This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Efficient Routing Protocol via Ant Colony Optimization (ACO)and Breadth First Search (BFS)
Reza Khoshkangini, Syroos Zaboli
International School of Information Management (ISIM)University of Mysore, India
Email: {reza.khosh, syroos}@isim.net.in
Mauro Conti
Department of MathematicsUniversity of Padua, Italy
Abstract—Wireless Sensor Networks (WSNs) consist of manysensor nodes, which are usually distributed across areas diffi-cult to be accessed in order to collect and send the data to themain sink location. Despite the fact that a number of protocolshave been proposed for routing and energy management, WSNsstill face problems in selecting the best path with efficientenergy consumption and successful delivery of the packets.In particular, these problems occur when WSNs are subjectedto critical situations such as node or link failure, and it iseven more critical in sensitive applications such as nuclearand healthcare.
In this paper, we propose the Ant Colony Optimization(ACO) combined with Breadth First Search (BFS) to searchand find the best and shortest path in order to improve datatransmission with the least amount of energy consumption,as well as reduce the probability of data loss. Using ourproposal, a balance between number of packets, time andenergy consumption can be determined which leads to increasethe network performance. Therefore, the main goal of the paperis to decrease energy consumption which leads to increaseof the network’s lifetime and enhancement of the number ofsuccessfully transmitted data with respect to other multipleants-based routing protocols. Moreover, the number of antsare optimized within the network to avoid network congestion.
Keywords-Sensor Network; Ant Colony Optimization (ACO);BFS; Routing; Cluster-Head;
I. INTRODUCTION
It is important to have efficient data transmission in
WSNs; considering the fact that a small change or loss in
data could lead to major problems in some applications.
For example, delay or poor quality of transmission in dam
building, military, nuclear or healthcare applications, could
manipulate a set of valuable information related to critical
decision making, leading to serious damage.
WSNs have a number of limitations such as increase
in the rate of energy consumption as the WSN begins its
communication state, which results in reduction in network
lifetime [1]. Low bandwidth and communication failure are
the other limitations which occur in WSNs affecting the per-
formance directly. Hence from a network design perspective;
Mauro Conti is supported by a Marie Curie Fellowship for the projectPRISM-CODE: Privacy and Security for Mobile Cooperative Devicesfunded by the European Commission (grant PCIG11-GA-2012-321980) andby the PRIN project TENACE: Protecting National Critical InfrastructuresFrom Cyber Threats (grant 20103P34XC) funded by the Italian MIUR.
one must consider various factors such as memory, security,
accuracy, speed and effective distance ranges, as well as their
priority with respect to their quality of service (QoS) re-
quirement in a specific application. For instance, security and
data transmission speed are often high priorities in a military
application [2],[3]. On the other hand, the designed routing
algorithm must be capable of increasing the quality of data
transmission, as well as handling certain communication
problems [4]. Nowadays, the previously designed protocols
for WSNs have lost their usability due to presence of new
technologies which lead to higher information transmission
and bigger networks. Therefore, there is a demand for the
current platforms to sustain their proper functionality by
applying the right protocols and efficient algorithms.
Marco Dorigo introduced the first ACO algorithm [5] in
order to solve combinational optimization problems such as
the Traveling Salesman Problem (TSP). Moreover, its other
variations as solutions to finding the shortest path on the
graph [6], and then enhancing the network lifetime and load
balancing in WSNs. In this paper we use this an artificial
intelligence algorithm to enhance the network performance
in WSNs, taking into account the characteristics of ACO
such as Positive Feedback [7] and Greedy Heuristic [8],
to find the best path to the base station and data packet
transmission. The structure of the network is as shown in
Figure 1.
Figure 1: ACO multi-path routing
2014 IEEE International Conference on Internet of Things (iThings 2014), Green Computing and Communications (GreenCom
2014), and Cyber-Physical-Social Computing (CPSCom 2014)
The black lines indicate the connection between the nodes
and their cluster head which the nodes (cluster members)
use, to send gathered data to their cluster head. Dotted lines
show the connection between cluster heads and intermediate
cluster heads, as well as cluster heads and sink where they
send their ants to carry the data toward the sink. τ is the
pheromone value of links between cluster heads and sink
which is explained in Equation 2.
