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Applied Soft Computing 12 (2012) 1913–1928

Contents lists available at ScienceDirect

Applied Soft Computing

journa l homepage: www.e lsev ier .com/ locate /asoc

nergy-efficient clustering in mobile ad-hoc networks using multi-objectivearticle swarm optimization

amid Ali, Waseem Shahzad, Farrukh Aslam Khan ∗

epartment of Computer Science, National University of Computer and Emerging Sciences, A.K. Brohi Road, H-11/4, Islamabad 44000, Pakistan

r t i c l e i n f o

rticle history:eceived 2 October 2010eceived in revised form 29 April 2011ccepted 12 May 2011vailable online 20 May 2011

eywords:obile ad hoc network (MANET)ulti-objective particle swarm

ptimization (MOPSO)lusteringluster-head (CH)nergy-efficient networksoad balance factor

a b s t r a c t

A mobile ad hoc network (MANET) is dynamic in nature and is composed of wirelessly connected nodesthat perform hop-by-hop routing without the help of any fixed infrastructure. One of the importantrequirements of a MANET is the efficiency of energy, which increases the lifetime of the network. Severaltechniques have been proposed by researchers to achieve this goal and one of them is clustering inMANETs that can help in providing an energy-efficient solution. Clustering involves the selection ofcluster-heads (CHs) for each cluster and fewer CHs result in greater energy efficiency as these nodesdrain more power than noncluster-heads. In the literature, several techniques are available for clusteringby using optimization and evolutionary techniques that provide a single solution at a time. In this paper,we propose a multi-objective solution by using multi-objective particle swarm optimization (MOPSO)algorithm to optimize the number of clusters in an ad hoc network as well as energy dissipation innodes in order to provide an energy-efficient solution and reduce the network traffic. In the proposedsolution, inter-cluster and intra-cluster traffic is managed by the cluster-heads. The proposed algorithmtakes into consideration the degree of nodes, transmission power, and battery power consumption of
the mobile nodes. The main advantage of this method is that it provides a set of solutions at a time.These solutions are achieved through optimal Pareto front. We compare the results of the proposedapproach with two other well-known clustering techniques; WCA and CLPSO-based clustering by usingdifferent performance metrics. We perform extensive simulations to show that the proposed approachis an effective approach for clustering in mobile ad hoc networks environment and performs better thanthe other two approaches.
. Introduction

A mobile ad hoc network (MANET) is a dynamic and self-dapting network in which no centralized control exists. It has a setf dynamic nodes that can move freely. These nodes have limitedrocessing speed, battery, storage, and communication capabilities.hese features of MANETs with non-existence of central base sta-ion bring many new problems and challenges for the researchers.lustering is a method of organizing objects into meaningful groupsith respect to their similarities. The objective of clustering inANETs is to identify the groups of nodes in such a way that the

dentified groups are exclusive and any instance in the networkelongs to a single group. The special nodes known as cluster-heads
CHs) are responsible for the formation of clusters, maintenancef the network topology, and the resource allocation to all nodeselonging to their clusters. Since the configuration of the cluster-
∗ Corresponding author. Tel.: +92 321 8551974; fax: +92 51 8314119.E-mail addresses: [email protected] (H. Ali), [email protected] (W.

hahzad), [email protected] (F.A. Khan).

568-4946/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2011.05.036

© 2011 Elsevier B.V. All rights reserved.

heads is constantly changing due to the dynamic nature of mobilenodes, minimizing the number of cluster-heads becomes essential.An optimal selection of the cluster-heads is an NP-hard problem.The neighbourhood of a CH is the set of nodes that lie within itstransmission range. Since energy efficiency is an important require-ment of a MANET, which increases its lifetime, clustering canprovide an energy-efficient solution as only few nodes are involvedin doing the main operations in the network such as routing, man-agement, data aggregation, etc. A wireless sensor network (WSN),which is a special type of ad hoc network consists of autonomoustiny devices that cooperatively monitor physical or environmentalconditions, such as temperature, vibration, pressure, motion, etc.These tiny devices or sensors have more limited battery power,memory and processing capabilities. Therefore, clustering can alsohelp achieve an energy-efficient solution for WSNs.

