Optimal Spatial Partitioning for
Resource Allocation
Kostas Kolomvatsos, Kakia Panagidi, Stathes Hadjiefthymiades
Pervasive Computing Research Group (http://p-comp.di.uoa.gr)
Department of Informatics and Telecommunications
National and Kapodistrian University of Athens
ISCRAM 2013
Baden Baden, Germany
Outline
 Introduction
 Problem Formulation
 Data Organization
 Proposed approach
 Case Study
Introduction
 Spatial Partitioning Problem




Segmentation of a geographical area
Optimal allocation of a number of resources
Resources could be vehicles, rescue teams, items, supplies, etc
The allocation is done according to:
 Population patterns
 Spatial characteristics of the area
 The process is affected by the following issues:
 Where to locate the resources
 Which area each resource will cover
 The number of resources
 Final objective: to maximize the area that the limited number of
resources will cover under a number of constraints.
Problem Formulation
 Nj (j=1, 2, …, R, R is the resources number) resources are
available to be allocated in an area A
 Each 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)
5
1
2
3
4
6
1
4
5
2
3
6
 In the optimal solution, we have:
Nj
 A  W0  H 0
l1 l
where Al is the area covered by the lth resource.
 The shape of each sub-area is not defined
 Overlaps should be eliminated
Data Organization
 Area related parameters
 Population attributes, density of population
 Type of area (hilly, flat, etc)
 Roads – road segments (length, speed limit, width, type, etc),
traffic
 Places 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 distance
 Crew or personnel
 Current Location
 Examples:
 Open Street Map could be the basis
 OSM 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 cells
 Size of each cell
x LR  x UL   y UL  y LR 
A 
c
2
Nc
 Define cell weights
 Use of AHP for attributes priority
 Users define the relative weight for each attribute - criterion
 Cell weight calculation
WC j  w i 
0  i  NA
,
 A ij 0  j  N c
A ij
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
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 cell
Fitness 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
D
C 
j
NH
 w  NH  1
i
i 1
D
T
60
S
T: time restriction, S: maximum speed,
wi: the weight of each cell in the neighbor,
NH: number of neighbors
N
j

| Ns | , |Ns |: neighbors
 Total covered area by the particle
i
i
i 1
C
number
N2
c
Case Study (1/2)
 Suppose Nj = 5 ambulances are available
 Their characteristics are:
No
1
2
3
4
5
Capacity
2
4
1
3
1
Max speed (Km/h)
60
180
160
150
5
Max travel distance (Km)
200
40
900
100
20
 We define maximum response time T = 5 minutes
 We select the desired area
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 management
 Preparation and prevention
 Early assessment
 International help request
 On-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