By applying the graph search algorithm of Breadth First
Search, the selection accuracy of hops in transferring data
is enhanced with minimum transmission time and the least
energy consumption, moreover avoiding the probability of
starvation in the WSN. Starvation in wireless sensor net-
works mostly occurs due to the presence of expired nodes
and the failure of live sensor nodes in finding the right path
to transfer data to the base station [9].
The rest of the paper is organized as follows. Section
II surveys the pertinent literature. Section III describes the
proposed method; while Section IV discusses the simulation
results. Finally, Section V concludes the paper.
II. RELATED WORK
There has been quite a significant amount of work done
on different methods of routing using ACO, which turns
out to be one of the most suitable methods for multi-path
routing and a dynamic network for data transmission. For
example, Ad-Hoc networks, WSNs and telecommunications
networks [10].
Jing Yang et al. [11] introduced a Multi-path Routing
Protocol (MRP) which consists of three main steps as fol-
lows. First dynamically generating a cluster format, second
to search multiple paths to the base station using ACO
and finally dynamic selection of a single path for data
transmission. MRP makes use of three types of ants; the
search ant (SANT) which is used to capture the information
of paths and nodes on it’s way, the backward ant (BANT)
which has the responsibility of updating the pheromone
values and resending the collected information (such as path
length, energy consumption and residual energy) back to the
source node, and finally the abnormal ant (ABANT) which
is used to prevent stagnation of the protocol.
In spite of the fact that MRP improves data transmission
reliability and network lifetime in WSN, the algorithm speed
is quite low; moreover, it requires an amount of overhead
in dynamic areas to find the best path [12]. Every cluster
head sends a SANT in order to get information of its
neighborhood using Equation 1.
Pij =ταij(t)× ηβij
Σταij(t)× ηβij(1)
Yang Sun and Jingwen Tian [13] introduced another
multi-directional path algorithm by integrating the genetic
algorithm (GA) into the ant colony optimization algorithm,
where the initial solution is generated by the ACO as the
population for the genetic algorithm and next, the best
solution is searched by further iterations of genetic algo-
rithms using crossover and mutation. Although this approach
is effective in the long term in the case of multiple-path
searches, ACO sometimes faces the problem of generating
the best population for GA (starvation), moreover, GA needs
a large number of fitness function evaluations based on the
number of nodes. Hence, due to the GA’s drawback the
algorithm may take a long time to find the best path. In
addition, there is no guarantee that GA will find the best
solution.
Ruud Schoonderwoerd et al. [14] proposed an adap-
tive routing algorithm for telecommunication network using
ACO algorithm by introducing two specific kinds of agents
called ants. The first kind is the load management ant that
takes the responsibility of the lowest level of control; these
ants are launched from a particular node to search for the
most appropriate route from the source node to other nodes
using the ACO algorithm. The second kind are the parent
agents which are applied to the next level of control; these
parent agents move randomly in the networks based on the
heuristics and information gathered in the network, Hence
they have the ability to handle and fix the specific locations
which are experiencing congestion. This method is only
effective in case of optimal routing and organized public
transportation schemes in telecommunication networks.
Nuria Gomez et al. proposed a local routing method [17]
using ant colony algorithm, which keeps track of the in-
formation sent to the destination node instead of storing the
whole information on the network. In this method each node
stores information about its neighbourhood nodes such as the
pheromone value, the MAC/ID of the source and destination
nodes which are used to transmit data packets from the
source to the destination node in their routing table. Despite
this method being suitable for memory limitation applica-
tions, it has the drawback of high energy consumption.
Many ACO algorithms use ant memory to save a list
of visited node, whereas in other ACO approaches which
are suitable for static nodes (Selcuk’s method) [1], the data
carried by the ant can be limited, hence energy is preserved.
Here, the node’s memory is used in order to save information
related to other neighbouring nodes visited by an ant as well
as the pheromone values, which gives a node the choice to
accept or deny an incoming ant by looking up the tabu list.
Once an ant reaches the sink, an acknowledgement message
is sent back to the node through the same path. Although
the method is very useful to search for the best links in
a large number of nodes, it has prematurity and memory
problems, this is due to the fact that a large number of ants
in the network may lead to much higher traffic than the other
methods.
376375
III. PROPOSED METHOD
Link failure is a common occurrence in WSNs, which
results in problems such as repetitive back and forth trans-
mission of data between source and sink of a failed link due
to a dead node. Causing the failure of a message in reaching
its destination, thus leading to reduction in bandwidth range
and wastage of energy.
