Hybrid Evolutionary Approaches to Maximum Lifetime Routing and Energy Efficiency in Sensor Mesh...

Hybrid Evolutionary Approaches to Maximum LifetimeRouting and Energy Efficiency in Sensor Mesh Networks

Evolutionary Computation, 2015DOI: 10.1162/EVCO a 00151

Alma RahatRichard Everson

Jonathan Fieldsend

Computer ScienceUniversity of Exeter

United Kingdom

Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 1 / 12

Wireless Sensors

Autonomous devicesSend data to a central basestationEnvironmental or processmonitoring

IndustrialHeritagePharmaceuticalsHealth-care

Battery poweredMonitor locations that aredifficult to accessTypically left unattended forlong periods of time

pictureSensor monitoring showcase environment

in Mary Rose Museum, UKRahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 2 / 12

Mesh Network and Routing Scheme

Sensors and gateway

Network connectivity mapMesh Topology: sensors send dataeither directly (e.g. S2 = 〈2,G〉) orindirectly (e.g. S ′

2 = 〈2, 5,G〉) tothe gateway

Alternative routesRange extension

A routing scheme for the network

R = 〈S1, S2,S3,S4, S5〉

MaximiseAverage lifetimeTime before the first node exhausts its battery (network lifetime)



Sensors and gatewayNetwork connectivity map

Mesh Topology: sensors send dataeither directly (e.g. S2 = 〈2,G〉) orindirectly (e.g. S ′




R = 〈S1, S2,S3,S4, S5〉




Sensors and gatewayNetwork connectivity mapMesh Topology: sensors send dataeither directly (e.g. S2 = 〈2,G〉) orindirectly (e.g. S ′




R = 〈S1, S2,S3,S4, S5〉



Node Costs

Node’s cost due to a routingscheme R:

C1 =T1,G + (R2,1 + T1,G)+ (R3,1 + T1,G)

=u1,GT1,G + u1,2R2,1

+u1,3R3,1

For all transmissions.Ti ,j Transmission cost at node vi

Rj,i Reception cost at node vi

ui ,j Edge utilisation between vi &vj for all routes


Node Costs


C1 =T1,G + (R2,1 + T1,G)+ (R3,1 + T1,G)

=u1,GT1,G + u1,2R2,1

+u1,3R3,1




T1,G


Node Costs


C1 =T1,G + (R2,1 + T1,G)+ (R3,1 + T1,G)

=u1,GT1,G + u1,2R2,1

+u1,3R3,1




T1,G

R2,1


Node Costs


C1 =T1,G + (R2,1 + T1,G)+ (R3,1 + T1,G)

=u1,GT1,G + u1,2R2,1

+u1,3R3,1




T1,G

R3,1


Node Costs


C1 =T1,G + (R2,1 + T1,G)+ (R3,1 + T1,G)

=u1,GT1,G + u1,2R2,1

+u1,3R3,1




u1,GT1,G

u1,2R1,2

u1,3R1,3


Objectives

Lifetime for node vi :

Li (R) = QiEi + Ci

Radio communication current

Quiescent current

Remaining battery charge

Maximise

Average lifetime: f1(R) = 1n

n∑i=1

Li (R)

Network lifetime: f2(R) = mini∈[1,n]

Li (R)


Objectives

Lifetime for node vi :

Li (R) = QiEi + Ci

Radio communication currentQuiescent current

Remaining battery charge

Maximise

Average lifetime: f1(R) = 1n

n∑i=1

Li (R)

Network lifetime: f2(R) = mini∈[1,n]

Li (R)


Search Space Size

How big is the search space?

