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

Hybrid Evolutionary Approaches to Maximum Lifetime
Routing and Energy Eﬃciency in Sensor Mesh Networks
Evolutionary Computation, 2015
DOI: 10.1162/EVCO a 00151
Alma Rahat
Richard Everson
Jonathan Fieldsend
Computer Science
University of Exeter
United Kingdom
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Eﬃciency GECCO, July 2015 1 / 12

Wireless Sensors
Autonomous devices
Send data to a central base
station
Environmental or process
monitoring
Industrial
Heritage
Pharmaceuticals
Health-care
Battery powered
Monitor locations that are
diﬃcult to access
Typically left unattended for
long periods of time
pictu
Sensor monitoring showcase environment
in Mary Rose Museum, UK

Mesh Network and Routing Scheme
Sensors and gateway

Sensors and gateway
Network connectivity map

Sensors and gateway
Mesh Topology: sensors send data
either directly (e.g. S2 = 2, G ) or
indirectly (e.g. S2 = 2, 5, G ) to
the gateway
Alternative routes
Range extension

Sensors and gateway
the gateway
Alternative routes
Range extension
A routing scheme for the network
R = S1, S2, S3, S4, S5

Sensors and gateway
the gateway
Alternative routes
Range extension
A routing scheme for the network
R = S1, S2, S3, S4, S5
Maximise
Average lifetime
Time before the ﬁrst node exhausts its battery (network lifetime)

Node Costs
Node’s cost due to a routing
scheme R:
C1 =T1,G + (R2,1 + T1,G)
+ (R3,1 + T1,G)
For all transmissions.
Ti,j Transmission cost at node vi
Rj,i Reception cost at node vi

Node Costs
scheme R:
C1 =T1,G + (R2,1 + T1,G)
+ (R3,1 + T1,G)
T1,G

Node Costs
scheme R:
C1 =T1,G + (R2,1 + T1,G)
+ (R3,1 + T1,G)
T1,G
R2,1

Node Costs
scheme R:
C1 =T1,G + (R2,1 + T1,G)
+ (R3,1 + T1,G)
T1,G
R3,1

Node Costs
scheme R:
C1 =T1,G + (R2,1 + T1,G)
+ (R3,1 + T1,G)
=u1,GT1,G + u1,2R2,1
+u1,3R3,1
ui,j Edge utilisation between vi &
vj for all routes
u1,GT1,G
u1,2R1,2
u1,3R1,3

Objectives
Lifetime for node vi :
Li (R) =
Qi
Ei + Ci
Radio communication current

Objectives
Li (R) =
Qi
Ei + Ci
Radio communication currentQuiescent current

Objectives
Li (R) =
Qi
Ei + Ci
Remaining battery charge

Objectives
Li (R) =
Qi
Ei + Ci
Remaining battery charge
Maximise
Average lifetime: f1(R) =
1
n
n
i=1
Li (R)
Network lifetime: f2(R) = min
i∈[1,n]
Li (R)

Search Space Size
How big is the search space?

Search Space Size
Number of possible loopless
paths for node v3: 1

Search Space Size

Search Space Size
Number of possible routing
schemes:
n
i=1
ai
ai : Number of available routes
from vi to vG

Search Space Size
schemes:
n
i=1
ai
from vi to vG
4032 solutions

Search Space Size
schemes:
n
i=1
ai
from vi to vG
243 solutions

Search Space Size
schemes:
n
i=1
ai
from vi to vG
243 solutions
Shorter paths are expected to
be energy eﬃcient
Limit the number of paths
available to each node by using
k-shortest paths algorithm
[Yen, 1972; Eppstein, 1999]
Maximum search space size: kn
Quicker approximation of
Pareto Front

Max-Min Lifetime Pruning
With no limits on the number of
routes per node, a linear program (LP)
can be derived to maximise network
lifetime [Chang et al., 2004]
max min
vi ∈V
Li
subject to:
Edge utilisation, uij ≥ 0
Energy usage ≤ available charge
Flow conservation

Max-Min Lifetime Pruning
Solving LP results in best
network lifetime and associated
edge utilisations
Remove unused edges (grey) to
reduce graph
Apply k-SP to extract search
space Ω
With no limits on the number of
routes per node, a linear program (LP)
can be derived to maximise network
lifetime [Chang et al., 2004]
max min
vi ∈V
Li
subject to:
Edge utilisation, uij ≥ 0
Energy usage ≤ available charge
Flow conservation

Multi-Objective Evolutionary Algorithm
1: A ← InitialiseArchive() Initialise elite archive randomly
2: for i ← 1 : T do
3: R1, R2 ← Select(A) Select two parent solutions
4: R ← CrossOver(R1, R2)
5: R ← Mutate(R )
6: A ← NonDominated(A ∪ R ) Update archive
7: end for
8: return A Approximation of the Pareto set
Crossover Select paths for each node from parents
Mutation Replace paths randomly from k-shortest paths for some
nodes