In this paper we propose a method using the ACO
algorithm along with BFS which is a tree-based search used
to enhance the accuracy of the best path selection. Here the
ACO consists on three type of ants, namely the frontward
ant, the Bfrontward ant and the backward ant [14], [15].
A. Frontward Ant
The frontward ant has the responsibility of finding the
best and shortest path by looking up the information on
neighboring nodes from the routing table. This ant considers
two distance factors; first is the distance between the current
node to its neighbourhood nodes and the second is the
distance of all the nodes (except the current node) from the
sink, which is placed at the center of area. It is important
for an ant to know each and every length between the nodes
and the sink which is shown in Table I [11].
Table I: Routing Table
ID MID LCN PHV DTS TBLST DTNx — x:20, y:45 0.5 25 y 25
y — x:15, y:53 0.6 30 z 31
ID, MID and LCN are the identification numbers, the
Mac addresses of each sensor node and the coordinates of
each cluster-head respectively. LCN is used to calculate the
distance between a cluster-head and the sink as well as the
distances between nodes. The pheromone value (PHV) of
each link increases every time as the frontward ant passes
through that link. DTS is the distance between the cluster
head and the sink. The tabu list (TBLST) contains the IDs of
nodes that a frontward ant arrives from. DTN is the distance
of a node to its neighbor. A frontward ant chooses and moves
towards the sink from one cluster head to another, based on
the Equation 2.
Pij =(τij)
α × (ηij)β × (Ej)
γ
Σ(τij)α × (ηij)β × (Ej)γ(2)
Where Pij is the selection probability of a cluster head
and τij is the pheromone value of a link between node i and
node j which can initially be assigned to 0 or 1. ηij , Ej are
the distance heuristic and energy level of node j respectively.
α, β, γ are the three controlling elements of the pheromone
value [1].
ηij =1
dij(3)
Where dij is the distance between nodes i and j, which
is shown in Equation 3. The shorter the distance, the higher
the probability, hence the frontward ant can select the closest
cluster-heads to the base station in its path.
ηij =1
djs(4)
Here djs is the distance between cluster-head j and the
sink which is illustrated in Figure 2. This helps the ant to
detect the next closest node to the base station. Since the
sensors are scattered across the area and the base station
is located at the centre, the movement of an ant starting at
any node in the area must be towards the centre taking the
closest cluster heads towards the sink into consideration.
ηij =1
dij+
1
djs(5)
Equation 5 which is derived from Equation 3 and 4, shows
the influence of the distance between nodes i and j as well
as the distance between node j to the sink on selection of
the next closest cluster head. Equation 6 is used to update
the pheromone value at the cluster heads links [5].
Δτij = (1− p)× τij +Δτij (6)
B. Backward Ant
Once the frontward ant carrying a data packet reaches
the destination, the base station extracts and processes the
received data packet. The sink adds the following headers;
the source node data header (Mac address and coordinate),
the destination data header (header of sender), and the stack
value of the latest received data packet. A backward ant
can take the same path back, as well as the algorithm
remarkably adapting to the network changes (this is illus-
trated in simulation section in Figure 7). In case of a link
failure during transmission, it has the ability to search for an
alternative closest intermediate cluster-head using Equation
3 according to the dead node. The proposed method uses
the node memory instead of ant memory for the advantage
of reduction in the ant’s packet load and decrease the packet
size which is directly related to the amount of energy
consumption [1]. Hence a tabu list made up of a stack is
used to keep a track of the node IDs from which an ant
comes from.
C. Energy Consumption Model
The LEACH model [16] is used for energy consumption
and it is implemented using Equation 7. The amount of
energy consumption depends on the distance between the
sender and receiver, as well as the size of the packets. In the
propose method, we use two types of energy consumption
models; first is free space (d2 reducing power) and second
is multi-path fading (d4 reducing power).
377376
Es =
{lEelect + lefpd
2 d ≤ ZomlEelect + lempd
4 d > Zom(7)
Where efp and emp are the energy consumption of
amplifying radio and Zom is the threshold value for the
distance.
