1
Addressing Coverage Problem in Wireless Sensor Networks
Based on Evolutionary Algorithms
Sahar Chehrazad
1
, Hadi S. Aghdasi
1
, Negin Shariati
2
and Mehran Abolhasan
2
1
Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
2
School of Computing and Communications, UTS, Sydney, Australia
Abstract—Wireless Sensor Networks (WSNs) are the key part of
Internet of Things, as they provide the physical interface between on-
field information and backbone analytic engines. An important role
of WSNs -when collecting vital information- is to provide a consistent
and reliable coverage. To Achieve this, WSNs must implement a
highly reliable and efficient coverage recovery algorithm. In this
paper, we take a fresh new approach to coverage recovery based on
evolutionary algorithms. We propose EMACB-SA, which introduces a
new evolutionary algorithm that selects coverage sets using a fitness
function that balances energy efficiency and redundancy. The proposed
algorithm improves network’s coverage and lifetime in areas with
heterogeneous event rate in comparison to previous works and hence,
it is suitable for using in disaster management.
Index Terms—Wireless sensor networks, internet of things, coverage
recovery, evolutionary algorithms, disaster management
I. INTRODUCTION
Wireless sensor networks (WSNs) consist of small devices
called sensor nodes which have limited sensing, processing and
communicating abilities [1], [2]. Monitoring the desired area (area
coverage) with the use of WSNs (as represented in Fig.1) plays a
very important role in disaster management by finding the exact
locations of trapped people and helps rescue teams in the optimal
management of disasters. Sensor nodes gather environmental infor-
mation (e.g. temperature, sound, and pictures) with the aim of fast
detection of disaster, identifying and helping trapped people and
helping rescue teams to provide a better management of resources
[3]–[8]. Scheduling sensor nodes (selecting a subset of sensor
nodes for covering whole area) in area coverage can provide us
with monitoring the area for a longer time and thus more time
for rescuing trapped people. Using evolutionary algorithms for
scheduling sensor nodes is beneficial as they scale well to higher
dimensional problems in one hand and can easily be adjusted to
the problem on the other hand. Therefore these algorithms are
obtained in this paper for solving the coverage problem.
Column generation method [9] uses heuristic algorithms to solve
Pricing Sub problem (PS). Provided that, heuristics are unable to
find a beneficial solution, integer linear programming (ILP) will
be utilized to solve PS . Maximum lifetime scheduling method
[10] at first, provides a multinomial time estimation procedure
for the situation where the density of target points is restricted,
and then a multinomial time constant factor estimation algorithm
for the general case. Energy-Efficient Probabilistic Area Coverage
method [11] first surveys the sensing probabilities of two points
with a distance of d and gets the basic mathematical relation
between them. If the sensing probability of one point is greater
than the specified amount, the other point is covered as well.
Hybrid Genetic Algorithm Using a Forward Encoding Scheme [12]
merges a genetic algorithm with schedule transition operations,
termed STHGA. The greatest gene value of each chromosome is
continuously grown with the quality of the solution, which pertains
to the number of disjoint complete coverage sets. Hybrid Memetic
Framework [13] deals with both disjoint set covers (DSC) and
dynamic-coverage-maintenance (DCM) problems simultaneously
Fig. 1. Area Coverage with Wireless Sensor Networks
to maximize the lifetime of WSNs. Ant-Colony-Based Scheduling
Algorithm [14] is concerned with finding the solution for the EEC
(Energy-Efficient Coverage) problem with a scheduling method
based on ant colony optimization in an unstructured WSN. The
pheromone field is initialized with the location of sensor nodes
and PoIs and the number of PoIs that can be covered by each
sensor node. By doing this, the possibility of selecting sensor
nodes which cover more PoIs at the beginning can be increased. In
the construction graph, ant k adds sensor nodes one at a time till
selected sensor set covers all PoIs. At the beginning, the ACB-SA
algorithm organizes the coverage set with few sensor nodes and
uses them continuously for several time steps. Once the energy of
the previously organized subset was nearly depleted, the ACB-SA
algorithm puts some new sensor nodes in the coverage set to cover
all PoIs.
