ACADEMIE ROYALE DES SCIENCES D OUTRE-MER BULLETIN DES SEANCES
Vol. 4 No. 3 June 2015 pp. 41-48
ISSN: 0001-4176
A learning automata leach-based wireless sensor network clustering algorithm LALEACH
Mina Shatzad, Mohammad Masdari
Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia, Iran
Abstract: An important problem of sensor network clustering is provide optimal cluster size, coverage of
all sensors in distributed network, energy consumption, connectivity in network, increase the network life
time. In this paper we proposed learning automata leach based sensor network clustering algorithm that are
provide an optimal cluster that in this paper, we propose a self-regulated deployment strategy based on
learning automata called LALEACH. Sensor network energy consumption clustering is a fundamental issue
that in this paper we have consider this parameter and maximized the coverage and several parameter are
consider for optimal cluster degree. Increased network life time with control intra-cluster and inter-cluster
communication and local cluster selection.
Key words: Sensor network LALEACH Energy consumption


optimizing the cluster head degree, optimizing cluster
number [6, 7]. Each of the proposed algorithms tried to
produce better results.
The proposed automata-based clustering algorithm is
independently run at each host in a fully distributed
fashion [8]. In the proposed schemes, each host is
equipped with a learning automaton [9]. The action-set
of each host contains an action for each of its
neighboring hosts as well as an action for itself [10].
In this the node are fixe and the network don’t clustered
again, but in several of proposed algorithm the reclustering phases are consider for allows the cluster
maintenance [11].
INTRODUCTION
Wireless sensor network is an infrastructure-less
self-organizing, self-configuring and multi-hop
communication network that can be effectively used in
disaster recovery, military operations, and battle fields
and so on, where no infrastructure is available or a
fixed infrastructure is difficult to install [1].
A sensor network is composed of many sensor nodes
which have been distributed randomly in the area in
order to gather special information from the
environment, process the gathered information and
finally send it to main nodes of information collectors
[2].
Each cluster is composed of a cluster-head and a
number of cluster members. Cluster-head is responsible
for managing the basic operations of the cluster
members such as channel access scheduling, power
measurements, and coordination of intra and intercluster communications [3].
One important problem which may arise in designing a
deployment strategy for a wireless sensor network is
how to deploy a specific number of sensor nodes so that
the covered section of the area is maximized [4].
Energy Cost of transmitting one separate bit of
information equals to processing of thousands of
functions in a sensor node [5].
The automata have an important role in optimizing of
sensor network clustering. So several studies are doing
in different area for increase network life time like:
localized
learning
automata-based
clustering,
Corresponding Author: Mohammad Masdari
RELATED WORK
In [12] Akbari et al. has proposed localized learning
automata-based clustering algorithm LLACA that
minimized the messaging overhead, and tried to reduce
the cluster heads number with the automaton and so
allows the cluster maintenance by a re-clustering stage.
In this algorithm each sensors are equipment with liner
automata and this scheme consists of three phases the
host actions set, cluster heads determines, and updating
the probability actions vector. Each host calculate its
cluster-degree, and if the host cluster-degree is less than
or equal to its dynamic threshold, the selected action is
rewarded and so this host updates its dynamic threshold
with current cluster-degree, otherwise the selected
action is given the penalized.
41
Kumar et al. [13] have proposed a new clustering
algorithm called ELACCA.
This scheme is an optimization technique that uses the
concept of learning based upon the input parameters
and produces an output. The area are divided to cell that
include several sensors, the automaton is assumed to be
deployed at each of the CH for capturing the
information from the environment and then adaptively
selects the operation to be performed. In this way with
consider distance between the two cluster heads,
average number of cluster heads, position of each node
in the cell, degree threshold of cluster heads can choose
the optimal action.
Jabari Lotf et al. [14] have proposed a learning
automata-based clustering algorithm LACA. In this
scheme initially each node sends a message for other
node for known itself neighbors and the probability
action set are detected. So each node send another
message according to probability vector for declare
cluster head. If the receiver of the message is not a
member of any cluster and its remaining energy is
bigger than or equal to threshold, then according to
learning algorithm its selection probability will increase
and if not it will be decreased.
