Dynamic Clustering using Binary Multi-Objective Particle Swarm Optimization for Wireless Sensor Networks N. M. Abdul Latiff C. C. Tsimenidis, B. S. Sharif, C. Ladha School of Electrical, Electronic and Computer Engineering Newcastle University Newcastle Upon Tyne, United Kingdom.
[email protected] Abstract- In wireless sensor networks, the use of energy efficient infrastructure such as clustering may be used to lengthen the network lifetime and prevent network connectivity degradation. In such systems, the performance of the clustering scheme is generally influenced by the cluster head selection method and the number of clusters. This paper presents a dynamic clustering method with multi-objectives that automatically determines the optimum number of clusters in the network. The algorithm, which is based on binary Particle Swarm Optimization (PSO), eliminates the need to set the number of clusters a priori. In addition, a multi-objective approach is utilized in the cluster head selection algorithm in order to select the best set of cluster heads. Simulation results demonstrate that the proposed protocol can achieve an optimal number of clusters, as well as prolong the network lifetime and increase the data delivery at the base station when compared to other well known clustering algorithms. Keywords-component; networks.
clustering; energy
efficient;
sensor
I. INTRODUCTION Wireless sensor networks (WSNs) generally consist of a large number of low-cost and low-power sensor nodes that are small in size and able to be employed in a wide range of applications such as in the military, environmental sensing and habitat monitoring [1]. Given that the sensor nodes are usually irreplaceable, the network protocol for WSNs should be designed so that important performance parameters are optimized, such as extended network lifetime, energy consumption, and data throughput. Clustering is one of the design methods that have been proven to result in significant improvements in wireless sensor networks by managing the network energy consumption efficiently [2]-[4]. The application of the clustering-based approach has the advantage of minimizing the number of nodes that take part in longdistance communication with the base station through the utilization of cluster head nodes and, consequently, reduce the energy consumption of the network.
Several cluster-based protocols have been proposed in the literature, with the objective of maximizing the sensor network lifetime. The LEACH (Low-Energy Adaptive Clustering Hierarchy) protocol presented in [2] is a distributed cluster-
978-1-4244-2644-7/08/$25.00 ©2008 IEEE
based protocol in which the cluster heads are selected with some probability. However, LEACH does not guarantee that the optimum number of cluster heads is selected and cluster heads are not evenly positioned across the network. In a centralized version of this protocol called LEACH-C [3], a better overall performance of the network is achieved due to improved cluster formation performed by the base station. In [4], a protocol that has the objective of minimizing the intracluster distance and optimizing the energy consumption of the network using PSO has been proposed. In [5], the authors used PSO to equalize the number of nodes and candidate cluster heads in each cluster in order to minimize the energy expended by the nodes while maximizing the data transmission. Nonetheless, in most of these algorithms, the number of clusters which is denoted as K, has to be predetermined before the cluster process begins. The value of K is indeed one of the key parameters that determines the lifetime of the sensor network. If there are fewer clusters, non-cluster head nodes are likely to spend too much energy transmitting data to their cluster heads because most of the clusters will be of a large size. However, this also means that fewer sensor nodes are cluster heads and can result in less total energy being consumed to communicate with the base station. Conversely, if there are too many clusters, the energy consumed by noncluster head nodes to transmit data to their cluster head decreases. At the same time, more cluster heads are required to transmit the data over a large distance to the base station. Therefore, in order to minimize the energy consumption the clustering scheme must be able to find the optimal number of clusters all the time. Based on this observation, this paper proposes a dynamic multi-objective clustering approach using binary PSO (DCBMPSO) algorithm which automatically decides the number of clusters in each round that can result in minimum total network energy dissipation. In addition, two clustering metrics are defined to select the best set of cluster heads, namely the total network energy consumption and intra-cluster distance. The remainder of this paper is organized as follows: In section II, the network and system models used in this paper are described. In section III, a detailed description of the algorithm using binary PSO and multi-objective approach is given. The
simulation study of the proposed algorithm is presented in section IV. Finally, conclusions are drawn in section V. II. THE SYSTEM MODEL We assume a sensor network model similar to those used in [4] where data fusion is performed by the cluster head to reduce the total amount of data sent. The radio energy model used in this work is similar to those used in [2]. In this model, the transmitter dissipates energy to run the radio electronics and the power amplifier, and the receiver dissipates energy to run the radio electronics. The radios can perform power control and hence use the minimum energy required to reach the intended recipients. In order to achieve an acceptable Signal-toNoise-Ratio (SNR) in transmitting an I-bit message over a distance d, the energy expended by the radio is given by:
(3)
where viis the particle velocity, Xi is the particle position, t is the number of iterations, CI, and C2 are two positive constants, referred to as the cognitive and social acceleration factors respectively, rl and rz are random numbers within the range [0,1], and w is the inertia weight. The particle's best position (pbest) is denoted as Pi, while P t, is the neighbouring best position (Ibest). After the velocity updates, a piece-wise linear function as follows is used to force the velocity values so that they are within the Vmin and Vmax • Vmax'
h(v; (1 + 1)) =
if d < do if d
~
do
(1)
where E e1ec is the energy dissipated per bit to run the transmitter or the receiver circuit, EFs and E TR are parameters that depend on the transmitter amplifier model used, and do is the threshold transmission distance. To receive an I-bit message, the radio expends:
ERX(/) = I· Eelec
A.