Optimization refers to finding one or more solutions of a prob-lem, which correspond to extreme values of one or more objectives.
It has been an active area of research as many real world optimiza-tion problems have become increasingly complex. Therefore betteroptimization algorithms are always needed. Most of the real worldproblems consist of several objectives that need to be optimized
dx.doi.org/10.1016/j.asoc.2011.05.036

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dx.doi.org/10.1016/j.asoc.2011.05.036

1914 H. Ali et al. / Applied Soft Comput

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cluster-heads can do the job of routing network packets within

Fig. 1. Optimal Pareto front.

imultaneously. These problems arise in many applications. When
olving multi-objective problems (MOPs) with traditional mathe-atical programming techniques, they generate a single solution
rom the set of solutions in one run. Therefore these techniques areot suitable to solve multi-objective optimization problems. Evolu-

Fig. 2. Flowchart

ing 12 (2012) 1913–1928

tionary algorithms paradigm is very suitable to solve MOPs becausethey are population based and can generate a set of solutions in onerun [1].

Optimization problems have great importance in scientific,engineering design and decision-making applications. When anoptimization problem has only one objective then the task of find-ing optimal solution is called single-objective problem. Normally ina single-objective problem we are interested in finding only a sin-gle solution except multimodal functions. When an optimizationproblem has more than one objective functions then the optimiza-tion problem is known as multi-objective optimization problem.In multi-objective problems multiple criteria are considered. Sincethere is no single solution that can be termed as optimal solu-tion, i.e., having multiple conflicting objectives, therefore, we areinterested in finding a number of optimal solutions [2].

In this paper, we present a multi-objective particle swarm opti-mization (MOPSO) based clustering algorithm for mobile ad hocnetworks. MOPSO efficiently manages the resources of the networkby finding optimal numbers of clusters in multi-objective fashion.Optimal number of clusters can make the MANET energy-efficientby efficiently managing the resources of the network so that the

the cluster or to the nodes of other clusters. The proposed clus-tering algorithm takes into consideration the transmission power,ideal degree, mobility of nodes, and battery power consumption

of MOPSO.

H. Ali et al. / Applied Soft Computing 12 (2012) 1913–1928 1915

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Fig. 3. Degree difference vs. energy consumption in case MOPSO in 100 m ×

f the mobile nodes for selecting the cluster-heads. MOPSO useshe evolutionary capability to optimize the number of clusters.nstead of assigning a weight to each of the parameters mentionedbove, we deal directly with the multi-objective problem in order tond out the Pareto-optimal solutions. The algorithm first finds theluster-head and then neighbours of the cluster-head. The neigh-ourhood of a cluster-head is the set of nodes that lie within itsransmission range. There are some requirements of clustering in

ANETs. The clustering algorithm must be distributed, since everyode in the network has only local knowledge and communicatesutside its group only through its cluster-head as in the case ofluster-based routing. The algorithm should be robust as the net-ork size increases or decreases and it should be able to adapt to

ll the changes. The clusters should be reasonably efficient, i.e., theelected cluster-heads should cover large number of nodes as muchs possible.

We compare the results of the MOPSO-based clusteringechnique with two other well-known clustering algorithms; com-rehensive learning particle swarm optimization (CLPSO) basedlustering [3] and weighted clustering algorithm (WCA) [4]. Thexperimental results show that the proposed approach covers thehole network with minimum number of clusters that can reduce

he routing cost of the network and consumes less energy. This will
elp minimize the number of hops and delays of packets transferred
n a cluster-based routing environment. The numbers of clusters arearge when the transmission ranges of nodes are small. It also hasdvantage of finding multiple solutions instead of a single solu-

area by fixing nodes (a) 15 nodes (b) 20 nodes (c) 25 nodes (d) 30 nodes.

tion. This diversity of solutions provides more flexibility for thedomain experts so that they can choose a solution according totheir requirements. The results show that the proposed cluster-ing approach is effective and flexible as compared to the otherapproaches and performs better than the other two algorithmsin a mobile ad hoc network environment. The algorithm has theability to optimize the parameters of mobile nodes for finding themulti-objective solution.