D. Implementation of BFS Technique
In nature, it is hard for an ant positioned at the wrong
location to find and collect food; this happens when some
of the nodes expire sometime after the transmission begins
as we apply ACO to WSN in the nodes. This could be
due to failure of a sensor node, which results in starvation,
reduction in performance and the transfer rate of packets
to the sink and vise versa (this is described in simulation
section IV). As a solution we implement BFS in the ACO
algorithm which overcomes the problem of getting trapped
during exploration unlike the previous multi-path routing
protocols that did not focus on this particular problem [1].
Breadth-First Search (BFS) [18] is a graph search algorithm
used to explore the neighboring nodes, starting from the end
branches towards the main branches level by level. It can
continue this process throughout the connected neighbors
until it finds the solution or a specific node based on its
requirement.
E. Bfrontward Ant
BFS applied to the propose method for an ant (Bfront-
ward) to find its shortest path as shown in Figure 2, such
that, an ant situated at node-i looks for the shortest path to
the sink considering the first set of neighboring nodes. This
can be described as a tree (the whole network) where the
aim of an ant is to find the shortest distance from a leaf
on a branch (source node) to the trunk (sink). For example,
node-j is chosen using step 1 (frontward) and its distance
to the sink is achieved using (frontward) step 2. Next, the
node closest to the sink among all the other neighboring
nodes (except the visited nodes in order to avoid loop trap)
is chosen using (Bfrontward) step 3, Equation 8.
Figure 2: Process of finding the minimum distance
Equation 9 shows the distance heuristic calculation in
order to determine the selection probability of the next
cluster-head.
ηij =1
dmj(8)
ηij =1
dij+
1
djs+
1
dmj(9)
Where dmj is the minimum distance after node-j to the
sink which is determined by the BFS algorithm, and it is
included along with the other two distance values.
Using the Bfrontward ant, the current node-i, gets en-
hanced with the ability to predict the cost of selecting the
next node as a path, for example, node-j or node-k in order to
send data for the next level of transportation. Therefore, the
process of node selection to transport the data towards the
sink is carried out with minimum cost of energy, resulting
in a longer network lifetime.
In spite of the fact that implementation of BFS in ACO
leads to additional node memory and time consumption
which are the weaknesses of the method, it increases the
search accuracy in finding the shortest path. Hence achieving
the balance between depth levels, number of moving ants
within the network, energy consumption and time is firmly
essential to enhance the network performance. The time and
memory complexity which is commensurate to the number
of nodes at the depth level expressed Equation 10 [19].
O((V ) + (E)) (10)
Where E is the cardinality of set of edges (number of
edge between each node) and V is the number of nodes. In
order to reduce the node memory consumption and search
time, we limit the ant to only one depth level in the process
of determination of distance from that node to sink as
mentioned in Equation 8 and Figure 2. Moreover, energy
consumption, network lifetime and timing stamp are directly
related to the number of ants moving within the network.
That is, the number of cluster heads that are to send the
ants carrying data toward the sink, have to be optimized.
Before the ants are sent to the sink by the cluster heads
or intermediate cluster heads, the cluster heads should have
been selected using a protocol such as LEACH [16] or
Fuzzy Logic [20], [21], etc. where the optimized number
of selected cluster heads send the ants as they receive data
from their cluster members, per unit of time.
In this paper, At first we use 30, 20, 15 and 10 percent
of all nodes as cluster heads to send the ants in order to
find the balance between energy consumption, packets sent,
time stamping and the number of ants in move within the
network. Then the method compared with two other ant-
based multi-path protocols.
378377
IV. SIMULATION
The simulation is done using MATLAB where the pro-
posed method is first evaluated with respect to the number
of ants, and one level depth via BFS within the network.
Next, the proposed method compared with two other ant-
based methods of literature [1]. The simulation describes
the relationship between, energy consumption, packets sent,
time stamping and the number of ants in move within the
network. In this part of simulation we use 30, 20, 15 and
10 percent of all nodes as cluster heads to send the ants
in terms of finding a balance between, energy consumption,
packets sent, time stamping and the number of ants in move
within the network with minimum cost. Table II shows the
parameters used for this simulation.