Number of possible routingschemes:

n∏i=1

ai

ai : Number of available routesfrom vi to vG

Shorter paths are expected tobe energy efficientLimit the number of pathsavailable to each node by usingk-shortest paths algorithm[Yen, 1972; Eppstein, 1999]Maximum search space size: kn

Quicker approximation ofPareto Front


Search Space Size

Number of possible looplesspaths for node v3: 1


n∏i=1

ai





Search Space Size



n∏i=1

ai





Search Space Size

Number of possible looplesspaths for node v3: 7Number of possible routingschemes:

n∏i=1

ai





Search Space Size


n∏i=1

ai


4032 solutions




Search Space Size


n∏i=1

ai


243 solutions




Max-Min Lifetime Pruning

Solving LP results in bestnetwork lifetime and associatededge utilisations

Remove unused edges (grey) toreduce graphApply k-SP to extract searchspace Ω′

With no limits on the number ofroutes per node, a linear program (LP)can be derived to maximise networklifetime [Chang et al., 2004]

max(

minvi ∈V

Li

)subject to:

Edge utilisation, uij ≥ 0Energy usage ≤ available chargeFlow conservation


Multi-Objective Evolutionary Algorithm

1: A← InitialiseArchive() . Initialise elite archive randomly2: for i ← 1 : T do3: R1,R2 ← Select(A) . Select two parent solutions4: R′ ← CrossOver(R1,R2)5: R′′ ← Mutate(R′)6: A← NonDominated(A ∪R′′) . Update archive7: end for8: return A . Approximation of the Pareto set

Crossover Select paths for each node from parentsMutation Replace paths randomly from k-shortest paths for some

nodes


Hybrid Evolutionary Approach

1 Gather connectivity map, G2 Solve LP and erase unused edges to reduce graph, G ′

3 Search space pruningApply k-SP on G to generate search space ΩApply k-SP on G ′ to generate search space Ω′

Two stages of optimisationSeparate optimisation: apply MOEA on Ω and Ω′; get resultingestimated Pareto set A and A′

Combined optimisationUse non-dominated solutions in A ∪ A′ as the initial archive forcombined stageApply MOEA in the combined search space Ω ∪ Ω′: resultingestimated Pareto front is A′′


Real Network: The Victoria & Albert Museum


Real Network: The Victoria & Albert Museum1st stage: optimising in Ω and Ω′ separately

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Average Lifetime (years)

Net

work

Life

time

(yea

rs)

ΩΩ′

30 nodes + gatewayk = 10; Ω and Ω′ arelimited to 1030 solutionseach.Initial population size:100Mutation and crossoverrate: 0.1Number of iterations:150, 000 (1st stage) and500, 000 (2nd stage).Run time: 2 minutes (1st

stage) and 4 minutes(2nd stage).


Real Network: The Victoria & Albert Museum1st stage: optimising in Ω and Ω′ separately2nd stage: optimising in Ω ∪ Ω′

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4


Net

work

Life

time

(yea

rs) Ω ∪ Ω′

ΩΩ′

30 nodes + gatewayk = 10; Ω and Ω′ arelimited to 1030 solutionseach.Initial population size:100Mutation and crossoverrate: 0.1Number of iterations:150, 000 (1st stage) and500, 000 (2nd stage).Run time: 2 minutes (1st

stage) and 4 minutes(2nd stage).



0 100000 200000 300000 400000 500000 600000 700000 8000001.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

Function Evaluations

Hyp

ervo

lum

eSingle-stage vs.Two-stage

Ω ∪ Ω′

Ω ∪ Ω′

Ω

Ω′



0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Lif

etim

eR

emai

nin

g(y

ears

)

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Ed

geU

tilisa

tion

0

12

3

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9

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1516 17

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29

30

1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.010.7

0.8

0.9

1.0

1.1

Average lifetime: 2 yearsNetwork lifetime: 0.7 years (node v19)

Avg. Lifetime

Net

.Li

fetim

e

Gateway



0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Lif

etim

eR

emai

nin

g(y

ears

)

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Ed

geU

tilisa

tion

0

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1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.010.7

0.8

0.9

1.0

1.1

Average lifetime: 1.76 yearsNetwork lifetime: 1.29 years (node v13)

Avg. Lifetime

Net

.Li

fetim

e

Gateway



0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Lif

etim

eR

emai

nin

g(y

ears

)

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Ed

geU

tilisa

tion

0

12

3

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1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.010.7

0.8

0.9

1.0

1.1

Average lifetime: 1.94 yearsNetwork lifetime: 1.11 years (node v21)

