Multi-basesstrategies toMaximize Lifetime inWirelessSensor Network

EricBourreau1,MarcSevaux2,FabienCastano3,AndréRossi2,Nubia Velasco31 UniversitédeMontpellier,LIRMM

2 UniversitédeBretagneSud,LABSTICC3 Universidad delosAndes,Bogota,Columbia

1

WirelessSensor Network

2

WSN(with connectivity constraints)

TargetsSensorsBase

Sensing RangeCommunicationRange

3

MaximumLifetime foraWSN(cover) (columns)

TargetsSensors sensingSensors communicating (80%)Base

Sensing RangeComunication Range 4

Resolution Scheme

RMP(Restricted MasterProblem):• Maximize durationofactivated

covers• Packing colums with battery

constraints

PS(Pricing Subproblem):• MIP(Bender’s)• VNS+MIP• EA+MIP• …• CP• EA+CP• ApproximationScheme +CP

5

MasterProblem (LP)

tj switch ontime Cj Columnssu sensign node S SensorsBi battery capacity ε Rolel consumption ratey activationboolean fornode swith l

DualVariablesonsu :πu

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1Column Generation(Weighted Node SteinerTree Problem)

G’:graphvariable(targets andbasesinthekernel)

Σu inG’ Costu =TotalCost

Onconnexiongraph:Obligatories Nodes (targets +bases)Cost πu onnodesWeighted PartialSpanning treeSuch asTotalCost <1

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AntiarborescencesouscontraintesSuper-Base

Bases

NeighbourhoodBases

Targets

TargetNeighbourhood

(watchers)

Relay

Senseors

Constraint Programming• CP(G)

Ø Variablewhere variationdomainISagraph

GrégoireDooms,YvesDeville,PierreDupont:CP(Graph):Introducing aGraphComputationDomaininConstraint Programming,CP2005

Ø Available in Choco 3.0 (09/2013)

• tree(G,1)Ø OutDegree =1Ø NoCircuitØ Connexity toanti-root

(articulationpoint<->dominator)Ø O(nm)<->O(n+m)

Xavier Lorca, Jean-Guillaume Fages : Revisiting the tree Constraint, CP 2011

Ø inChoco 3.3extensions(11/2014)https://github.com/chocoteam/choco-graph

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Maximizing Lifetime …anobservation

0

1

2

3

4

5

6

7

100 200 300 400 500

Moy

Min

Max

• Average sizeofcovers :16,96(min15,max20)• 100/16,96=5,89theoritical lifetime (LT)• Average computed LT:4(min3,max5)?!

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

EJOR,vol241,Issue1,2014Exactapproaches forlifetime maximization inconnectivity constrained wireless multi-role sensornetworks,F.Castano E.BourreauNVelasco ARossiMSevaux

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Maximizing Lifetime …anidea

• Don’t waste time(andenergy)inconnectivity

Lifetime =5 Lifetime =6 10

Baserepartition Strategies

• Random

• Grid

• Circular

• K-means (p-center)

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LTImprovement

Nœuds/Bases Random Circulaire Grille K-means100 4,14 4,20 4,16 4,161 4,07 4,06 4,07 4,073 4,13 4,25 4,15 4,074 4,13 4,25 4,15 4,259 4,21 4,25 4,25 4,25200 4,93 4,97 4,96 4,951 4,84 4,94 4,95 4,953 4,95 5,00 4,95 4,954 4,95 4,95 4,95 4,959 4,98 5,00 5,00 4,95300 4,89 4,93 4,93 4,931 4,80 4,90 4,92 4,923 4,92 4,96 4,92 4,924 4,92 4,92 4,92 4,929 4,92 4,96 4,96 4,96400 4,90 5,00 5,00 5,001 4,60 5,00 5,00 5,003 5,00 5,00 5,00 5,004 5,00 5,00 5,00 5,009 5,00 5,00 5,00 5,00500 5,52 5,53 5,53 5,531 5,53 5,53 5,53 5,533 5,53 5,53 5,53 5,534 5,53 5,53 5,53 5,539 5,52 5,53 5,53 5,53

