Download Efficient Routing Protocol via Ant Colony Optimization

2014 IEEE International Conference on Internet of Things (iThings 2014), Green Computing and Communications (GreenCom
2014), and Cyber-Physical-Social Computing (CPSCom 2014)
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
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) requirement 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.
Abstract—Wireless Sensor Networks (WSNs) consist of many
sensor nodes, which are usually distributed across areas difficult to be accessed in order to collect and send the data to the
main sink location. Despite the fact that a number of protocols
have been proposed for routing and energy management, WSNs
still face problems in selecting the best path with efficient
energy consumption and successful delivery of the packets.
In particular, these problems occur when WSNs are subjected
to critical situations such as node or link failure, and it is
even more critical in sensitive applications such as nuclear
and healthcare.
In this paper, we propose the Ant Colony Optimization
(ACO) combined with Breadth First Search (BFS) to search
and find the best and shortest path in order to improve data
transmission with the least amount of energy consumption,
as well as reduce the probability of data loss. Using our
proposal, a balance between number of packets, time and
energy consumption can be determined which leads to increase
the network performance. Therefore, the main goal of the paper
is to decrease energy consumption which leads to increase
of the network’s lifetime and enhancement of the number of
successfully transmitted data with respect to other multiple
ants-based routing protocols. Moreover, the number of ants
are optimized within the network to avoid network congestion.
Keywords-Sensor Network; Ant Colony Optimization (ACO);
BFS; Routing; Cluster-Head;
I. I NTRODUCTION
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 performance directly. Hence from a network design perspective;
Mauro Conti is supported by a Marie Curie Fellowship for the project
PRISM-CODE: Privacy and Security for Mobile Cooperative Devices
funded by the European Commission (grant PCIG11-GA-2012-321980) and
by the PRIN project TENACE: Protecting National Critical Infrastructures
From Cyber Threats (grant 20103P34XC) funded by the Italian MIUR.
978-1-4799-5967-9/14 $31.00 © 2014 IEEE
DOI 10.1109/iThings.2014.69
Mauro Conti
Department of Mathematics
University of Padua, Italy
Email: [email protected]
Figure 1: ACO multi-path routing
375
374
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 algorithms 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.
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 networks 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.
Ruud Schoonderwoerd et al. [14] proposed an adaptive 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.
II. R ELATED W ORK
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 follows. 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 =
β
τijα (t) × ηij
β
Στijα (t) × ηij
Nuria Gomez et al. proposed a local routing method [17]
using ant colony algorithm, which keeps track of the information 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 applications, 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.
(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,
375
376
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.
III. P ROPOSED M ETHOD
Link failure is a common occurrence in WSNs, which
results in problems such as repetitive back and forth transmission 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].
ηij =
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].
ηij =
LCN
x:20, y:45
x:15, y:53
PHV
0.5
0.6
DTS
25
30
Δτij = (1 − p) × τij + Δτij
TBLST
y
z
(τij )α × (ηij )β × (Ej )γ
Σ(τij )α × (ηij )β × (Ej )γ
1
dij
(6)
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 illustrated 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.
(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 =
(5)
B. Backward Ant
DTN
25
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 =
1
1
+
dij
djs
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].
Table I: Routing Table
MID
—
—
(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.
A. Frontward Ant
ID
x
y
1
djs
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).
(3)
376
377
Es =
lEelect + lef p d2
lEelect + lemp d4
d ≤ Zom
d > Zom
Equation 9 shows the distance heuristic calculation in
order to determine the selection probability of the next
cluster-head.
1
(8)
ηij =
dmj
(7)
Where ef p and emp are the energy consumption of
amplifying radio and Zom is the threshold value for the
distance.
ηij =
D. Implementation of BFS Technique
1
1
1
+
+
dij
djs
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 enhanced 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].
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 (Bfrontward) 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.
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 antbased multi-path protocols.
Figure 2: Process of finding the minimum distance
377
378
IV. S IMULATION
6
3
Number of packets send to Sink
The simulation is done using MATLAB where the proposed 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 antbased 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.
x 10
30% Ant
20% Ant
15% Ant
10% Ant
2.5
2
1.5
1
0.5
0
0
100
200
500
600
700
800
Figure 4: Packets sent
Value
30j
10-15-20-30
Center
Static
4000bit
Ef s ,Emp
150×150
50×0.000000001j
800
0.5
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.
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
35
Energy Consumption
30
10
30% Ant
20% Ant
15% Ant
10% Ant
9
8
7
6
Time
400
Number of Round
Table II: Parameters
Parameter
Total Energy for all Ants
Number of Cluster Head
Location of Sink
Location of Cluster Head
Packet Size
Transmit Amplifier Type
Coordinate Area
ETX, ERX
Round
Pheromone Value
300
5
30% Ant
20% Ant
15% Ant
10% Ant
25
20
15
10
5
4
0
3
0
100
200
300
400
500
600
700
800
Number of Round
2
Figure 5: Energy consumption
1
0
0
100
200
300
400
500
600
700
800
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
Number of Round
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
378
379
30
Table III: Parameters
Value
1.5j
20
Center
Randomly Distibutes
4000bit
Ef s , Emp
150×150
50×0.000000001j
800
0.5
20
15
10
5
0
Number of Packets Sent to Sink
200
300
400
500
600
700
800
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.