Table II: Parameters
Parameter ValueTotal Energy for all Ants 30jNumber of Cluster Head 10-15-20-30
Location of Sink Center
Location of Cluster Head Static
Packet Size 4000bit
Transmit Amplifier Type Efs,Emp
Coordinate Area 150×150
ETX, ERX 50×0.000000001jRound 800
Pheromone Value 0.5
Figure 3 describes the total round trip time to send and
receive data packets from nodes to sink and vice versa. The
X-axis shows the number of round and the Y-axis shows
the total round trip time (unit of time) taken by the different
number of ants, where, 30 and 10 percent ant are the worst
and the best time respectively to send and receive the packets
0 100 200 300 400 500 600 700 8000
1
2
3
4
5
6
7
8
9
10
Number of Round
Tim
e
30% Ant20% Ant15% Ant10% Ant
Figure 3: Time stamp
Figure 4, indicates the impact of number of ants carrying
the data packets on the performance level of the system,
where having the number of ants as many as 15 to 20
0 100 200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5
3x 10
6
Number of Round
Num
ber
of p
acke
ts s
end
to S
ink
30% Ant20% Ant15% Ant10% Ant
Figure 4: Packets sent
percent of the total number of nodes, dramatically has the
highest number of data packets sent. Subsequently, it is
absolutely clear in Figure 5 that the 30 percent (number
of ants) runs out of energy in 150th iteration as it has the
highest energy consumption with respect to the rest, with the
result of network failure. Having said that, more number
of ants initially send more packets toward the sink, they
consume more energy and take much time. Furthermore,
the network goes down faster than the others. On the other
hand, the network with 15 and 20 percent ants has a better
performance in terms of sending packets, time stamp and
energy consumption during the transaction for long time.
0 100 200 300 400 500 600 700 8000
5
10
15
20
25
30
35
Number of Round
Ene
rgy
Con
sum
ptio
n
30% Ant20% Ant15% Ant10% Ant
Figure 5: Energy consumption
The next part of the simulation is done with respect to two
important factors in WSNs; First, the energy preservation
and second the number of packets sent per round during the
network lifetime. Table III shows the parameters used for
simulation.
The nodes are randomly distributed across the area of size
150× 150 , and their positions have been maintained for all
379378
Table III: Parameters
Parameter ValueInitial Energy 1.5j
Number of Cluster Head 20
Location of Sink Center
Location of Cluster Head Randomly Distibutes
Packet Size 4000bit
Transmit Amplifier Type Efs, Emp
Coordinate Area 150×150
ETX, ERX 50×0.000000001jRound 800
Pheromone Value 0.5
three methods with a node initial energy value of 1.5j and
default pheromone value of 0.5. The packet size is fixed to
4000 bit for every transaction.
Figure 6 shows that the proposed method results in much
more energy preservation with respect to the other two
methods by the end of the simulation; Where although all
three methods start with the same amount of energy level
30, by the 800th iteration the ANT-BFS method preserves
significantly higher amount of energy.
0 100 200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
6
Number of Round
Num
ber
of P
acke
ts S
ent t
o S
ink
ANTANT−BFSANT−Selcuk
Figure 6: Packets sent
The proposed method consumes much less energy; as a
result the number of packets sent to the sink are larger,
which leads to a longer network lifetime. Figure 7 having the
number of sent packets on y-axis and number of rounds on
x-axis describes the results of simulation comparison where
the ANT-BFS method is leading in terms of higher number
of successfully transmitted data packets with respect to other
two methods.
V. CONCLUSIONS
One of the major challenges in WSNs is to determine
the best path to transmit data from nodes to the base station
which directly affects the amount of energy consumption and
network lifetime. In this paper, the ACO algorithm with three
types of ants, namely Frontward, Bfrontward and Backward
0 100 200 300 400 500 600 700 8000
5
10
15
20
25
30
Number of Round
Ene
rgy
Rem
inde
ANTANT−BFSANT−Selcuk
Figure 7: Energy saving
ant, is used along with a tree Breadth First Search (BFS)
making the ants capable to search and find the best and
shortest path to the destination, in order to carry and transfer
the data packets to the base station and vice versa. This
method resulted in the least amount of energy consumption
and loss of data packets. As the future work, we will apply
ant colony algorithm to enhance the security of the location
of the base station from external attackers in WSN.
REFERENCES
[1] S. Okdem and D. Karaboga, ”Routing in wireless SensorNetwork Using an Ant Colony Optimization (ACO) RouterChip”, Sensors, pp. 909-921, 2009.