Naseri et al. in [15] have proposed clustering algorithm
based on weakly connected dominating set and learning
automata that each host in the network is equipped with
a learning automatons. This algorithm consists of three
phases and the first step in cluster formation is
recognition of the neighbors, in the second phases after
number of iterations the weakly dominator set is made
by activating randomized number of automata and
clusters are formed, and finally in third phases the reclustering. In this scheme each node sends a message to
each other for known its neighbor’s node. So the node
that resaved this message replied a message contains
sending the node's ID fields and energy level field.
Using this method the transmitter determines the
number of neighbors and the energy level of the nodes.
Also after compare energy level in each iteration, if the
current node energy level is higher than the average
energy of other nodes in the cluster then action is
rewarded otherwise the action is penalized.
Kumar et al., have proposed a learning automata based
clustering algorithm [16] LA-EEHSC. This scheme is
heterogeneous, consisted of two type node normal and
advanced node that each node is equipped with LA.
This algorithm minimizes the energy consumption and
increase the network lifetime, so optimized the CH
number and for calculate optimal cluster number
consider tree minimum value of distance from midpoint
of BS, SN and CH.
If the normal nodes energy are equal zero and the
random number is equal or less than threshold, then
selected action is rewarded otherwise the action is
penalized, and if the advanced nodes are equal one and
the random number is equal or less than advanced node
threshold then are rewarded otherwise be penalized.
Akbari et al have proposed a distributed learning
automata-based clustering algorithm DLA-CC [17] that
obtains a near optimal solution to the minimum WCDS
(the weakly connected dominating set) which network
is divided into several regions. In this scheme the
automata create the WCDS, and so tried to minimize
the cluster head degree. If the set size of the cluster
head is smaller than the minimum cluster head set
discovered so far, it is rewarded and is declared as a
minimum set; otherwise, it is penalized and the
comparison process continues.
LEARNING AUTOMATA
Learning automata (LA) are adaptive decision-making
devices that operate on unknown random environments.
A learning automaton has a finite set of actions that are
select from and at each stage, so it choice action
depends upon its action probability vector [18]. The
environment responds the taken action in turn with a
reinforcement signal.
The action probability vector is updated based on the
reinforcement feedback from the environment.
The goal of a learning automaton is find the optimal
action from the action-set, so the selected action is
received penalty or reward.
The stochastic automata are represented with quintuple
} is represents
{ , , , , ∅}, where = { , , . . . ,
}
the action set of the automata,
= { , ,...,
represents the input set, and the F is the production
function and automata new state, G is an output
function that maps the current state and input into the
current output, G is a set of automata internal state [19].
Fig. 1: Learning automata and its environment
The environment can be descript by a = { , , }
where = { , , … , } represents the finite set of the
} denotes the set of the
inputs,
= { , ,...,
values that can be taken by the reinforcement signal,
and = { , , … , } denotes the set of the penalty
probabilities, where the element
is associated with
the given action [20].
If the penalty probabilities are constant, the random
environment is said to be a stationary random
environment, and if they vary with time, the
42
environment is called a non-stationary environment
[21].
( + 1) = ( ) + [1 − ( )]
∀,
( + 1) = (1 − ) ( )
≠
When the taken action is penalized by the
environment (i.e. and β(n) = 1).
( + 1) = (1 − ) ( )
In distributed algorithms, several aspects must be
considered that each is important in its category. One of
the very important aspects in distributed network is
process of selection the optimum cluster heads number,
and the node that will be cluster head. Also should be
noted that, due to the amount of energy nodes and the
loss of a number of nodes in the network lifetime,
network topology and cluster head node must be
changed during the life of the network.
Therefore, most of the proposed methods are not
comprehensive due to the all measures are not together.
