BICRITERIA OPTIMIZATION OF ENERGY EFFICIENT
PLACEMENT AND ROUTING IN HETEROGENOUS
WIRELESS SENSOR NETWORKS
Mustafa Gökçe Baydoğan
School of Computing, Informatics and Decision Systems Engineering
Arizona State University (ASU) Tempe, AZ, USA
Nur Evin Özdemirel, PhD
Department of Industrial Engineering
Middle East Technical University (METU) Ankara,Turkey
11/10/2010
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
MOTIVATION
SOCIOECONOMIC
–
–
–
Environmental monitoring
–
Air, soil or water monitoring
–
Habibat monitoring
–
Seismic detection
Military surveillance
–
Battlefield monitoring
–
Sniper localization
–
Nuclear, biological or chemical attack detection
Disaster area monitoring
RESEARCH…
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
DESIGN ISSUES IN WSNs
Deployment
random vs deterministic; one-time vs iterative
Mobility
mobile vs immobile
Heterogeneity
homogeneous vs heterogeneus
Communication modality
radio vs light vs sound
Infrastructure
infrastructure vs ad hoc
Network Topology
single-hop vs star vs tree vs mesh
Römer and Mattern, 2004, The Design Space of Wireless Sensor Networks, IEEE Wireless Communications, 11:6, 54-6
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
PROBLEM CHARACTERISTICS
There are some events (targets) to be sensed in the monitoring area
Locate sensors to possible locations so that events are sensed(detected) with a given probability
Determine the rate of data flow between sensors and sink node (base station)
Sink
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
LITERATURE
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
PROBLEM DEFINITION
OBJECTIVES
–
Minimize total cost of sensors deployed
–
Maximize lifetime of the network
DECISIONS
–
Location of heterogeneous sensors
–
Data routing
CONSTRAINTS
–
Connectivity
–
Node (sensor) and channel (link) capacity
–
Coverage
–
Battery power
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
p
PROBLEM DEFINITION
CONNECTIVITY
A sensor of type k located at location i can communicate with a sensor of type k located at
location j if

dist ij  min crki , crkj

crki
crki
i
j
dist ij
crkj
(a)
7
i
dist ij
crkj
(b)
Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
j
p
PROBLEM DEFINITION
COVERAGE
Denoted as the detection probability of a target at point p
By a sensor of type k located at location i
  k distip

,
e
prikp  

0,
if dist ip  srk
decreases as distance increases†
otherwise
Detection probability of a target at point
prp  1 
Strength of the sensor signal
p
 1  pr 
x ik
i , k B p
ikp
† Zou and Chakrabarty, 2005, A Distributed Coverage- and Connectivity- Centric Technique for Selecting Active Nodes in
Wireless Sensor Networks, IEEE Transactions on Computers
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
PROBLEM DEFINITION
ENERGY CONSUMPTION MODEL †
Sources of energy consumption in a sensor
–
Generating data
–
Receiving data
eg k  
erij  
–
Transmitting data
etij     * dist ijm


is a distance-independent constant term
is a coefficient term associated with the distance dependent term
distij
m
is the distance between two locations
is the path loss index
† J. Tang, B. Hao, and A. Sen, 2006, Relay node placement in large scale wireless sensor networks, Computer Communications,
29:4, 490-501
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
PROBLEM FORMULATION
total cost of sensors located
lifetime of the network
one sensor can be located at each location
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
PROBLEM FORMULATION
data flow balance at a sensor
all data is routed to sink node
sensor capacity
channel (link) capacity
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
PROBLEM FORMULATION
coverage
battery power
location decision
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data flow decision
Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
THE BICRITERIA PROBLEM
DOMINATION
z , z 
'
1
if
'
2
dominates
z
''
1
, z2''