PROTOCOLS DESCRIPTION
Binary PSO evolutionary computing technique that is based on the principle such as bird flocking [6]. In PSO, each particle represents a candidate solution to the optimization problem. In the binary version ofPSO, a binary value of 0 or 1 is assigned to each particle with a certain probability [7]. Velocity values of each particle are restricted to some minimum and maximum values, Vmin and Vmax • During each generation, each particle uses the information about its previous best individual position and neighbourhood best position to maximize the probability of moving towards the optimal solution. The velocity of each particle is therefore updated using the equation:
pso is an
(t+ I)..
Vmin' If
(t + 1) > Vmax
Vi
if Vi
Iv; (1 + 1~ s V
max
(t + 1) < Vmin
(4)
Since each Vi E 9\ , a sigmoid function is used to map the real values between 0 and 1. The sigmoid function is defined as:
(5) Then, the position of each particle is updated as follows:
(2)
For the simulations described in this paper, the communication energy parameters are set as Eelec = 50 nJ/bit, e Is = 10 pf/bit/rrr' and Etr = 0.0013 p.l/bit/rn", The data fusion model used in our simulations assumes that the overall information collected by a cluster of n nodes, where each node collects k bits of data, can be compressed to k bits regardless of the number of nodes in that cluster. In our simulations, the energy cost for data aggregation is set as E DA = 5nJ/bit. III.
Vi
{
if
(6) where r3 is a random number within the range [0,1]. B.
Multi-objective Approach There are two important factors that are taken into account when selecting the cluster heads in the network which are network energy consumption and intra-cluster distance. The goal is to find the optimal cluster heads positions that can minimize the energy expenditure in a cluster based network topology and at the same time to produce clusters with minimum intra-cluster distance. Assume an area of A = M x M square meters over which N nodes are uniformly distributed. Each cluster head dissipates energy receiving signals from the member nodes, processing or aggregating the data bit and transmitting the aggregate signals to the base station. For simplicity, it is also assumed that the sensor nodes inside a cluster have short distance, djtoCH to cluster head,
whereas each cluster head has long distance, dktoBS to the base station. Thus, based on the radio energy model used, the first fitness function is given as:
f
_~~I((
J 1-
c: ~ k=l]=l
) Etrd~OBS Ic I
E e1ec + E DA +
k
+
ICkl-1I E e1ec + eIsd 2 -Ic
JtoCH
k
1
(7)
IC I
where k is the number of total nodes in the cluster k. Due to the space limitation, the derivation of the above equation is omitted. For the second fitness function, the aim is to reduce the maximum distance between member nodes and their respective cluster heads as defined by:
TABLE!.
SYMBOLS USED IN THE DC-BMPSO ALGORITHM
Meaning
Symbols
K max
The maximum number of clusters.
Km;n
The minimum number of clusters.
NE
The total number of eligible nodes.
Z
={n; Ii =1,..., N}
The set of nodes that are eligible to be cluster head candidates in the network.
ZE M={mklk
The set of nodes in the network.
