to test the e cacy of a heuristic process presented in a companion paper (Cova
and Church, 1997). Further research is needed in testing alternative approaches for solving the
CCM.
The general issue of mapping event-risk (eg ¯ooding) was discussed along with how the CCM
model can be used to map evacuation risk. Details on the integration of the CCM with GIS were
also presented. Finally, results of a loosely coupled model system using ARC/info GIS and the
CCM were presented and discussed. Results from this model as presented in map form have
a€ected the perception of such risk in the Santa Barbara area. Local ®re department o cials,
homeowners, and public o cials are currently working to address this problem in one of the areas
identi®ed as higher than average risk (in terms of both event-risk and evacuation risk).
Acknowledgements
The authors appreciate the helpful comments provided by the reviewers of the original draft of
the manuscript. Network data was supplied by Navigational Technologies, under an agreement to
the National Center for Geographic Information and Analysis. Support by the National Science
Foundation (NSF SBR96-00465) is gratefully acknowledged.
References
Cova, TJ, Church, RL, 1997. Modeling community evacuation vulnerability using GIS. International Journal of
Geographic Information Science 11, 763±784.
Dymon, UJ, Winter, NL, 1993. Evacuation mapping: the utility of guidelines. Disasters 17, 12±24.
Hobeika, AG, Jamei, B., 1985. MASSVAC: a model for calculating evacuation times under natural disasters.
Emergency Planning, Simulations Series 15, 23±28.
Jin, LM, Chan, SP, 1992. A genetic approach for network partitioning. International Journal of Computer
Mathematics 42, 47±60.
Johnson, DS, Aragon, CR, McGeoch, LA, Schevon, C., 1989. Optimization by simulated annealing: an
experimental evaluation; part I, graph partitioning. Operations Research 37, 865±892.
Kernighan, BW, Lin, S., 1970. An e cient heuristic procedure for partitioning graphs. Bell Systems Technical Journal
49, 291±307.
Laguna, M., Feo, TA, Elrod, HC, 1994. A greedy randomized adaptive search procedure for the two-partition
problem. Operations Research 42, 677±687.
Lindell, MK, Perry, RW, 1991. Understanding evacuation behavior: an editorial introduction. International Journal
of Mass Emergencies and Disasters 9, 133±136.
O ce of Emergency Services, 1992. The East Bay Hills Fire ± A Multi-agency Review of the October 1991 Fire in the
Oakland/Berkeley Hills. East Bay Hills Fire Operations Review Group, Governor's O ce, Sacramento, CA.
Owen, M., Galea, ER, Lawrence, PJ, 1996. The EXODUS evacuation model applied to building evacuation
scenarios. Fire Engineers Journal 56, 26±30.
Perry, R., 1985. Comprehensive Emergency Management: Evacuating Threatened Populations. JAI Press, London.
Pidd, M., Eglese, R., de Silva, FN, 1997. CEMPS: a prototype spatial decision support system to aid in planning
emergency evacuations. Transactions in GIS 1, 321±334.
RL Church, TJ Cova / Transportation Research Part C 8 (2000) 321±336 335
Pirkul, H., Rolland, E., 1994. New heuristic solution procedures for the uniform graph partitioning problem: extensions
and evaluation. Computers and Operations Research 21, 895±907.
She , Y., Mahmassani, H., Powell, WB, 1982. A transportation network evacuation model. Transportation Research
16A, 209±218.
Shough, WH, Magdalena, AT, Stalberg, CE, 1992. Hazard mitigation report for the East Bay ®re in the Oakland-
Berkeley hills. FEMA, FEMA-919-DR-CA.
Sinuany-Stern, Z., Stern, E., 1993. Simulating the evacuation of a small city: the e€ects of tra c factors. Socio-
Economic Planning Sciences 27, 97±108.
Sorensen, JH, Vogt, BM, Mileti, D., 1987. Evacuation: An Assessment of Planning and Research. Oak Ridge
National Laboratory ORNL-6376, Tennessee.
Southworth, F., 1991. Regional Evacuation Modeling: A State-of-the-Art Review. Oak Ridge National Laboratory
ORNL-11740, Tennessee.
Stern, E., Sinuany-Stern, Z., 1989. A behavioral-based simulation model for urban evacuation. Papers of the Regional
Science Association 66, 87±103.
Tufekci, S., Kisko, TM, 1991. Regional evacuation modelling system REMS: a decision support system for emergency
area evacuations. Computers and Industrial Engineering 21, 89±93.
336 RL Church, TJ Cova / Transportation Research Part C 8 (2000) 321±336