kostas kolomvatsos, kakia panagidi, stathes hadjiefthymiades pervasive computing research group ()...
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Kostas Kolomvatsos, Kakia Panagidi, Stathes Hadjiefthymiades
Pervasive Computing Research Group (http://p-comp.di.uoa.gr)
Department of Informatics and TelecommunicationsNational and Kapodistrian University of Athens
Optimal Spatial Partitioning for Resource Allocation
ISCRAM 2013Baden Baden, Germany
OutlineIntroductionProblem FormulationData OrganizationProposed approachCase Study
IntroductionSpatial Partitioning Problem
Segmentation of a geographical areaOptimal allocation of a number of resourcesResources could be vehicles, rescue teams,
items, supplies, etcThe allocation is done according to:
Population patternsSpatial characteristics of the area
The process is affected by the following issues:Where to locate the resourcesWhich area each resource will coverThe number of resources
Final objective: to maximize the area that the limited number of resources will cover under a number of constraints.
Problem FormulationNj (j=1, 2, …, R, R is the resources number)
resources are available to be allocated in an area AEach resource is of type Tj
The area has an orthogonal scheme (width: W0, height: H0)
A number of constraints should be fulfilled (Cjk, k=1,2, …, K)
In the optimal solution, we have:
where Al is the area covered by the lth resource.The shape of each sub-area is not defined Overlaps should be eliminated
1
26
5
43
1
23
4 5
6
jN
1l 0H0WlA
Data OrganizationArea related parameters
Population attributes, density of populationType of area (hilly, flat, etc)Roads – road segments (length, speed limit, width,
type, etc), trafficPlaces of interest - PoIs (schools, hospitals, fuel
stations, etc)Resource related parameters
Type (e.g., vehicle, rescue team, supplies, etc)Maximum speed in emergency and maximum
travel distanceCrew or personnelCurrent Location
Examples:Open Street Map could be the basisOSM data could be retrieved by CloudMade or
Mapcruzin.com
Proposed Approach (1/2)Split the area
Area A is defined by [(xUL, yUL), (xLR, yLR)] – upper left and lower right corners
Area A is divided into Nc X Nc cellsSize of each cell
Define cell weightsUse of AHP for attributes priorityUsers define the relative weight for each attribute -
criterionCell weight calculation
where wi is the ith attribute weight defined by AHP, Aij is the ith attribute value in cell j (e.g., schools, hospitals, fuel stations, etc), NA is the attributes number
2cN
LRyULyULxLRxcA
cNj0
NAi0,
ijA
ijA
iwjWC
Proposed Approach (2/2)Particle Swarm Optimization
We generate M particles (M vectors p of all resources coordinates)
p = [(x1, y1), (x2, y2), …, (xN, yN)]Coordinates are the center of a specific cellFitness Function F(p): Covered Area by each particle
(each resource)The best solution p* maximizes F(p*)If we consider that resources are vehicles
Area covered by a resource
T: time restriction, S: maximum speed, wi: the weight of each cell in the neighbor, NH: number
of neighborsTotal covered area by the particle , |Nsi|:
neighbors number
1NHNH
1ii
w
D
jC
S60
TD
2c
N
jN
1i|i
Ns|
C
Case Study (1/2)Suppose Nj = 5 ambulances are availableTheir characteristics are:
We define maximum response time T = 5 minutesWe select the desired area
No Capacity Max speed (Km/h)
Max travel distance (Km)
1 2 60 2002 4 180 403 1 160 9004 3 150 1005 1 5 20
Case Study (2/2)Resource locations are presented in the map
Numerical Results
Supported by European Commission The provided system:
Supports all stages of disaster managementPreparation and preventionEarly assessment International help requestOn-site cooperation
Integrates various available data sources and facilitates communication
Implements European and International disaster management procedures
Advances the state of the art in tools needed to support disaster response
Is easy to use and useful for handling tactical decision and strategic overview
Thank you!!http://p-comp.di.uoa.gr