The solutions to these problems are not fixed solution,
so the application of intelligent methods will produce
better results. Distributed intelligent way that is
beneficial for this problem, is learning automata that a
few algorithms have been using this method.
According to the evaluation algorithm based on
LEACH and automaton the main problem that occurs is
this that not consideration all of needed factors and
necessarily the absolute superiority of one factor over
another area. The leach algorithm itself is a series of
shortcomings and disadvantages. The algorithm
LEACH cluster head node selection process is done
randomly and nodes with high competence not take into
consideration the probability of unforeseen nodes.
Therefore, deserve factors such as the amount of energy
or of neighboring nodes is not more attention and so the
number of selected cluster head is not controlled.
In the proposed method, we have tried, to eliminate the
disadvantages of other algorithms and also to
implement the intelligent making. In the result
improved performance of node in the network and
increasing the lifetimes.
The proposed scheme has two-phase, cluster formation
and stable phase. Initially each of the sensor nodes is
equipped with learning automata. In the first phase after
node distribution identification neighbor and clustering
process is performed using learning automata.
Clustering process consists of several stages and at each
stage; the node competency is checked for bee cluster
head.
Initially, all actions have equal probability, first the
selection probability distribution of Node in the
network is 0.05. If an action is rewarded, then increases
the probability, otherwise reduced this probability.
The clustering algorithm formation is fully distributed,
where each of node select its cluster head based on
local information that is received from its neighboring
hosts.
In the second phase is done collection sensed data by
common nodes in the network and send them to the
cluster head according to the schedule specified. Finally
data is sent to the cluster head also will be transmitted
to the sink.
(1)
(2)
(3)
( + 1) =
1 − ) ( ), ∀
(4)
−1 (
≠
Where
is the reward parameter, b is the penalty
parameter, and r is the number of actions [22].
When value is either 0 or 1, environment is called PModel (Probabilistic model). ( ) = 1 as penalty and
( ) = 0as reward [23]. In the case of environment of
Q-Model,
( ) is output of set with more than two
values between [0, 1]. In S-Model,
( ) is a
continuous random variable within the range [0, 1].
LEACH
The operation of Low-Energy Adaptive Clustering
Hierarchy or LEACH is divided into rounds [24]. Each
round begins with a set-up phase when the clusters are
organized, followed by a steady-state phase when data
are transferred from the nodes to the BS. Furthermore,
the setup phase consists of the following sub phases:
 Advertisement
 Cluster setup
 Broadcast schedule
During the set-up phase, each node n chooses a random
number between 0 and 1, so if the number is less than a
threshold ( ), the node becomes a cluster head for
the current round [25]. Threshold value is set through
this formula:
T(n) =
1−
0
∗
∈
1
(5)
Where, G is set of nodes that have not been selected as
CHs in previous 1/ rounds, P is suggested percentage
of CH, r is current round. If nodes become CHs in
current round, these nodes will be CHs after next 1/p
rounds [26]. In LEACH, the Cluster Heads compress
data arriving from member nodes and send an
aggregated packet to the BS in order to reduce the
amount of information that must be transmitted to the
BS [27].
PROPOSED CLUSTERING ALGORITHM
43
• The node that in first clustering step is not in the range
of cluster heads, according to specified probability and
number of times that was cluster head, declares itself as
a cluster head.
• Each common node should have a cluster head
neighbor that can send its data into it.
• The aim of this approach is to increase the number of
cluster heads. As a result, efforts have been made to
reduce the degree of clustering and increase the number
of cluster head.
Clustering phases: In the clustering phase, select the
cluster heads and cluster formation occurs. A node that
has more energy than the average energy of its
immediate neighbors, and also the degree of clustering
is less than or equal to a predetermined value, the
selected action will be rewarded, otherwise penal tied.
After role of all nodes in the cluster is determined, that
node are cluster head either common. The first phase
consists of four stages, each of which is as follows:
Step 1: One of the most important parameters for the
clustering is number of cluster heads and we intend to
raise the number of cluster head nodes in the network.