= 1,..., K max}
The set of K maxcluster heads. The swarm of s particles such that Xi indicates particle i with x;,k E {O,l} for k = 1,...,Kmax such that if x;,k = 1 , then the corresponding
(8)
where d mk n j is the distance between the cluster head
mk
and its
cluster member node nJ. Intuitively, each cluster shall be as compact as possible because it will take less power for a sensor node to communicate with its cluster head if they are close to each other, which consequently reduces the energy dissipation. The fitness functions defined above is thus a multi-objective problem. In order to deal with more than one objective functions, we use the approach proposed in [8]. In this approach, a local lbest is found for each swarm member selected from the 'closest' two swarm members. The computation of the distance between each particle and its neighbours that measures the closeness depends on the second objective function, 12. Subsequently, the selection of local optima among the neighbours of a particle is based upon the first objective function, fi. In the next sub-section, the steps of the algorithm will be described in detail. The DC-BMPSO Algorithm The proposed algorithm borrows some ideas from the algorithm introduced in [9], which automatically determines the optimum number of clusters and simultaneously clusters the data set with minimal user interface. However, the work in [9] is concerned with the application in unsupervised image classification, while the algorithm in this work is only concerned with the application in a sensor network area. To describe the development of the proposed algorithm, we used the symbols as defined in Table 1. Initially, each particle is constructed randomly by employing the following equation:
S
={xl. ... ,x;,...,xs}
mk in M is not part of the solution proposed by Xi. V ={VI,... , Vi
where P init = 0.25 is a user-specified probability used to initialize Xi and rk is a random number within the range [0,I]. The operation of the proposed protocol is based on a centralized control algorithm that is implemented at the base station, which is a node with a large amount of energy supply. The protocol operates in rounds, where each round begins with a setup phase at which clusters are formed. This is followed by
, ... , Vs}
The velocities of s particles. The number of clusters used by the clustering represented solution by such Xi
K;
Kmax
that: K;
= LX;
, with K;
s K max .
k=l
The clustering solution represented by Xi such that M; = (mk), "ifk: x;,k =1 with M; ~ M .
M;
K'1i
The number of clusters used by the clustering solution represented by pbest with
K'1i ~Kmax· The number of clusters used by the clustering solution represented by the global best particle Kr
C.
(9)
cluster head mk in M has been chosen to be part of the solution proposed by particle Xi. Otherwise if x;,Ie = 0 then the corresponding
(gbest), Pg such that:
x, Mr
Kmax
x, = LPgk
with
k=l
~Kmax'
The clustering solution represented by Pg such that M t =(mk ), "ifk : Pgk =1 with Mr~M.
The set of cluster heads in M which have not been chosen by i.e. Pg
Mr
vk : Pgk
M, =(mk) Mr~M
(i.e.
=0
M; r.M; =
with
0
and
MruM r =M).
a steady state phase in which data communication takes place. At the starting of each setup phase, all nodes send information about their current energy status and locations to the base station. Based on this information, the base station computes the median energy level of all nodes. Only nodes with an energy level above this value are eligible to be a cluster head candidate for this round and included in ZE. Next, the base station runs the DC-BMPSO algorithm to determine the best cluster heads that optimize the cost function defined. The following describes the details ofthe proposed algorithm: (i) Select cluster head mk EM, Vk = I, ... , K max randomly from ZE. (ii) Initialize each particle using (9).