Avg. Lifetime

Net

.Li

fetim

e

Gateway


Multipath Routing Schemes

Multiple routes available for eachnode for sending data to the basestation

D routes per node (D-RS):

R = 〈R1,R2, . . . ,RD〉

R1 active for time τ1R2 active for time τ2

R1 active until node 1 expiresR2 active until node 5 expires

τ1 τ2

Optimal time share linearprogram

max(τ1 + τ2)

subject to:Time share, τi ≥ 0Remaining charge ≥ 0

Linear program solved computa-tionally for each proposed routingscheme

Hybrid evolutionary approachEvolve 1-RS solutions in Ωand Ω′ separatelyEvolve D-RS solutions in Ωand Ω′ separatelyEvolve D-RS solutions incombined search spaceΩ ∪ Ω′

65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉


R1 active until node 1 expires

R2 active until node 5 expires

Node 1

Node 5Char

ge

Time

τ1 τ2


max(τ1 + τ2)




65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉



Node 1

Node 5Char

ge

Time

τ1 τ2


max(τ1 + τ2)




65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉

R1 active for time τ12-RS

R2 active for time τ2


Node 1

Node 5Char

ge

Time

τ1

τ2


max(τ1 + τ2)




65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉

R1 active for time τ12-RS R2 active for time τ2


Node 1

Node 5Char

ge

Time

τ1 τ2


max(τ1 + τ2)




65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉



τ1 τ2


max(τ1 + τ2)



Optimising in Ω and Ω′ separately

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4


Net

work

Life

time

(yea

rs)

ΩΩ′


65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉



τ1 τ2


max(τ1 + τ2)



Optimising in Ω and Ω′ separately

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4


Net

work

Life

time

(yea

rs)

ΩΩ′

〈R1〉

〈R1,R2,R3〉 Hybrid evolutionary approachEvolve 1-RS solutions in Ωand Ω′ separatelyEvolve D-RS solutions in Ωand Ω′ separatelyEvolve D-RS solutions incombined search spaceΩ ∪ Ω′

65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉



τ1 τ2


max(τ1 + τ2)



Optimising in Ω and Ω′ separatelyOptimising in combined search space Ω ∪ Ω′

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4


Net

work

Life

time

(yea

rs) Ω ∪ Ω′

ΩΩ′


65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉



τ1 τ2


max(τ1 + τ2)




1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4


Net

work

Life

time

(yea

rs) Ω ∪ Ω′

ΩΩ′

98.4% Hybrid evolutionary approachEvolve 1-RS solutions in Ωand Ω′ separatelyEvolve D-RS solutions in Ωand Ω′ separatelyEvolve D-RS solutions incombined search spaceΩ ∪ Ω′

65.8% 31.3% 2.9%





R = 〈R1,R2, . . . ,RD〉



τ1 τ2


max(τ1 + τ2)




1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.000.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4


Net

work

Life

time

(yea

rs) Ω ∪ Ω′

ΩΩ′

98.4%


0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Lif

etim

eR

emai

nin

g(y

ears

)

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Ed

geU

tilisa

tion

0

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1.0

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1.4

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1.8

2.0

2.2

Lif

etim

eR

emai

nin

g(y

ears

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2.5

5.0

7.5

10.0

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20.0

Ed

geU

tilisa

tion

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0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Lif

etim

eR

emai

nin

g(y

ears

)

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

Ed

geU

tilisa

tion

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65.8% 31.3% 2.9%


Summary

Multi-objective optimisation ofrouting schemes to extend batterypowered mesh network lifetimeNovel search space pruning basedon exact solution from solving alinear program for network lifetimeTwo-stage evolutionary approach tobetter approximate the trade-offbetween network lifetime andaverage lifetimeOptimal time distribution betweenmultiple routing schemes to achieveimproved network lifetimeAbout 22% overall performancegain compared to previous results

510152025

Robustness

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

Net

wor

kL

ifet

ime

(yea

rs)

1-RS

2-RS

Current WorkEstimate the trade-off betweennetwork lifetime and robustness(tolerance against edge failure)


Hybrid Evolutionary Approaches to Maximum Lifetime Routing and Energy Efficiency in Sensor Mesh...

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