hybrid evolutionary approaches to maximum lifetime routing and energy efficiency in sensor mesh...
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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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12
Mesh Network and Routing Scheme
Sensors and gatewayNetwork connectivity map
Mesh 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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12
Mesh Network and Routing Scheme
Sensors and gatewayNetwork 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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12
Mesh Network and Routing Scheme
Sensors and gatewayNetwork 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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12
Mesh Network and Routing Scheme
Sensors and gatewayNetwork 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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12
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
T1,G
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12
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
T1,G
R2,1
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12
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
T1,G
R3,1
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12
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
u1,GT1,G
u1,2R1,2
u1,3R1,3
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 1
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 2
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 3
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 4
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 5
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 6
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 7
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 7Number 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 7Number of possible routingschemes:
n∏i=1
ai
ai : Number of available routesfrom vi to vG
4032 solutions
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 7Number of possible routingschemes:
n∏i=1
ai
ai : Number of available routesfrom vi to vG
243 solutions
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
Search Space Size
Number of possible looplesspaths for node v3: 7Number of possible routingschemes:
n∏i=1
ai
ai : Number of available routesfrom vi to vG
243 solutions
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 7 / 12
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 7 / 12
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 8 / 12
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′′
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 9 / 12
Real Network: The Victoria & Albert Museum
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
Real Network: The Victoria & Albert Museum
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
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
Average Lifetime (years)
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
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
Average Lifetime (years)
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
Real Network: The Victoria & Albert Museum
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′
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
Real Network: The Victoria & Albert Museum
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
4
5
6
7
8
9
10
11
12
13
14
1516 17
18
19
20
21
22
23
24
25
26
27
28
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
Real Network: The Victoria & Albert Museum
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
4
5
6
7
8
9
10
11
12
13
14
1516 17
18
19
20
21
22
23
24
25
26
27
28
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: 1.76 yearsNetwork lifetime: 1.29 years (node v13)
Avg. Lifetime
Net
.Li
fetim
e
Gateway
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
Real Network: The Victoria & Albert Museum
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
4
5
6
7
8
9
10
11
12
13
14
1516 17
18
19
20
21
22
23
24
25
26
27
28
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: 1.94 yearsNetwork lifetime: 1.11 years (node v21)
Avg. Lifetime
Net
.Li
fetim
e
Gateway
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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 expires
R2 active until node 5 expires
Node 1
Node 5Char
ge
Time
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
Node 1
Node 5Char
ge
Time
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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 τ12-RS
R2 active for time τ2
R1 active until node 1 expiresR2 active until node 5 expires
Node 1
Node 5Char
ge
Time
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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 τ12-RS R2 active for time τ2
R1 active until node 1 expiresR2 active until node 5 expires
Node 1
Node 5Char
ge
Time
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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 τ12-RS R2 active for time τ2
R1 active until node 1 expiresR2 active until node 5 expires
Node 1
Node 5Char
ge
Time
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
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′
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
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′
〈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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
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
Average Lifetime (years)
Net
work
Life
time
(yea
rs) Ω ∪ Ω′
ΩΩ′
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
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
Average Lifetime (years)
Net
work
Life
time
(yea
rs) Ω ∪ Ω′
ΩΩ′
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
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
Average Lifetime (years)
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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
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
Average Lifetime (years)
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′
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
4
5
6
7
8
9
10
11
12
13
14
1516 17
18
19
20
21
22
23
24
25
26
27
28
29
30
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
4
5
6
7
8
9
10
11
12
13
14
1516 17
18
19
20
21
22
23
24
25
26
27
28
29
30
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
4
5
6
7
8
9
10
11
12
13
14
1516 17
18
19
20
21
22
23
24
25
26
27
28
29
30
65.8% 31.3% 2.9%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 12 / 12