(iii) Randomly generate the velocity,
J
Vi,
of each
Xi
such
that, Vi E [- 5,5 (iv) For each Xi in S, find the fitness values: a Assign each node n., i=I, ... ,N in the network to the closest (in terms of the Euclidean distance) cluster head in M;. b. Calculate the fitness functions fi and 12 . (v) For each Xi, find the two neighbours in terms of 12 : a Calculate the distances of the current particle from other particles in the fitness value space of12 . b. Find the nearest two particles that have the closest distance with current particles based on the distances calculated above. c. Find the local optima, A; among the neighbours in terms of the fitness value offi . (vi) Apply the velocity update on all particles using (3). (vii)Restrict the velocity values using (4). (viii) Apply the binary position update using (5) and (6). (ix) Repeat step (iv) to find the fi and 12 . (x) For each Xi in S, update pbest, Pi as follows: Pi (t + 1) = Xi (t + 1) if and only if
II(xi(t+I))
II(Pi(t))
AND
12 (Xi (t + 1)) s 12 (Pi (t))
AND
~
Start
Initialize algorithm constant, s, K max, K min,
w, ci,
C2, Vm;n, V max
Randomly select M from ZE Randomly initialize each particle's position, X; and particle's velocity, V; Set iteration, t = 1 Calculate the fitness, fi (x;) andfi(x;) for each particle Find the particle's neighbourhood best, A Apply binary PSO velocity update and position update Calculate the fitness, fi(x;) andfi(x;) for each particle Find the particle's best, p; , and global best P,
K i (t + 1) ~ K 1]; (t )
(xi) Find the gbest solution,
Pg which
is the best solution
among Pi based onfi and/2 : pg(t + 1) = Pi(t + 1) if and only if
h(P;(t+I))~h(Pg(t)) AND
12 (pi (t + 1)) ~ 12 (p g (t )) (xii)Randomly re-initialize M; from ZE, set M ruM 'f = M . (xiii) Repeat steps (ii) through (xii) until the maximum iteration is reached. When the algorithm terminates, M T will be the resulting optimum set of cluster heads and K T will be the optimum number of clusters in Z. Then, the base station transmits to the network the information that contains the cluster head identification of all sensor nodes. We adopt similar approach as in [2] during the steady state phase. Fig. 1 shows the flowchart of main procedures of DC-BMPSO. IV.
SIMULATIONS AND ANAL YSIS
The proposed algorithm is implemented in Network Simulator (ns2) version 2.2.7 [10]. We ran the simulations for 100 nodes in a 500 m x 500 m network area. All nodes are given equal initial energy of 2 1. The base station is located in the middle of network area with coordinate (250,250). We set K min = 1 whileK max = 10. The length of each round is set at 20 seconds. The performance of DC-BMPSO algorithm is
End: Output, P,
Figure 1. Main procedures ofDC-BMPSO algorithm.
compared with the well known clustering algorithms, LEACH [2] and LEACH-C [3], as well as PSO-C proposed in [4]. For these three algorithms, the number of clusters is set as K = 5 since it has been shown in [3] that the optimum number of clusters for a 100 node network is between 3 to 5. Throughout the simulation, we considered several random network topologies to get the average results. The simulations continued until all the nodes in the network had consumed all their energy. For both DC-BMPSO and PSO-C algorithms, we used swarm size of 30 particles, CI = C2 = 2 and w = 0.72 and these values are set empirically. We set p = 0.5 in PSO-C to give equal contribution of each sub-objective defined in [4]. Fig. 2 shows the plot of the number of clusters obtained by DC-BMPSO algorithm in each round. It can be seen that the number of clusters in DC-BMPSO varies in between 3 to 5 throughout the simulation time. The plot confirms that the proposed algorithm can achieve the optimal number of clusters that leads to greater energy saving in the network. Fig. 3 demonstrates the system lifetime, defined by the number of nodes remain alive over time for the simulation in the network area considered. It can be observed that the network lifetime for DC-BMPSO algorithm increases significantly compared to PSO-C, LEACH-C and LEACH. This improvement is based on three reasons. Firstly, significant energy saving is achieved by DC-BMPSO algorithm through the use of dynamic
clustering with the proposed objective functions. Although the number of clusters from the analytical model in [3] is 5, the exact number varies slightly over time depending on the current cluster topology and the distribution of the nodes (Le. the distance from non-cluster head nodes to cluster head and the distance from cluster head to the base station). By using the proposed dynamic clustering approach, the DC-BMPSO algorithm can achieve the optimal number of clusters throughout the simulations which leads to lower network energy expenditure. Secondly, the objective functions defined can produce better network partitioning with minimum network energy dissipation and minimum intra-cluster distance. Thirdly, the multi-objective PSO technique adopted in DC-BMPSO attempts to produce a set of good compromises or trade-offs where the values of all the objective functions are acceptable to the system requirements. As a result, this algorithm can obtain an optimal set of cluster heads that are evenly distributed across the network with optimal network configuration, which further reduces the total network energy dissipation.
6r-------.----...,..---
21.....---.l.--------........-------..I..o-~ 100
v.
[2]
[3]
400
500
LEACH LEACH- C -0- PSO-C ~ DC-8MPSO -~-
--I!r
400
100 4 X 10
"C Q)
.?;
600
Figure 3. Number of nodes alive over time.