All above-mentioned algorithms did not have a special look
at heterogeneous event rate in their works. Since the events are
distributed unequally in the area with heterogeneous event rate,
if sensor nodes which are placed in the areas with more event
rates are used for successive time steps, they will be depleted
after a short time. Therefore, in some applications like disaster
management, the network may be unable to cover some areas
after a while. The proposed algorithm is based on evolutionary
algorithms. It not only meets the criteria in the previous works, but
also considers event rate heterogeneous in the environment. The
EMACB-SA algorithm improves network’s coverage and lifetime
in comparison to previous ACB-SA algorithm. The organization
of this paper is as follows: In Section II, System Model and a list
of abbreviations used in this paper are demonstrated. In Section
III theoretical analysis and detailed description of the proposed
algorithm are represented. Section IV provides an overview of
Simulation Results which shows that the proposed algorithm is
more efficient in comparison to the existing algorithms. Finally
Section V is allocated to the conclusion of the proposed EMACB-
SA algorithm. Table I represents a list of abbreviations used in
this paper.
978-1-74052-390-5/17/$31.00 ©2017 IEEE
2
Fig. 2. Rs and Ru of a sensor node
II. SYSTEM MODEL
Our area of interest contains N sensor nodes which are small and
capable of communicating in short distances. In this paper, we used
a probabilistic sensor detection model which is more realistic [14].
Sensor nodes detect the event at the Point of Interest (PoI ) by the
intensity of the received signal or energy. This intensity is reduced
as the distance between the PoI and the sensor node increases.
The probability of event detection is a decreasing function of
the distance between the PoI and the center of the sensor node.
The equation for this model is as follows. λi(j) is the detection
probability of the sensor node i about events at PoIj.
λi(j)=
⎧
⎪
⎨
⎪
⎩
0, if d
ij
>Rs+ Ru
e
−a(d
ij
−Rs)
m
, if Rs < d
ij
≤ Rs + Ru
1, if d
ij
≤ Rs
(1)
Where d
ij
is the Euclidean distance between the sensor node i
and PoIj. The variables a and m are decay factors. Rs and Ru are
sensing range of a sensor node and its range of uncertainty in event
detection respectively (Fig.2). Events at PoIj are definitely detected
by sensor node I when d
ij
is less than Rs.Asd
ij
increases, the
detection probability is reduced. When d
ij
is greater than Ru,
the detection probability becomes zero. The variables a, m, Rs,
and Ru depend on the characteristics of the sensor node and the
environment.
III. PROPOSED ALGORITHM
In this paper, the proposed algorithm improves area coverage
and extends network’s lifetime. In the EMACB-SA algorithm,
the selection of new coverage set occurs in each time step. A
new fitness function is presented to balance energy efficiency and
redundancy. A coverage set in which sensor nodes have more
remaining energy and cover less redundant PoIs is selected in
each time step. The importance of these criterion can be defined
by coefficients a and b as represented in the equation 3. These
coefficients get the values between zero and 1. If the remaining
energy is more important to us, a higher amount is given to
a. Else, b will get a higher amount. In order to further reduce
the redundancy, a greedy algorithm is used in the EMACB-SA
algorithm due to which each ant adds selected sensor node to its
coverage set if it covers any new PoI.
A. Efficient Modified Ant Colony Based Scheduling Algorithm
(EMACB-SA)
Suppose that a lot of sensor nodes are distributed in the
environment. Table II represents the list of acronyms which are
used in this paper.
At the beginning to initialize the pheromone field, the location
of sensor nodes and PoIs are calculated [14] and put in two matrix
named LSen and LPoI respectively. At the beginning of each time
TABLE I
L
IST OF ABBREVIATIONS
Abbreviation Definition
ACB-SA Ant Colony Based Scheduling Algorithm
DCM Dynamic-Coverage-Maintenance
DSC Disjoint Set Covers
EC Energy for Coverage in each active time step
which equals to 0.1
EEC Energy-Efficient Coverage
EI(ts)
Initial Energy which is equal to 1 at ts=0
and the remaining energy of sensor
I at each time step (ts) is saved in it.
