Mesh network topologies are becoming increasingly popular in battery-powered wireless sensor networks, primarily because of the extension of network range. However, multihop mesh networks suffer from higher energy costs, and the routing strategy employed directly affects the lifetime of nodes with limited energy resources. Hence when planning routes there are trade-offs to be considered between individual and system-wide battery lifetimes. We present a multiobjective routing optimisation approach using hybrid evolutionary algorithms to approximate the optimal trade-off between the minimum lifetime and the average lifetime of nodes in the network. In order to accomplish this combinatorial optimisation rapidly, our approach prunes the search space using k-shortest path pruning and a graph reduction method that finds candidate routes promoting long minimum lifetimes. When arbitrarily many routes from a node to the base station are permitted, optimal routes may be found as the solution to a well-known linear program. We present an evolutionary algorithm that finds good routes when each node is allowed only a small number of paths to the base station. On a real network deployed in the Victoria & Albert Museum, London, these solutions, using only three paths per node, are able to achieve minimum lifetimes of over 99% of the optimum linear program solution’s time to first sensor battery failure. The link for the paper: http://www.mitpressjournals.org/doi/abs/10.1162/EVCO_a_00151#.Vv6oZmErJhE More information on our work can be found on: http://emps.exeter.ac.uk/computer-science/wsn/

1. 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

2. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 2 / 12

3. Mesh Network and Routing Scheme
Sensors and gateway
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12

4. Mesh Network and Routing Scheme
Sensors and gateway
Network connectivity map
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12

5. Mesh Network and Routing Scheme
Sensors and gateway
Network connectivity map
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12

6. Mesh Network and Routing Scheme
Sensors and gateway
Network connectivity map
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
A routing scheme for the network
R = S1, S2, S3, S4, S5
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12

7. Mesh Network and Routing Scheme
Sensors and gateway
Network connectivity map
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
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 3 / 12

8. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12

9. 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
T1,G
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12

10. 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
T1,G
R2,1
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12

11. 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
T1,G
R3,1
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 4 / 12

12. Node Costs
Node’s cost due to a routing
scheme 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

13. Objectives
Lifetime for node vi :
Li (R) =
Qi
Ei + Ci
Radio communication current
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12

14. Objectives
Lifetime for node vi :
Li (R) =
Qi
Ei + Ci
Radio communication currentQuiescent current
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12

15. Objectives
Lifetime for node vi :
Li (R) =
Qi
Ei + Ci
Radio communication currentQuiescent current
Remaining battery charge
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12

16. Objectives
Lifetime for node vi :
Li (R) =
Qi
Ei + Ci
Radio communication currentQuiescent current
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)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 5 / 12

17. Search Space Size
How big is the search space?
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

18. Search Space Size
Number of possible loopless
paths for node v3: 1
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

19. Search Space Size
Number of possible loopless
paths for node v3: 2
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

20. Search Space Size
Number of possible loopless
paths for node v3: 3
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

21. Search Space Size
Number of possible loopless
paths for node v3: 4
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

22. Search Space Size
Number of possible loopless
paths for node v3: 5
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

23. Search Space Size
Number of possible loopless
paths for node v3: 6
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

24. Search Space Size
Number of possible loopless
paths for node v3: 7
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

25. Search Space Size
Number of possible loopless
paths for node v3: 7
Number of possible routing
schemes:
n
i=1
ai
ai : Number of available routes
from vi to vG
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

26. Search Space Size
Number of possible loopless
paths for node v3: 7
Number of possible routing
schemes:
n
i=1
ai
ai : Number of available routes
from vi to vG
4032 solutions
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

27. Search Space Size
Number of possible loopless
paths for node v3: 7
Number of possible routing
schemes:
n
i=1
ai
ai : Number of available routes
from vi to vG
243 solutions
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

28. Search Space Size
Number of possible loopless
paths for node v3: 7
Number of possible routing
schemes:
n
i=1
ai
ai : Number of available routes
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 6 / 12

29. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 7 / 12

30. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 7 / 12

31. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 8 / 12

32. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 9 / 12

33. Real Network: The Victoria & Albert Museum
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

34. Real Network: The Victoria & Albert Museum
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

35. 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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

36. 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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

37. 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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

38. Real Network: The Victoria & Albert Museum
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
Average Lifetime (years)
NetworkLifetime(years)
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

39. Real Network: The Victoria & Albert Museum
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
Average Lifetime (years)
NetworkLifetime(years)
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).
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

40. Real Network: The Victoria & Albert Museum
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

41. Real Network: The Victoria & Albert Museum
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

42. Real Network: The Victoria & Albert Museum
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: 1.76 years
Network lifetime: 1.29 years (node v13)
Avg. Lifetime
Net.Lifetime
Gateway
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

43. Real Network: The Victoria & Albert Museum
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: 1.94 years
Network lifetime: 1.11 years (node v21)
Avg. Lifetime
Net.Lifetime
Gateway
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 10 / 12

44. 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

45. Multipath Routing Schemes
R1 active until node 1 expires
Node 1
Node 5
Charge
Time
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

46. Multipath Routing Schemes
R1 active until node 1 expires
R2 active until node 5 expires
Node 1
Node 5
Charge
Time
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

47. Multipath Routing Schemes
R1 active for time τ1
2-RS
R1 active until node 1 expires
R2 active until node 5 expires
Node 1
Node 5
Charge
Time
τ1
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

48. Multipath Routing Schemes
R1 active for time τ1
2-RS
R2 active for time τ2
R1 active until node 1 expires
R2 active until node 5 expires
Node 1
Node 5
Charge
Time
τ1 τ2
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

49. Multipath Routing Schemes
R1 active for time τ1
2-RS
R2 active for time τ2
R1 active until node 1 expires
R2 active until node 5 expires
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

50. Multipath Routing Schemes
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
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

51. Multipath Routing Schemes
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
R1
R1, R2, R3
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

52. Multipath Routing Schemes
Optimising in Ω and Ω separately
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
Average Lifetime (years)
NetworkLifetime(years)
Ω ∪ Ω
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

53. Multipath Routing Schemes
Optimising in Ω and Ω separately
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
Average Lifetime (years)
NetworkLifetime(years)
Ω ∪ Ω
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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

54. Multipath Routing Schemes
Optimising in Ω and Ω separately
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
Average Lifetime (years)
NetworkLifetime(years)
Ω ∪ Ω
ΩΩ
98.4% 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
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

55. Multipath Routing Schemes
Optimising in Ω and Ω separately
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
Average Lifetime (years)
NetworkLifetime(years)
Ω ∪ Ω
ΩΩ
98.4%
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
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
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%
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 11 / 12

56. 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
NetworkLifetime(years)
1-RS
2-RS
Current Work
Estimate the trade-off between
network lifetime and robustness
(tolerance against edge failure)
Rahat, Everson & Fieldsend Max. Lifetime Routing and Energy Efficiency GECCO, July 2015 12 / 12