5
4
~
-0
-e-
LEACH-C PSO-C DC-8MPSO
~
/0
m
2 ro "C
ro
"0
..G- ..
,...--0---
E 3
CONCLUSIONS AND FUTURE WORKS
500
6F;::::==:::::::!:====:::!:;"--,-------r----::it;::=::::fit---ip --v- LEACH
Q)
u
~
I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, "A survey on sensor networks," IEEE Comm. Mag., Aug. 2002, pp. 102114. W.R. Heinzelman, A.P. Chandrakasan, and H. Balakrishnan, "Energyefficient communication protocol for wireless microsensor networks," in Procs. of the 33rd Hawaaian Int. Conf on System Sciences., Jan. 2000. W.B. Heinzelman, A.P. Chandrakasan, and H. Balakrishnan, "An application-specific protocol architecture for wireless microsensor networks," IEEE Trans. Wireless Commun., vol. 1, no.4, Oct. 2002, pp. 660-70.
300
Time (s)
1 OO __~---l~.....e--=:--=~~--~--~--.....,
tJ)
REFERENCES [1]
200
Figure 2. Number of clusters obtained by DC-BMPSO during simulation.
Fig. 4 gives the result of the total data messages received at the base station before all nodes run out of energy. The plot clearly indicates the effectiveness of DC-BMPSO algorithm in delivering more data messages than other algorithms under consideration. The proposed algorithm offers improvement in data delivery by factors of 291 percent over LEACH, 138 percent over LEACH-C and 46 percent over PSO-C. Hence, the results prove that significant energy saving obtained by DC-BMPSO algorithm can leads to more data messages being delivered to the base station.
In this paper, we have proposed a dynamic clustering algorithm for WSNs using a binary multi-objective PSO algorithm. The use of dynamic clustering eliminates the requirement to fix the number of clusters in the simulation. In addition, the multi-objective PSO is employed with the defined cost function that takes into account the expected network energy consumption and intra-cluster distance. Simulation results have shown that the proposed algorithm can achieve an optimal number of clusters in each round during simulation. Moreover, the proposed algorithm also offers improvement in network lifetime and data delivery compared to algorithms such as LEACH, LEACH-C and PSO-C. In the future work, we plan to investigate the DC-BMPSO algorithm properties such as the effect of varying algorithm parameter, P init on the number of clusters, as well as on network performance.
r----""""T"'---oro-----,
J'",¥
.-..-k~
. § .... ~ .......
"0"- _ -
e- ..
-e - -()- -
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~ ~ ~
:r:r - - - v- - - ~ - - -v- - - -v - - - ~ - - -
t-
O 0
100
200rime {~OO
400
500
Figure 4. Total data messages received at the base station over time. [4]
N. M. Abdul Latiff, C. C. Tsimenidis, B. S. Sharif, "Energy-aware clustering for wireless sensor networks using particle swarm optimization," in IEEE Int. Symp. PIMRC., Athens, Greece, Sept. 2007. [5] J. Tillet, R. Rao, and F. Sahin, "Cluster-head identification in ad hoc sensor networks using particle swarm optimization," in IEEE Int. Conf on Personal Wireless Commun., New Delhi, India, 2002, pp. 201-205. [6] J. Kennedy and R.C. Eberhart, "Particle swarm optimization," in IEEE Int. Conf on Neural Networks., Perth, Australia, vol. 4, 1995, pp. 19421948. [7] J. Kennedy and R. C. Eberhart, "A discrete binary version of the particle swarm algorithm," in Procs. of the Conf on SMC97, Piscataway, NJ, USA, 1997, pp. 4104-4109. [8] X. Hu and R. Eberhart, "Multiobjective optimization using dynamic neighbourhood particle swarm optimization,": in Proc. of the 2002 Congress on Evol. Comput., May 2002. [9] M. G. H. Omran, A. P. Engelbrecht, and A. Salman, "Dynamic clustering using particle swarm optimization with application in unsupervised image classification," in Proc. of World Academy of Science, Engineering and Technology, vol. 9, pp. 199-204, Nov. 2005. [10] The Network Simulator ns2. Available at: http://www.isi.edu/nsnam/nsl.