EMACB-SA Efficient Modified Ant Colony Based
Scheduling Algorithm
ILP Integer Linear Programming
LPoI Location of PoI
LSen Location of Sensor
MaxIter Maximum Iteration
NA Number of Ants
NP Number of PoIs
NS Number of Sensor nodes
PoI Point of Interest
PS Pricing Sub problem
Rs Sensing Range of sensor node
Ru Range of Uncertainty
ts time step
WSNs Wireless Sensor Networks
step, Icov and Tow
I
are calculated. Ants start their travel using
the proposed construction graph. Ant k chooses a sensor node by
roulette-wheel selection randomly in which each sensor node I has
the selection probability of P(I):
P (I)=Tow
I
/
NS
n=1
Tow
I
(2)
Each ant selects sensor nodes one at a time. Then greedy
algorithm checks whether the selected sensor node covers any
new PoI. At the beginning of the EMACB-SA algorithm, the
PoIs covered by each sensor node are saved in a matrix named
Sen-POI. Total number of PoIs covered by selected sensor nodes
are kept in another matrix named Ant-POI. Each time a new
sensor node is selected and added to the coverage set, Ant-POI
is updated. Therefore uncovered PoIs can be found. The sensor
node is added to the coverage set if it covers any new PoI.
Otherwise, it is dropped. A simple example of the greedy algorithm
is demonstrated in Fig.3. This will prevent the selection of sensor
nodes which have no benefit. By using this method, sensor nodes
are not activated uselessly and the lifetime of the network is
increased.
If ant k finds a set of sensor nodes which cover all PoIs, ant
k +1 will start its travel. After all ants (MaxAnt) finish their
selections, the best solution can be found with the use of proposed
fitness function which balances energy efficiency and redundancy.
In order to find the best solution two criterion, the cost of the
selected sensor nodes and redundancy, should be considered. The
higher the remaining energy of the sensor node I is, the lower
3
TABLE II
L
IST OF ACRONYMS
Acronyms Definition
a,b Numbers between zero and one and a + b =1
Bcost
Matrix which contains the lowest C
A
(ka)
in each iteration
Bcover
Matrix which contains the coverage set with
lowest C
A
(ka) in each iteration
C
A
(ka) Cost of selected sensor set by ant ka
Cost
W
Worst cost which happens when the ant selects all
sensors as the solution of the problem
Icov(ts)
A matrix which includes the number of POIs that is
covered by sensor I and is calculated at
the beginning of each time step
Cost(I) Cost of sensor node I that is equal to K
EI
K random number between zero and one
n
Number of sensor nodes in the selected coverage set
by ant
Red
A
(ka,ts)
Number of times that each PoI is covered by more
than one sensor node in time step (ts) which
equals to
n
n=1
Icov(ts) − NP
Red
W
Worst redundancy happens when the ant selects all
sensor nodes as the solution of the problem which
equals to
NS
n=1
Icov(1) − NP
Tow
I
(ts)
Pheromone field which is updated for each sensor
node I at the beginning of each time step which
equals to EI(ts) × Icov(ts)
Cost(I) will be. In this case the C
A
(ka) will get a lower value.