The rest of the paper is organized as follows: In Section2 we give an overview of the previous clustering algorithmsfor mobile ad hoc networks. Section 3 describes multi-objectiveclustering approach while Section 4 provides an overview of multi-objective particle swarm optimization. Section 5 describes ourproposed MOPSO-based clustering algorithm. The experimentalresults are presented in Section 6 while Section 7 concludes thepaper.

2. Related work

Baker and Ephremides [5] proposed the lowest-ID, known asidentifier-based clustering algorithm. It assigns a unique ID to eachnode and chooses the node with the lowest ID as a cluster-head.It means that whenever a new node with a lowest ID appears,
it will become the cluster-head. Gerla and Tsai [6] proposed thehighest connectivity algorithm for clustering. It is multi-cluster,multi-hop packet radio network architecture for wireless adaptivemobile information systems. In this technique the degree of nodes

1916 H. Ali et al. / Applied Soft Computing 12 (2012) 1913–1928

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Fig. 4. Number of clusters vs. transmission range in case of WCA, C

s calculated, which describes the number of neighbours of a givenode. Each node broadcasts its identifier for the election proce-ure. After computing its degree, the node having the maximumegree becomes the cluster-head. A genetic algorithm based clus-ering algorithm was proposed in Ref. [7]. Genetic algorithm wassed to optimize the number of clusters in an ad hoc network. It

s a weight-based clustering algorithm, which assigns a weight toach objective of the problem and is set by the user. Chatterjeet al. [4] proposed the weighted clustering algorithm. It elects clus-er heads according to their weights. The weights are computedy combining a set of parameters such as battery power, mobil-

ty and transmission range. This was the first weighted clusteringlgorithm proposed for MANETs. The time required to identify theluster-heads depends on the diameter of the underlying network.he non-periodic procedure for the selection of cluster heads isnvoked on-demand and is aimed to reduce the computation andommunication costs.

Another clustering algorithm based on d-hops has been pro-osed in Ref. [8]. It forms variable diameter clusters based onobility pattern of the nodes in MANETs. A new metric is used to

nd the variation of distance between nodes over time in order to
stimate the relative mobility of two nodes. The authors also esti-ate the stability of clusters based on relative mobility of clusterembers. The diameter of clusters is not restricted to two hops as
ther clustering algorithms do. The diameter of clusters is flexible

, and MOPSO in 100 m × 100 m area by fixing nodes from 30 to 60.

and determined by the stability of clusters. Nodes are grouped intoone cluster, which have similar moving pattern.

Shahzad et al. [3] proposed a comprehensive learning par-ticle swarm optimization based clustering algorithm for mobilead hoc networks. It finds the optimal or near-optimal numberof clusters to efficiently manage the resources of the network.The cluster-heads are used for routing network packets withinthe cluster or to the nodes of other clusters. It takes into con-sideration the transmission power, ideal degree, mobility of thenodes and battery power consumption of the mobile nodes. Itis also a weighted clustering algorithm that assigns a weight toeach of these parameters of the network. Each particle containsinformation about the cluster-heads and the members of eachcluster.

The basic problem with all these heuristic-based algorithms isthat none of them include all the basic parameters of MANETs.WCA was the first algorithm that includes maximum number ofparameters but it does not find optimal number of clusters in thenetwork. It assigns weight to each objective function and makesthe multi-objective problem single-objective and finds only a sin-gle final solution. Whereas, the proposed MOPSO based clustering
algorithm finds multiple solutions. Since our problem is continuousin nature, therefore, we used PSO as it has been successfully appliedto solve continuous optimization problems and our problem caneasily be encoded in PSO.