6
ANT
ANT−BFS
ANT−Selcuk
R EFERENCES
3.5
[1] S. Okdem and D. Karaboga, ”Routing in wireless Sensor
Network Using an Ant Colony Optimization (ACO) Router
Chip”, Sensors, pp. 909-921, 2009.
3
2.5
2
[2] S. Roy, M. Conti, S. Setia and S. Jajodia, ”Secure Data
Aggregation in Wireless Sensor Networks: Filtering out the
Attacker’s Impact”, Information Forensics and Security, IEEE
Transactions on, No. 99, Vol. PP, 20 February 2014.
1.5
1
0.5
0
100
Figure 7: Energy saving
x 10
4
0
Number of Round
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.
4.5
ANT
ANT−BFS
ANT−Selcuk
25
Energy Reminde
Parameter
Initial Energy
Number of Cluster Head
Location of Sink
Location of Cluster Head
Packet Size
Transmit Amplifier Type
Coordinate Area
ETX, ERX
Round
Pheromone Value
0
100
200
300
400
500
600
700
[3] M. Conti, R. D. Pietro and L. V. Mancini, ”Secure cooperative
channel establishment in wireless sensor networks”, Pervasive
Computing and Communications Workshops, Fourth Annual
IEEE International Conference on, pp.5, 331, 13-17 March
2006.
800
Number of Round
Figure 6: Packets sent
[4] K. Kamal and N. Gupta, ”Application Based Study on
Wireless Sensor Network”, International Journal of Computer
Applications, Vol. 21, pp. 1, 2011.
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.
[5] M. Dorigo and L. M. Gambardella, ”Ant Colony System: A
Cooperative Learning Approach to the Traveling Salesman
Problem”, IEEE Transaction Evol Computer,
pp. 53-66,
1997.
[6] M. Dorigo, ”Ant colony optimization”, Creative Commons
Attribution NonCommercial ShareAlike 3.0 Unported License, Vol. 1461, Belgium 2007.
V. C ONCLUSIONS
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
[7] M. Dorigo, M.Birattari, C. Blum, M. Clerc and Sttzle, ”Ant
Colony Optimization and Swarm Intelligence”, 4th International Workshop, ANTS, Vol. 3172, Belgium, September
2008.
379
380
[8] A. Chaudhuri, ”A Dynamic Algorithm for the Longest Common Subsequence Problem using Ant Colony Optimization
Technique”, Proceedings of 2nd International Conference on
Mathematics, Cairo, Egypt, 2007.
[15] K. S. Ali and K. Sindhanaiselvan, ”Ant Colony Optimization
Based Routing in Wireless Sensor Network”, Int.J.Advanced
Networkingand Applications, pp. 1685-1689, 2013.
[16] W. Heinzelman, A. Chandrakasan and H. Balakrishnan,
”Energy-efficient communication protocol for wireless micro
sensor networks”, Proc. of the 33rd Annual Hawaii International Conference on System Sciences (HICSS), pp. 30053014, January 2000.
[9] C. Izu, ”A Throughput Fairness Injection Protocol for Mesh
and Torus networks”, IEEE High Performance Computing
(HiPC), pp. 294-303, December 2009.
[10] Z. Jingjing, H. Yongxi and C. Yufei, ”Wireless sensor network
multi-path routing protocols”, Journal of Computer Engineering and Design, No. 22, Vol. 28, pp. 5417-5420, 2008.
[17] N. Gomez, L. Fernando and A. Arteta, ”Simulation Tools
in Wireless Sensor Networks: Ant Colony Optimization of a
Local Routing Algorithm”, International journal of computers
and communications, No. 3, Vol. 6, 2012.
[11] J. Yang, M. Xu, W. Zhao and B. Xu, ”Ant Colony Optimization and Swarm Intelligence”, Sensors (Basel), pp. 45214540, May 2010.
[18] M. Kurant, A. Markopoulou and P. Thiran, ”On the bias of
BFS”, International Teletraffic Congress (ITC), pp. 1-9, April
2010.
[12] H. Goudarzi, A. H. Salavati and M. R. Pakravan, ”An antbased rate allocation algorithm for media streaming in peer
to peer networks: Extension to multiple sessions and dynamic
networks”, J. Netw. Comput. Appl, Vol. 34, 2011.
[19] S. Russel and P. Norvig, ”Artificial Intelligence: A Modern
Approach”, Prentice Hall, December 2002.
[13] H. Goudarzi, A. H. Salavati and M. R. Pakravan, ”WSN
Path Optimization Based on Fusion of Improved Ant Colony
Algorithm and Genetic Algorithm”, Journal of Computational
Information System, No. 6, pp. 1591-1599, 2010.
[20] R. Khoshkangini, S. Zaboli and S. Sampalli, ”Energy Efficient Clustering using Fuzzy Logic”, Internatianl Journal of
Computer Science and Mobile Computing (IJCSM), No. 13,
Vol. 2, pp. 8-14, December 2013.
[14] R. Schoonderwoerd, O. Holland and J. Bruten and L.
Rothkrantz, ”WSN Path Optimization Based on Fusion of
Improved Ant Colony Algorithm and Genetic Algorithm”,
Adaptive Behaviour, Vol. 5, pp. 169-207, 1996.
[21] E. Saeedian and M. Jalali, ”CFGA:Clustering Wireless Sensor Network Using Fuzzy Logic And genetic Algorithm”,
Intrernational conference on sensor networks,
pp. 1-4,
September 2011.
380
381