This increases the probability of selecting the coverage set in
which sensor nodes have higher remaining energy. On the other
hand, as the redundancy of the selected coverage set increases,
the C
A
(ka) gets a higher value. This reduces the probability of
coverage set with higher redundancy.Following fitness function by
adaptive weighted sum method [15] was proposed to make a trade-
off between these criterion:
C
A
(ka)=a × ((
n
I=1
Cost(I))/Cost
W
)
+(b × Red
A
(ka, ts))/Red
W
(3)
The selected coverage set with the lowest C
A
(ka) and its cost
are saved in two matrix named Bcover (Best cover) and Bcost
(Best cost) respectively. In the next iteration, Tow
I
is updated for
the sensor nodes in Bcover as follows:
Tow
I
= Tow
I
+(Bcost/
NA
ka=1
C
A
(ka)) (4)
In the next iteration, all above-mentioned works are done. The
ant with the lowest C
A
(ka) is selected. If its cost is lower than the
one saved in Bcost, it will be replaced by Bcost. Then the selected
coverage set in new iteration will be replaced by the one in Bcover.
For selecting a coverage set in each time step, MaxIter iteration
is completed and the coverage set which is in the matrix Bcover
is activated in that time step. At the end of each time step, EC (a
predefined amount) is reduced from the remaining energy (EI)of
each active sensor node. if there is a sensor node with EI<EC,
the percent of lost coverage with the death of that sensor node
is calculated (the percent of PoIs that are not covered anymore is
Fig. 3. An Example of the Greedy Algorithm
calculated and reduced from the coverage of the last time step).
Finally, dead sensor nodes and uncovered PoIs are omitted from
the matrix of sensor nodes and PoIs respectively. Otherwise, it is
continued in the next time step. It is also checked at the end of
each time step, whether all sensor nodes are dead. In this case, the
network is dead and our algorithm stops working. Otherwise, it is
continued in the next time step.
In the proposed algorithm, the death time of sensor nodes is
delayed, and sensor nodes which cover more PoIs can be used in
several time steps. In fact, it enables us to have full coverage of
the environment in WSNs for a longer time. The flowchart of the
EMACB-SA algorithm is represented in Fig.4.
IV. SIMULATION RESULTS
All simulations were implemented on a PC with an Intel(R) Core
i7-5500u operating at 3 GHz and 12 GB of RAM. We implemented
the simulator in MATLAB. The network is modelled as a (100 ×
100) square grid in a (100m × 100m) Euclidean plane. 40 sensor
nodes and 10000 PoI s are located on the grid points respectively
(one PoI on each point). The sensing range of sensor nodes (Rs)
and Range of uncertainty (Ru) are both considered 20m. Both a
and m are set to 0.5. EI is set to one at the beginning and it is saved
in a matrix named E with the size of 1×40. In each time step, EC
is reduced from EI of all active sensor nodes. In the simulation,
40 ants are used. The matrix Sen-POI with the size of 40 × 10000
includes PoIs which are covered by each sensor node. The matrix
Ant-Sen with the size of 40 × 40 includes sensor nodes which are
selected by each ant. The matrix Ant-POI with the size of 40 ×
10000 includes PoIs which are covered after selection of sensor
nodes. Two scenarios are considered for simulating the proposed
algorithm to illustrate its efficiency in disaster management. As ant
colony algorithms are based on random selection of sensor nodes,
the proposed algorithm was run several times and the simulation
results were saved in the structure. By averaging the saved results
for both scenarios, the area coverage, the number of all sensor
nodes (active & sleep) and redundancy were computed. To evaluate
the performance of the EMACB-SA algorithm, it simulation results
were compared with the ACB-SA algorithm.
A. First Scenario
In this scenario, each sensor node senses one event at each active
time step and EC =0.1 is reduced from its EI. Sensor nodes
are distributed in the area randomly to cover 10000 PoIs
. In the
EMACB-SA algorithm, the new coverage set is selected in each
time step. In the ACB-SA algorithm, the selected coverage set is
activated for 10 successive time steps. All sensor nodes have died
at the end of 10th-time step. Therefore, the new coverage set is
selected in each ten-time steps.
4
Fig. 4. Flowchart of the proposed algorithm
B. Second Scenario
In this scenario, some sensor nodes are in the regions with
heterogeneous event rate. These sensor nodes sense more than
one event at each active time step. Consequently, EC =0.2 is
reduced from their EI. Other sensor nodes sense one event at each
active time step, and EC =0.1 is reduced from their EI. Sensor
nodes are distributed in the area randomly to cover 10000 PoIs.