If the cluster head nodes have a balanced neighboring
degree, cluster heads energy consumption will be
substantially reduced and early discharge energy of
cluster head can be avoided. In the first phase offer
nodes distribution in the operating environment each of
them begin to identifying their neighbors. Each node
identifies around neighborhood and the total number of
neighbors is calculated. Also each node within a
message will notice to neighbors its energy levels and
the energy average of neighbors of each node is
calculated.
P


1
T ( n )  1  P  ( r mod )
P


reward functions are selected by (1), (2) and (3), (4)
formulas.
Clustering parameters to be considered, as follows:
• Node energy rate: because the cluster head node is
responsible for collecting information that are sent from
the cluster and send it to the sink, where he is expected
to have more energy. In this method, the candidate
cluster head node energy is compared with the average
energy of neighboring nodes.
• The capacity of cluster heads: one of the criteria for
the maximum size of the cluster is connected. If the
number of members of a cluster head node cluster is too
much more energy to receive and send data to the sink
will lose and its energy is discharge faster, therefore by
increasing the number of nodes in the cluster member
the probability sending data by all the nodes in the
cluster head is reduced.
• Number of cluster head: an important purpose of this
procedure is to establish the network connection. In this
way with increasing number of cluster head, all nodes
are covered and also with increasing number of cluster
head the member nodes can easily transfer its data.
Step 3: until the probability value of node is less than ε,
the node process and rewards and penalties will
continue and also if the probability of node is more than
ε, the node is selected as cluster head. The condition of
the cluster head possibility is compared dynamically
with a random number in the interval [0, 1]. If the node
probability is greater than the random number, declares
itself as a cluster head. That this value is different for
each individual node.
Step 4: the node that their state is not specified in
previous step entered this stage. In this stage initially
the node which was not any role, decides the current
round is to be cluster head based on the cluster heading
percentage that is previously identified the number of
times has been cluster head. This decision of node is
done based on selecting a random number between zero
and one, if the number is less than the threshold value T
(n), the node will be cluster head in the current round.
The threshold value is calculated based the following
formula:
With the addition this step the number of cluster head
node increases and as a result, the network connection
is maintained. Each node that in two final stages chose
itself as a cluster head, notice to other node sends a
message. Non-cluster head node, maintains received
notice message from cluster head node for use in the set
up phase. After the clustering phase is complete, the
non-cluster head node selects a cluster head for these
stages. The decision will be taken based on the signals
received from the cluster head.
Construction scheduling: cluster head node receive
the messages cluster members and according to the
number of nodes in the cluster create a schedule which
(6)
Step 2: In this step, using automaton node for the
cluster head is selected. To use this technique, consider
learning automata for each node and also each node can
have one of two states cluster heads or normal,
corresponding automaton can select one of two states
according to probability vector. The nodes that is grated
probability to be as CH and the node that have less
probability will be chosen as the CN. First, the selection
probability of each sensor node is equal to 0.05.
The node that have more energy than the neighbors
energy average and also number of nodes in the cluster
is less than or equal to the specified capacity as the
cluster head node probability is increased by the
automaton (rewarded). Otherwise, the probability of
selecting a cluster head node is reduced (penalized).
With the selection of cluster head node may decrease or
increase based on various parameters. Penalty and
44
Stability phase: Once the clusters been established,
data transfer can be started, assuming that the nodes
determines that when each node can send its data the
scheduling is sent for all nodes in the cluster.
Algorithm LALEACH ( )
Input host
Begin algorithm
Let T(n) the denote the be Cluster head in the previous step
Let R denote the stage number which is initially set to 1
Let E denote the host energy
Host
detects its neighbors
Host compute its Neighboring degree and denote its HOST_DEGREE
Host compute its neighbor _ energy average and denote its ENG_AVG
Host forms its action set
Host
randomly choose one of its actions according to its action probability
Repeat
IF E >= ENG_AVG AND HOST_DEGREE <= Threshold
Reward choose action
Else
Penalty choose action
← +1
Until the probability with which host chooses its CH is greater than
IF Host
HOST_DEGREE = zero
IF rand <= T (n) host chooses itself as a CH
END algorithm
Fig. 2: Pseudo-code of learning automata-based leach clustering algorithm
Always have data to send during the time that is
allocated to them sends their data to the cluster head.