[2] S. Roy, M. Conti, S. Setia and S. Jajodia, ”Secure DataAggregation in Wireless Sensor Networks: Filtering out theAttacker’s Impact”, Information Forensics and Security, IEEETransactions on, No. 99, Vol. PP, 20 February 2014.
[3] M. Conti, R. D. Pietro and L. V. Mancini, ”Secure cooperativechannel establishment in wireless sensor networks”, PervasiveComputing and Communications Workshops, Fourth AnnualIEEE International Conference on, pp.5, 331, 13-17 March2006.
[4] K. Kamal and N. Gupta, ”Application Based Study onWireless Sensor Network”, International Journal of ComputerApplications, Vol. 21, pp. 1, 2011.
[5] M. Dorigo and L. M. Gambardella, ”Ant Colony System: ACooperative Learning Approach to the Traveling SalesmanProblem”, IEEE Transaction Evol Computer, pp. 53-66,1997.
[7] M. Dorigo, M.Birattari, C. Blum, M. Clerc and Sttzle, ”AntColony Optimization and Swarm Intelligence”, 4th Interna-tional Workshop, ANTS, Vol. 3172, Belgium, September2008.
380379
[8] A. Chaudhuri, ”A Dynamic Algorithm for the Longest Com-mon Subsequence Problem using Ant Colony OptimizationTechnique”, Proceedings of 2nd International Conference onMathematics, Cairo, Egypt, 2007.
[9] C. Izu, ”A Throughput Fairness Injection Protocol for Meshand Torus networks”, IEEE High Performance Computing(HiPC), pp. 294-303, December 2009.
[10] Z. Jingjing, H. Yongxi and C. Yufei, ”Wireless sensor networkmulti-path routing protocols”, Journal of Computer Engineer-ing and Design, No. 22, Vol. 28, pp. 5417-5420, 2008.
[11] J. Yang, M. Xu, W. Zhao and B. Xu, ”Ant Colony Optimiza-tion and Swarm Intelligence”, Sensors (Basel), pp. 4521-4540, May 2010.
[12] H. Goudarzi, A. H. Salavati and M. R. Pakravan, ”An ant-based rate allocation algorithm for media streaming in peerto peer networks: Extension to multiple sessions and dynamicnetworks”, J. Netw. Comput. Appl, Vol. 34, 2011.
[13] H. Goudarzi, A. H. Salavati and M. R. Pakravan, ”WSNPath Optimization Based on Fusion of Improved Ant ColonyAlgorithm and Genetic Algorithm”, Journal of ComputationalInformation System, No. 6, pp. 1591-1599, 2010.
[14] R. Schoonderwoerd, O. Holland and J. Bruten and L.Rothkrantz, ”WSN Path Optimization Based on Fusion ofImproved Ant Colony Algorithm and Genetic Algorithm”,Adaptive Behaviour, Vol. 5, pp. 169-207, 1996.
[15] K. S. Ali and K. Sindhanaiselvan, ”Ant Colony OptimizationBased Routing in Wireless Sensor Network”, Int.J.AdvancedNetworkingand Applications, pp. 1685-1689, 2013.
[16] W. Heinzelman, A. Chandrakasan and H. Balakrishnan,”Energy-efficient communication protocol for wireless microsensor networks”, Proc. of the 33rd Annual Hawaii Interna-tional Conference on System Sciences (HICSS), pp. 3005-3014, January 2000.
[17] N. Gomez, L. Fernando and A. Arteta, ”Simulation Toolsin Wireless Sensor Networks: Ant Colony Optimization of aLocal Routing Algorithm”, International journal of computersand communications, No. 3, Vol. 6, 2012.
[18] M. Kurant, A. Markopoulou and P. Thiran, ”On the bias ofBFS”, International Teletraffic Congress (ITC), pp. 1-9, April2010.
[19] S. Russel and P. Norvig, ”Artificial Intelligence: A ModernApproach”, Prentice Hall, December 2002.
[20] R. Khoshkangini, S. Zaboli and S. Sampalli, ”Energy Effi-cient Clustering using Fuzzy Logic”, Internatianl Journal ofComputer Science and Mobile Computing (IJCSM), No. 13,Vol. 2, pp. 8-14, December 2013.
[21] E. Saeedian and M. Jalali, ”CFGA:Clustering Wireless Sen-sor Network Using Fuzzy Logic And genetic Algorithm”,Intrernational conference on sensor networks, pp. 1-4,September 2011.