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