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. Multi-objective clustering

Multi-objective problems have a number of objectives that areinimized or maximized simultaneously. These problems have a

umber of constraints, which a solution must satisfy. In multi-bjective optimization we have a multi-dimensional search space.here are n objective functions: f(s) = (f1(s), f2(s),. . ., fn(s)) in whichach objective function can be either minimized or maximized. s* isareto optimal solution if there exists no feasible vector of decisionariables s ∈ F which would decrease some objective value with-ut causing a simultaneous increase in at least one other objectivealue. This concept almost always gives not a single solution, butather a set of solutions called the Pareto optimal set or Pareto opti-al solutions. The vector corresponding to the solutions included

n the Pareto optimal set is called non-dominated vector. The plotf the objective functions whose non-dominated solutions are inhe Pareto optimal set is called the Pareto front [9].

In multi-objective optimization we are interested to find the setf Pareto-optimal solutions that are close to true Pareto-optimalront. Those solutions, which are not close to the true Pareto-frontre not desirable solutions. The set of optimal solutions should be
iverse. Multi-objective problems have two spaces, one is decisionariables space and another is objective space. Diversity can beefined in both of these spaces. Multiple Pareto-optimal solutionsan exist if and only if the objectives are conflicting to each other

in a problem. If the objectives are not conflicting to each other thenPareto-optimal set is just one. In single-objective solution, there isonly one search space, i.e., the decision variable space. But the dif-ficulty with multi-objective problems is that it involves two searchspaces instead of one.

A solution s1 is said to dominate the other solution s2 if and onlyif following two conditions are true which are given below:

• The solution s1 is no worse than s2 in all objectives.• The solution s1 is strictly better than s2 in at least one objective.

If any of the above mentioned condition is false, the solutions1 does not dominate the solution s2. If solution s1dominates thesolution s2 then solution s1 is better than solution s2.

When two solutions are compared with respect to all objectivefunctions and if none of them is better than the other or in otherwords none of these dominate the other then the two solutions arecalled non-dominated solutions. If all objectives are equally impor-tant then we cannot say which of these solutions is better than theother. For a given set of solutions, we can perform all possible pair-wise comparisons and find which solution dominates the other and
which solutions are non-dominated with respect to each other. Atthe end we have a set of solutions, which do not dominate eachother and these solutions are called Pareto-optimal solutions. Theseall non-dominated solutions are joined with a curve and all solu-

1918 H. Ali et al. / Applied Soft Comput

Table 1Proposed MOPSO algorithm.

(1) Randomly initialize the positions of all the nodes.(2) Initialize the velocity of each node.(3) Initialize the general parameters of MOPSO(4) FOR each particle X

DO(a) WHILE whole network is not covered

DOi. Randomly select a cluster head Xi

ii. Find the neighbours of the cluster head(b) Remove the cluster head ‘i’ and its neighbours for next cluster head

selection process(c) END WHILE

(5) END FOR(6) Evaluate each of the particles in POP(7) Store the best cluster heads vectors(8) Find the Pareto front with non-dominated sorting,(9) Store cluster heads vectors that represent non-dominated vectors in therepository REP(10) Find the global cluster heads vector from the repository(11) WHILE maximum number of cycles not reached

DO(a) Compute the velocity (VEL) of each cluster heads vector(b) Compute the new cluster heads vectors of the solutions adding the

velocity produced from the previous step(c) Evaluate each of the particles in POP(d) Update the contents of REP(e) When the current combination of cluster heads of the solution is better

than the combination of cluster heads contained in its memory, the particle’sposition is updated

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ions lying on this curve are called Pareto-optimal solutions. Theurve formed by these solutions is known as Pareto-optimal front10]. This can be seen from Fig. 1 in which we have two objectiveunctions that are conflicting with each other.

As our problem is multi-objective clustering in which we grouphe mobile nodes according to multiple objectives, we used fourbjective functions from mobile ad-hoc networks environment.sually we do not have only a single best solution for this kindf problem. Hence, we are interested in finding a set of optimallusters.

. Multi-objective particle swarm optimization

Evolutionary algorithms have been widely used for finding mul-iple solutions in multi-objective optimization problems. Theselgorithms are capable of finding multiple solutions at a timenstead of a single solution. A number of evolutionary algo-ithms have been developed that use different mechanisms tovolve the solutions, for example, genetic algorithm [12], artifi-ial immune system, differential evolution and swarm intelligence1,3,10,13–17], etc.