This sending is used of the minimum amount of energy.
When all the data was received cluster head node
performs signal processing operations until data is
compressed into a units signal. This state is stability in
the sensor network.
The proposed clustering algorithm based on learning
automata pseudo-code is presented below in this
method we have optimized LEACH algorithm and by
learning automata clustering process and selection of
appropriately cluster head is done at the network level.
The sink establishment position in (50, 50),
respectively. A test for the number of sensor nodes is
equal to 100 and the number of the program running in
each round is 1000. The EXT, ERX, EDA Data
aggregation and the amount of energy used for
membership in the cluster and the reinforcement signal
(the response to actions taken by the automaton is
issued by the environment) is equal to 0.000000005.
Different criteria have been considered to compare the
performance of proposed algorithm which is divided
into two categories the first group to study the life of
nodes and the second is the quality of the proposed
algorithm Criteria are as follows: 1) Energy 2) number
of dead nodes 3) number of alive nodes 4) send packets
in to BS 5) send packet in to CH
SIMULATION
The efficiency of the proposed algorithm is evaluated
using different tests. Matlab software is used to perform
tests. The proposed method by various aspects is
compared with leach algorithm each on a separate chart
provided.
The sensor simulation environment is 100*100 m and
the assumption is that n sensors (n number of
distributed sensor nodes) randomly distributed in the
environment also sensor radio range is 30 m , primary
energy in each of the sensor nodes is 0.5 joules.
Fig. 3: LEACH –based sensor networks clustering
45
First test: The lifetime of the sensor network is one of
the basic criteria in sensor networks that in this scheme
tied by selecting the optimal cluster head and network
connecting have finally the productivity of all the nodes
in our environment.
This increases the lifetime of network due to a more
balanced clusters of appropriate size and determine the
cluster head with higher energy so by reducing the
amount of energy transferred to another node of the
cluster head responsibility. In the following charts the
energy used by LEACH clustering algorithm and the
proposed algorithm is compared. Where proposed
method uses less energy and consequently will be
increase the lifetime of network.
Fig. 6: Comparing the number of dead nodes in the LALEACH
and LEACH method
Fig. 4: LALEACH-based sensor networks clustering
Fig. 7: Comparing the number of dead nodes in the LALEACH
and LEACH method
Third Test: The overall objective of setting up a sensor
network to collect information about the operating
environment. That by the way we have tried with data
aggregation by CH data will be sent to BS. According
to the figs in the algorithm LALEACH (3-4) and (3-5),
the number of packets sent by CH to BS compared with
LEACH algorithm has been enhanced. The amount of
information transmitted from the CH to CN has
increased due to increased network life time.
Fig. 5: Comparison of remaining energy by nodes in LEACH and
LALEACH
Second test: In this test, the number of live nodes and
the number of dead nodes during the life of the network
can be compared that LALEACH nodes due to the
increase the lifetime the number of dead nodes is less
than LEACH algorithm and therefore the number of
alive nodes in the proposed algorithm is also more.
46
Fig. 8: Comparing the number of packets sent to the BS in the
LEACH and LALEACH method
REFERENCES
1. J.W. Branch, Ch. Giannella, B. Szymanski, R.
Wolff, H. Kargupta”, In-network outlier detection
in wireless sensor networks”, Knowledge and
Information Systems 2013, Volume 34, pp. 23-54.
2. A. A. Abbasi, “A survey on clustering algorithms
for wireless sensor networks”, Computer
Communications 30 (2007), pp. 2826–2841.
3. B.C.P. Laua, E.W.M. Maa, T.W.S. Chow,
“Probabilistic fault detector for Wireless Sensor
Network”, Elsevier Probabilistic fault detector for
Wireless Sensor Network Volume 41, 2014, pp.