z1'  z1'' and z 2'  z 2''
z1'  z1'' and z 2'  z 2'' or
20
Network Lifetime
18
16
14
12
10
8
6
10
12
14
16
18
20
22
Sensor Cost
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
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A BICRITERIA PROBLEM
FINDING PARETO OPTIMAL SOLUTIONS
Network Lifetime
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Solve for z1 to find lower bound on cost
18
Solve for z2
16
s.t. cost  z1
14
to find lower bound on lifetime
12
Solve for z2 to find upper bound on lifetime
10
Solve for z1
8
6
10
s.t. lifetime  z2
12
14
16
18
20
22
24
26
to find upper bound on cost
Sensor Cost
For all integral z1 values
solve for z2
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
GENETIC ALGORITHM
Nondominated sorting approach (Goldberg, 1989)
Convergence to Pareto optimal front
Diverse set of solution along Pareto
optimal front
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
GENETIC ALGORITHM
REPRESENTATION
type of the sensor located on the corresponding location
1
2
3
0
1
2
i
-------
1
i 1
3
-------
n2
n 1
0
3
n
0
Disadvantages
–
Flow allocation is not stored
–
Lifetime cannot be determined
–
Finding feasible solutions after mutation and crossover operators is very hard
Advantages
–
Problem reduces to LP with given sensor locations
–
By solving LP, maximum lifetime and constraint violations can be determined
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
GENETIC ALGORITHM
FITNESS
Based on nondominated sorting idea
considering three objectives
– Total sensor cost
– Network lifetime
– Overall constraint violation
•
Connectivity
•
Coverage
•
Capacity violations
(channel and sensor)
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
GENETIC ALGORITHM
INITIAL POPULATION GENERATION
– Two phase approach
– Sensor location
– Location according to target coordinates
– Relay location
– Location according to sensor coordinates
MUTATION
– Repair and improve
– Repair coverage constraints
– Improve cost and lifetime objectives
– Repair connectivity constraints
– Improve cost objective
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
GENETIC ALGORITHM
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
TEST PROBLEMS
Small problems
–
–
41 possible locations
25 possible locations
PS24
BS
10
Problems with 24 possible locations
Problems with 40 possible locations
PS40
BS
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
50 targets are dispersed across the monitoring area
Each target has a random coverage threshold uniformly distributed between 0.7 and 1
The rate of data generated for each target is a random integer between 1 Kbps and 3 Kbps
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
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9
10
COMPUTATIONAL RESULTS
PERFORMANCE MEASURES
Proximity Indicator (PI)
For each solution found, find the Pareto
optimal solution with closest normalized
Tchebychev distance
Reverse Proximity Indicator (RPI)
For each Pareto optimal solution, find the
solution with closest normalized Tchebychev
distance
Hypervolume Indicator (HI)
Find the ratio of area bounded by nadir point
that cannot be covered
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
COMPUTATIONAL RESULTS
Smaller Problems
GA performance measures
Number of solutions
Problem Constraint # of feasible
size
tightness problems
RPI
PI
HI
e -constraint GA GA=Exact
PS24
0.0317 0.0220 0.0558
LC
30/30
10.20
9.27
3.70
0.0761 0.0574 0.1734
TC
29/30
7.47
6.57
1.93
(1)
PS40
LC
0.0464 0.0489 0.1164
10/10
13.60
12.80
1.30
LC(2)
20/20
13.00
14.20
0.0744 0.0780 0.1957
TC
30/30
11.60
11.10
1.13
(1)
Results across 10 instances that are solved exactly by the e -constraint approach.
(2)
Results across 20 instances that are solved approximately by the e -constraint approach.
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
CPU time (s)
e -constraint GA
1118
70
110
110
100088
798
85983
12865
821
797
COMPUTATIONAL RESULTS
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
COMPUTATIONAL RESULTS
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
COMPUTATIONAL RESULTS
TEST PROBLEMS
We also introduce larger test problems
Problems with 99 possible locations
20
20
15
15
10
10
5
5
0
0
0
25
Problems with 111 possible locations
5
10
15
20
0
Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
5
10
15
20
COMPUTATIONAL RESULTS
Larger Problems
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
CONCLUSION
COMMENTS and FURTHER RESEARCH
– GA provides reasonable solution quality with better solution times
 We can obtain better solutions than the exact approach has by representing the
area with more grids (approximation of the continuous space) even with better
solution times
Future research
– Modification of ε-constraint approach
– Use of sensitivity analysis results (in progress)
– Incorporating decision maker’s preferences
– Different objectives such as minimization of total delay, total hop count or average
path length
– Special network requirements such as K-coverage or K-connectivity
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
THANK YOU...
QUESTIONS AND COMMENTS?
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
OUTLINE
– MOTIVATION
– PROBLEM DEFINITION
– GENETIC ALGORITHM
– COMPUTATIONAL RESULTS
– CONCLUSION
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
EXACT SOLUTION
TEST PROBLEMS
41 possible locations
25 possible locations
PS24
BS
10
Small problems
–
Problems with 24 possible locations
–
Problems with 40 possible locations
PS40
BS
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
50 targets are dispersed across the monitoring area
Sensor type k  1
Sensor type k  2
Relay k  3
Sensor type k  1
Sensor type k  2
Each
scap target has a random coverage threshold uniformly
scap distributed between 0.7 and 1
100 Kpbs
k
200 Kpbs
150 Kbps
40 Kpbs
k
Relay k  3
80 Kpbs
40 Kbps
srk rate of data
srk integer 2between
The
1 Kbps
2 m generated3 for
m each target
0 mis a random
m
3 m and 3 Kbps0 m
crk
3m
5m
3m
crk
3m
5m
3m
ck
1
2
1
ck
1
2
1
k
0.15
0.1
-
k
ek
30
-5
10 EnergyUnits
-5
1.5x10 EnergyUnits
-5
10 EnergyUnits
ek
0.15
-5
10 EnergyUnits
Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
0.1
-5
1.5x10 EnergyUnits
-5
10 EnergyUnits
EXACT SOLUTION
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
GENETIC ALGORITHM
Why evolutionary algorithms?
• Classical search and optimization methods
– find single solution in every iteration
– need repetitive use of a single objective optimization method
– assumptions like linearity, continuity
• Evolutionary Algorithms
–
–
–
–
use a population of solutions in every generation
no assumptions
eliminate the need of parameters (like weight, ε or target vectors)
find and maintain multiple good solutions
• Emphasize all nondominated solutions in a population equally
• Preserve a diverse set of multiple nondominated solutions
Near optimal, uniformly disributed, well extended set of solutions for MO
problems
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
COMPUTATIONAL RESULTS
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
COMPUTATIONAL RESULTS
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin
CONCLUSION
– RPI and HI worsen as the problem size increases from 24 to 40 when capacity
constraints are loose
– TC instances are harder to solve for the GA compared to LC instances, whereas
they are easier for the ε-constraint approach.
– Performance measures for tight capacity are about twice as large as those for
loose capacity.
– The problem size has less effect on the performance measures when the capacity
constraints are tight.
– When the capacity constraints are loose, the GA solves problems of size 24 in one
tenth of the ε-constraint CPU times. For problems of size 40, GA CPU time is about
100 times shorter than ε-constraint time.
– For the tight capacity case, GA CPU times are slightly longer than ε-constraint
times with 24 possible locations, but they are 15 times shorter with 40 possible
locations.
– For problems with 99 and 111 possible locations, the GA converges to a solution in
about 160 minutes.
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Mustafa Gokce Baydogan and Nur Evin Ozdemirel
11/10/2010 INFORMS Annual Meeting/Austin