In the EMACB-SA algorithm, the new coverage set is selected in
each time step. In the ACB-SA algorithm, if any sensor node in
the selected coverage set belongs to a region with heterogeneous
event rate, the coverage set will be activated for five successive
time steps. At the end of the fifth-time step, some sensor nodes are
dead. Sensor nodes which belong to the region with homogenous
event rate still have EI =0.5 and will be activated in another
time steps. If the selected coverage set includes sensor nodes from
both regions and some sensor nodes have EI =0.5, it can be
activated only for 5 successive time steps. Therefore, in the ACB-
SA algorithm, the new coverage set is selected in each ten or
five-time steps.
C. Area Coverage
The results in Fig.5 indicate that in the first scenario, the
coverage of the ACB-SA algorithm reaches to less than 50 at
50th-time step. This occurs at 63rd time step in the EMACB-
SA algorithm. It can be concluded that the EMACB-SA algorithm
is 1.26 times better than the ACB-SA algorithm. In the second
scenario, the coverage of the ACB-SA algorithm reaches to less
than 30 at 39th-time step, while in the EMACB-SA algorithm this
occurs at 50th time step. It can be concluded that EMACB-SA
algorithm is 1.3 times better than the ACB-SA algorithm in this
case.
D. Number of all sensor nodes (active & sleep)
Fig.6 demonstrates that the number of alive sensor nodes in
the EMACB-SA algorithm is 1.23 times more than the ACB-
Fig. 5. Area Coverage in both scenarios
SA algorithm. The reason for the early death of sensor nodes
in the ACB-SA algorithm is activating selected coverage set for
successive time steps. In the EMACB-SA algorithm, the death time
of first sensor node occurs at 17th steps, while this occurs in the
ACB-SA algorithm at 10th-time step. It can be deduced that the
death time of first sensor node using the EMACB-SA algorithm
occurs 1.7 times later than the ACB-SA algorithm.
In the second scenario, the death time of first sensor node occurs
at 15th time step in the EMACB-SA algorithm, while this occurs at
the 10th-time step in the ACB-SA algorithm. It is derived that the
death time of first sensor node using the EMACB-SA algorithm
occurs 1.5 times later than the ACB-SA algorithm.
E. Redundancy
Fig.7 (the first scenario) illustrates that the redundancy of the
EMACB-SA algorithm is 7 percent better than the ACB-SA
algorithm. After 50th time step, the redundancy of the EMACB-SA
algorithm is 98 percent better than the ACB-SA algorithm.
In the second scenario (Fig.8), the redundancy of the EMACB-
SA algorithm is 1.73 times higher than the ACB-SA algorithm
5
Fig. 6. Number of sensor nodes (active & sleep) in both scenarios
Fig. 7. Redundancy in the environment with homogeneous event rate
Fig. 8. Redundancy in the environment with heterogeneous event rate
till 29th-time step. After 29th time step, the redundancy of the
EMACB-SA algorithm is 66 percent better than the ACB-SA
algorithm.
V. C
ONCLUSION
This paper presented EMACB-SA algorithm considering differ-
ent scenarios. In the first scenario, the event rate is homogenous
while in the second scenario, the heterogeneous event rate is
considered. For both scenarios, the area coverage, number of
sensor nodes (active & sleep) and redundancy were computed.
In the proposed algorithm, a new coverage set is selected at each
time step which increases the redundancy. In order to reduce the
redundancy, a new fitness function and a greedy algorithm was
proposed. Each sensor node is checked while being selected. The
selected sensor node will be added to ant’s coverage set if it covers
anewPoI. Otherwise, the sensor node will be dropped.
Simulations results prove that the EMACB-SA algorithm has
increased the area coverage as well as the network’s lifetime.
It delayed the death time of the first sensor node. Hence the
proposed algorithm is a promising solution for area coverage in
the environments with heterogeneous event rate.
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