Hybrid Evolutionary Approach
1 Gather connectivity map, G
2 Solve LP and erase unused edges to reduce graph, G
3 Search space pruning
Apply k-SP on G to generate search space Ω
Apply k-SP on G to generate search space Ω
Two stages of optimisation
Separate optimisation: apply MOEA on Ω and Ω ; get resulting
estimated Pareto set A and A
Combined optimisation
Use non-dominated solutions in A ∪ A as the initial archive for
combined stage
Apply MOEA in the combined search space Ω ∪ Ω : resulting
estimated Pareto front is A

Real Network: The Victoria & Albert Museum

1st stage: optimising in Ω and Ω separately
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
Average Lifetime (years)
NetworkLifetime(years)
ΩΩ
30 nodes + gateway
k = 10; Ω and Ω are
limited to 1030
solutions
each.
Initial population size:
100
Mutation and crossover
rate: 0.1
Number of iterations:
150, 000 (1st
stage) and
500, 000 (2nd
stage).
Run time: 2 minutes (1st
stage) and 4 minutes
(2nd
stage).

1st stage: optimising in Ω and Ω separately
2nd stage: optimising in Ω ∪ Ω
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
Ω ∪ Ω
ΩΩ
30 nodes + gateway
k = 10; Ω and Ω are
limited to 1030
solutions
each.
Initial population size:
100
Mutation and crossover
rate: 0.1
Number of iterations:
150, 000 (1st
stage) and
500, 000 (2nd
stage).
Run time: 2 minutes (1st
stage) and 4 minutes
(2nd
stage).

0 100000 200000 300000 400000 500000 600000 700000 800000
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
Function Evaluations
Hypervolume Single-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
LifetimeRemaining(years)
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
EdgeUtilisation
0
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
1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01
0.7
0.8
0.9
1.0
1.1
Average lifetime: 2 years
Network lifetime: 0.7 years (node v19)
Avg. Lifetime
Net.Lifetime
Gateway

0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
EdgeUtilisation
0
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
1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01
0.7
0.8
0.9
1.0
1.1
Average lifetime: 1.76 years
Avg. Lifetime
Net.Lifetime
Gateway

0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
EdgeUtilisation
0
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
1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2.00 2.01
0.7
0.8
0.9
1.0
1.1
Average lifetime: 1.94 years
Avg. Lifetime
Net.Lifetime
Gateway

Multipath Routing Schemes
Multiple routes available for each
node for sending data to the base
station
D routes per node (D-RS):
R = R1, R2, . . . , RD

R1 active until node 1 expires
Node 1
Node 5
Charge
Time

Node 1
Node 5
Charge
Time

R1 active for time τ1
2-RS
Node 1
Node 5
Charge
Time
τ1

2-RS
Node 1
Node 5
Charge
Time
τ1 τ2

2-RS
Node 1
Node 5
Charge
Time
τ1 τ2
Optimal time share linear
program
max(τ1 + τ2)
subject to:
Time share, τi ≥ 0
Remaining charge ≥ 0
Linear program solved computa-
tionally for each proposed routing
scheme

Optimising in Ω and Ω separately
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
ΩΩ
Hybrid evolutionary approach
Evolve 1-RS solutions in Ω
and Ω separately
Evolve D-RS solutions in Ω
and Ω separately
Evolve D-RS solutions in
combined search space
Ω ∪ Ω

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
ΩΩ
R1
R1, R2, R3
and Ω separately
and Ω separately
Ω ∪ Ω

Optimising in combined search space Ω ∪ Ω
1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
Ω ∪ Ω
ΩΩ
and Ω separately
and Ω separately
Ω ∪ Ω

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
Ω ∪ Ω
ΩΩ
98.4% Hybrid evolutionary approach
and Ω separately
and Ω separately
Ω ∪ Ω

1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
Ω ∪ Ω
ΩΩ
98.4%
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
EdgeUtilisation
0
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
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
EdgeUtilisation
0
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
0
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
65.8% 31.3% 2.9%

Summary
Multi-objective optimisation of
routing schemes to extend battery
powered mesh network lifetime
Novel search space pruning based
on exact solution from solving a
linear program for network lifetime
Two-stage evolutionary approach to
better approximate the trade-oﬀ
between network lifetime and
average lifetime
Optimal time distribution between
multiple routing schemes to achieve
improved network lifetime
About 22% overall performance
gain compared to previous results
510152025
Robustness
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1-RS
2-RS
Current Work
Estimate the trade-oﬀ between
network lifetime and robustness
(tolerance against edge failure)

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

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