Swarm intelligence is an evolutionary technique inspired by theatural world. It has been used to solve various difficult optimiza-ion problems. There are two main approaches under the umbrellaf swarm intelligence, one is particle swarm optimization and others ant colony optimization. We speak of swarming behaviour withegard to social insects, ants, bees, termites and wasps. An insectest contains hundreds, thousands, or millions of individual insects.he individual insect is not a very intelligent creature, but the socialrganism makes a collective intelligence, i.e., the ants efficientlyather food, the bees in the hive help regulate temperature, etc.ach individual insect is a reactive agent responding to local stimuli
n a very simple way without reasoning. Kennedy and Eberhart [11]roposed an algorithm in 1995 inspired by the choreography of aird flock, known as particle swarm optimization (PSO). In this algo-ithm best personal and best global behaviour guide each individual
ing 12 (2012) 1913–1928

in the flock. These behaviours quickly converge each individual tonear-optimal geographical positions.

In PSO, a complete single solution of the problem is called aparticle. The group of all these particles becomes a swarm, whichsearches for an optimum solution. A group of swarms is used inmulti-objective problems instead of a single swarm. A particle iis defined by its position vector �Xi. The dimension of the vectoris equal to the number of attributes in a problem. The position ofits personal best solution and its velocity found so far are �Pi and�Vi, respectively. All the particles know their best solution foundso far. Initially, particle positions and velocities are generated ran-domly and then proceed iteratively. The velocities and positionsare calculated as follows:

vid = wvid + c1r1(pid − xid) + c2r2(pgd − xid) (1)

xid = xid + vid (2)

where d = 1,2,..,D; i = 1,2,..,N, N is the size of the population, w is theinertia weight, c1 and c2 are two positive constants, r1 and r2 aretwo random values in the range [0.1].

The new velocity of the ith particle is calculated using Eq. (1) bytaking into consideration three terms; the particle’s previous veloc-ity, the best personal position and the global best position. Eq. (2) isused for new position of a particle. The inertia weight is employedto control the impact of the previous history of velocities on thecurrent velocity. If we do not want to include the previous historythen we simply exclude the inertia weight. Particle swarm opti-mization is initialized with a group of random particles (solutions)and then it searches for optima by updating these particles gener-ation by generation. In every generation, each particle updates thepersonal best value achieved and the global best position obtainedso far by any particle in the population. When a particle takes partof the population as its topological neighbours, the best value is alocal best and is called lbest [13].

PSO has attracted a high level of interest during the past fewyears. It is very popular due to simplicity in its implementation.It requires only a few parameters to be tuned. It is computation-ally cheap in the updating of individual, as it requires only twosimple equations as compared to mutation and crossover oper-ators in genetic algorithms. Many researchers have worked onimproving its performance in different ways, which derives severalinteresting variants. One of the variants [18] introduces a parame-ter called inertia weight w into the original PSO algorithm, whichis used to balance the global and local search capabilities. Thereare numerous variants for the PSO algorithm but solving multi-dimensional problems is still the main deficiency of the standardPSO. Many problems handled by PSOs are often having a singleglobal optimum in single objective problems. In the initial PSO pro-posed by Ref. [11], each particle in a swarm population adjustsits position in the search space based on the best position it hasfound so far, and the position of the known best-fit particle in theentire population (or neighbourhood) [14]. PSO has recently beenextended to deal with multi-objective optimization problems. Dur-ing the past few years, researchers focused on how to modify PSOto handle multiple objective optimization problems and have pro-posed multi-objective particle swarm optimization [2,9] algorithmto solve such problems. Many real world problems are dynamic, i.e.,they change over time. In such cases, the optimization algorithmhas to track a moving optimum [5,6,19].