3703-3711.
4. R. Arora, S. S. Sandhu, P. Agarwal, “A Proposal
for Deployment of Wireless Sensor Network in
Day-to-Day Home and Industrial Appliances for a
Greener Environment, Advances in Intelligent
Systems and Computing”, 2014, Volume 236, pp.
1081-1086.
5. D. Ma, J. Ma, P. Xu, “An Adaptive Virtual Area
Partition Clustering Routing Protocol Using Ant
Colony Optimization for Wireless Sensor Networks,
Advances in Wireless Sensor Networks”,
Communications in Computer and Information
Science 2014, Volume 418, pp. 23-30.
6. B.H. Liu, K.W. Su , “Enhanced algorithms for
deploying the minimum sensors to construct a
wireless sensor network having full coverage of
critical square grids”, Springer Wireless Networks
February 2014, Volume 20, pp. 331-343.
7. S. Rajasegarar, Ch. Leckie, M. Palaniswami,
“Hyperspherical cluster based distributed anomaly
detection in wireless sensor networks”, Journal of
Parallel and Distributed Computing January 2014,
Volume 74, Pages 1833:1847.
8. Y. Deng, Sh.Wu, Sh. Li, Y. Xiong, T. Zhang,
“Lower Bound Estimation for Required Number of
Nodes in the Opportunistic Communication – Based
Wireless Sensor Network”, Advances in Computer
Science and its Applications Lecture Notes in
Electrical Engineering 2014, Volume 279, pp. 869875.
9. K.
Bhargava,
A.
Kashyap,
T.
A.
Gonsalves,”Wireless sensor network based advisory
system for Apple Scab prevention”, IEEE 2014, pp.
1-6.
10.G. P. Hancke, V. ÇağrıGüngör, G. P. Hancke,
“Guest Editorial Special Section on Industrial
Wireless Sensor Networks”, IEEE Transactions On
Industrial Informatics february 2014, VOL. 10, PP.
762-765.
11.K. Narendra, V. Varun, G. H. Raghunandan, “A
Comparative Analysis of Energy-Efficient Routing
Protocols in Wireless Sensor Networks, Emerging
Research in Electronics”, Computer Science and
Fig. 9: Comparing the number of packets sent to the CH in the
LEACH and LALEACH method
In this way LEACH algorithm has been improved and
equipped with recruiting automata. Service quality
parameters such as energy consumption in sensor
networks, Lifetime network and cluster degree, the
number of cluster head node have been considered and
improved. Our experiments show that the proposed
method is optimum performance. Clustering algorithm
based automaton that we have given in this way, we
consider various metrics to increase the lifetime of the
sensor network as well as a series of quality standards
such as the balance degree the cluster, increasing the
number of nodes in the cluster head to cover the entire
network were considered.
CONCLUSIONS
The main purpose of these algorithms to optimize the
algorithm LEACH and equipped it with learning
automata and also increases the life of the network. At
the beginning of each sensor nodes deployed in the
environment dedicated learning automata and then start
identify to identify their neighboring nodes. With
information obtained each node detects its neighbors
and is calculated average energy. To determine suitable
and balanced cluster head take into account energy
metrics and nodes degree and thus the probability of a
cluster head node increases or decreases.
After selecting a cluster head node, the node that their
condition is specified entered to the next stage. At this
stage to cover the entire network and connecting nodes
that are not neighbors, responsibility of the cluster
heading takes place itself. In general, because the
choice of a balanced clusters and the use of learning
automata network lifetime is increases. In the clustering
method based on local information, exchange of
messages between the cluster reduced and also energy
consumption is reduced between the clusters.
47
Technology Lecture Notes in Electrical Engineering
2014, Volume 248, pp. 399-405.
12.J. AkbariTorkestani, M. R. Meybodi, “LLACA: An
adaptive localized clustering algorithm for wireless
ad hoc networks”, Computers & Electrical
Engineering July 2011, Volume 37, PP. 461–474.