3,50

4,00

4,50

5,00

5,50

6,00

100 200 300 400 500

Nœuds/Bases Random Circulaire Grille K-means100 4,14 4,20 4,16 4,161 4,07 4,06 4,07 4,073 4,13 4,25 4,15 4,074 4,13 4,25 4,15 4,259 4,21 4,25 4,25 4,25200 4,93 4,97 4,96 4,951 4,84 4,94 4,95 4,953 4,95 5,00 4,95 4,954 4,95 4,95 4,95 4,959 4,98 5,00 5,00 4,95300 4,89 4,93 4,93 4,931 4,80 4,90 4,92 4,923 4,92 4,96 4,92 4,924 4,92 4,92 4,92 4,929 4,92 4,96 4,96 4,96400 4,90 5,00 5,00 5,001 4,60 5,00 5,00 5,003 5,00 5,00 5,00 5,004 5,00 5,00 5,00 5,009 5,00 5,00 5,00 5,00500 5,52 5,53 5,53 5,531 5,53 5,53 5,53 5,533 5,53 5,53 5,53 5,534 5,53 5,53 5,53 5,539 5,52 5,53 5,53 5,53

Nœuds/Bases Random Circulaire Grille K-means100 4,14 4,20 4,16 4,161 4,07 4,06 4,07 4,073 4,13 4,25 4,15 4,074 4,13 4,25 4,15 4,259 4,21 4,25 4,25 4,25200 4,93 4,97 4,96 4,951 4,84 4,94 4,95 4,953 4,95 5,00 4,95 4,954 4,95 4,95 4,95 4,959 4,98 5,00 5,00 4,95300 4,89 4,93 4,93 4,931 4,80 4,90 4,92 4,923 4,92 4,96 4,92 4,924 4,92 4,92 4,92 4,929 4,92 4,96 4,96 4,96400 4,90 5,00 5,00 5,001 4,60 5,00 5,00 5,003 5,00 5,00 5,00 5,004 5,00 5,00 5,00 5,009 5,00 5,00 5,00 5,00500 5,52 5,53 5,53 5,531 5,53 5,53 5,53 5,533 5,53 5,53 5,53 5,534 5,53 5,53 5,53 5,539 5,53 5,53 5,53 5,53

4strategies x5graphsizesx4basessizex16instancesè 1280benchmarks

4,00

4,50

5,00

5,50

6,00

1 3 4 9

100

200

300

400

500

3,50

4,00

4,50

5,00

5,50

6,00

100 200 300 400 500

Nodes/Bases Random Circular Grid K-means100 4,14 4,20 4,16 4,161 4,07 4,06 4,07 4,073 4,13 4,25 4,15 4,074 4,13 4,25 4,15 4,259 4,21 4,25 4,25 4,25200 4,93 4,97 4,96 4,951 4,84 4,94 4,95 4,953 4,95 5,00 4,95 4,954 4,95 4,95 4,95 4,959 4,98 5,00 5,00 4,95300 4,89 4,93 4,93 4,931 4,80 4,90 4,92 4,923 4,92 4,96 4,92 4,924 4,92 4,92 4,92 4,929 4,92 4,96 4,96 4,96400 4,90 5,00 5,00 5,001 4,60 5,00 5,00 5,003 5,00 5,00 5,00 5,004 5,00 5,00 5,00 5,009 5,00 5,00 5,00 5,00500 5,52 5,53 5,53 5,531 5,53 5,53 5,53 5,533 5,53 5,53 5,53 5,534 5,53 5,53 5,53 5,539 5,53 5,53 5,53 5,53

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750000sCPUL

Nodes/Bases Random Circular Grid K-means

Conclusion• Newdirections(moretocome)

– Fiability incommunications(robustness,disjointpaths)

– Morerealistic relationbetween Battery Consumption vsCommunication• Benchmarksavailable

– http://or-labsticc.univ-ubs.fr/?q=content/wireless-sensor-networkscover breach,bandwith,adjustable range,directional,Q-coverage,multiplerôle,mobile,…

• Budget/PublicationS

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