13.N. Kumar, J. Kim, “ELACCA: Efficient Learning
Automata Based Cell Clustering Algorithm for
Wireless Sensor Networks”, Wireless Personal
Communications December 2013, Volume 73, pp.
1495-1512.
14.J. Jabarilotf, S. H. Hosseini, Rasim M. Alguliev, “A
Learning Automata-based Clustering Algorithm for
Sensor Networks”, 2010 2nd International
Conference on Mechanical and Electronics
Engineering (ICMEE 2010).
15.N. Abtahi Naseri, M. R. Meybodi, J. Akbari
Torkestani, “A Novel Algorithm Based on Weakly
Connected Dominating Set and Learning Automata
and Its Application to Clustering and Routing the
Sensor Networks”, Proceedings of the 5th
International Conference on IT & Multimedia at
UNITEN (ICIMU 2011) Malaysia, November 2011.
16.N. Kumar, S. Tayagi, D. Deng, “LA-EEHSC:
Learning automata based energy efficient
heterogeneous selective clustering for wireless
sensor network “journal of network and computer
application, 12 July 2014.
17.F.S. Gharehchopogh, S. Ebrahimi, “A Novel
Approach for Edge Detection in Images based on
Cellular Learning Automata” International Journal
of Computer Vision and Image Processing
(IJCVIP), Volume 2, No. 4, pp. 64, 2012.
18.F.S.Gharehchopogh, L.Ebrahimi, I.Maleki, S.Jodati,
"A New Novel PSO based Approach with Hybrid of
Fuzzy C-Means and Learning Automata in Software
Cost Estimation", Indian Journal of Science and
Technology, Volume 7, Issue 6, pp:795-803, June
2014
19.F.S. Gharehchopogh, L. Ebrahimi, I. Maleki, S.
Jodati, “A Novel PSO based Approach with Hybrid
of Fuzzy C-Means and Learning Automata in
Software Cost Estimation”, Indian Journal of
Science and Technology, Volume 7, Issue 6, pp.
795-803, 2014.
20.N. Kumar, R. Iqbal , A. James , A. Dua, “Learning
Automata Based Contention Aware Data
Forwarding Scheme for Safety Applications in
Vehicular Ad Hoc Networks”, e-Business
Engineering (ICEBE), 2013 IEEE 10th International
Conference on, pp. 385 – 392.
21.J. de Lope, D. Maravall ,” Data clustering using a
linear
cellular
automata-based
algorithm”,
Neurocomputing Volume 114, 19 August 2013,
Pages 86–91.
22.J. Torkestani ,M. R. Meybodi, “Finding minimum
weight connected dominating set in stochastic graph
based on learning automata”, Information Sciences
Volume 200, 1 October 2012, Pages 57–77.
23.A.Wanga, D. Yanga, D. Sunc,” A clustering
algorithm based on energy information and cluster
heads expectation for wireless sensor networks”,
Computers & Electrical Engineering Volume 38,
Issue 3, May 2012, Pages 662–671.
24.D. Aminea, B. Nassreddinea, K. Bouabdellahb,”
Energy Efficient and Safe Weighted Clustering
Algorithm for Mobile Wireless Sensor Networks ”,
Procedia Computer Science Volume 34, 2014, p.p
63–70.
25.X. Di , “A Novel Coverage-Preserving Clustering
Algorithm for Wireless Sensor Networks”, 2012
International Conference on Medical Physics and
Biomedical Engineering, Physics Procedia 33 ( 2012
) , p.p1054 – 1059.
26.Z. Yonga, Q. Peia, “A Energy-Efficient Clustering
Routing Algorithm Based on Distance and Residual
Energy for Wireless Sensor Networks”, 2012
International Workshop on Information and
Electronics
Engineering
(IWIEE),
Procedia
Engineering 29 (2012) , p.p 1882 – 1888.
27.P. Kuila, P. K. Jana, “A novel differential evolution
based clustering algorithm for wireless sensor
networks”, Applied Soft Computing Volume 25,
December 2014, p.p 414–425.
48