5. Proposed technique

PSO can handle both continuous as well as discrete variableproblems. The implementation of PSO is very easy and few linesof code are required for implementation. It is also computationallyinexpensive in terms of memory as well as speed and is suitable


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or multi-objective optimization. These features suggest that PSOs a potential algorithm for optimizing clustering in a mobile ad hocetwork. In this work, we use a multi-objective particle swarm opti-ization algorithm to solve the problem of clustering in a mobile

d hoc network. Each particle in MOPSO represents coordinatesf N number of cluster-heads. The proposed MOPSO algorithm isomposed of the following steps as shown in Table 1.

MOPSO starts with population P0 of N randomly generatedluster-heads vector T, which has a unique ID in the network. Eachector T covers the whole network for communication.

It is important to note that each of these particles has the fol-owing characteristics: (1) completeness, and (2) uniqueness. It

eans that each particle covers the whole network as well asas the unique cluster-heads. For each solution the objectives arealculated using the respective equations. First of all we find theeighbours of the cluster-head, which is at first position in theluster-heads vectors T and calculate the energy consumption ofhat cluster-head, mobility, and transmission range. In the sameay we calculate all objectives for all cluster-heads. The degreeifference is calculated for each cluster-head by the equation � =

d − ı| where � is degree difference, d is the total number of cluster-ead neighbours and ı is a predefined threshold. In the same waye calculate the objectives for all cluster-heads in a single solution

n the population. After that we sum up all the values of each objec-


tive of cluster-heads. These summations are the overall objectivevalues of a single solution in a population. In the same manner wecalculate the objectives of all the population.

After finding the objective values, the comparison of currentobjective values and old objective values is taken place to find thepersonal best cluster-heads vector. Non-domination sorting is usedfor optimal Pareto front, which is used for global best cluster-headsvector.

Velocity of each individual is calculated with the help of currentpositions, personal best positions of the cluster-heads of the cur-rent individual and the positions of global best cluster-heads vectorpositions. The current positions and the velocity of each cluster-head in the current vector are used for new cluster-heads vector.After comparison an individual is selected from new cluster-headsvector or the current cluster-heads vector. This process is pictoriallyshown in Fig. 2.

6. Experimentation and evaluation

In this section, we describe the experimental setup and theresults of our experiments performed for comparison of the pro-posed technique with other techniques for clustering in mobile adhoc networks.


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.1. Experimental setup

We have implemented the proposed algorithm in MATLAB 7.8.0.e conducted the experiments using a machine with 1.75 GHz

ual processors and 512 MB of RAM. We performed experimentsf M different nodes on an initial 100 m × 100 m grid. All the nodesan move in all possible directions with displacement varyingniformly between 0 and maximum value (max disp). The trans-ission range of each node varies from 10 to 60. In our experiments,is varied between 20 and 60. The threshold for degree difference

s set to 10. This restriction will ensure load balancing for an ad hocetwork.

The parameters of MOPSO and CLPSO are initialized as follows:

The population size is set to 100;The maximum generations are set to 150;The inertia weight w is set to 0.694;The learning factors c1 and c2 are set to 2.

We compare the MOPSO-based clustering with two other well-
nown algorithms for wireless networks clustering, i.e., weightedlustering algorithm and comprehensive learning particle swarmptimization based clustering. The same values of all differentarameters are used for the three algorithms. The results are

obtained after performing ten simulations of each algorithm andthen taking their averages.

6.2. Experimental results

The multi-objective evolutionary algorithms are very useful incase of conflicting objectives. In this problem the degree differenceand energy consumption are conflicting objects, which are shownin Fig. 3. We compare the performance of the proposed approachwith other two clustering algorithms by using three performancemetrics: (i) the number of cluster-heads, (ii) energy consumed ina network, and (iii) load balance factor (LBF). The experimentalresults have been produced by varying the transmission range,number of nodes in the network, grid size, and the displacement.

The dominant set in a network defines the number of cluster-heads in the network. The energy consumed in a network iscalculated by adding the energy consumed within a cluster andfrom cluster-head to the receiver. Load balance factor is a ratio
between the actual number of neighbours of the cluster-head andthe number of neighbours achieved by the algorithm. These param-eters are studied by varying the transmission range, number ofnodes in the network, grid size, and the maximum displacement.


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Fig. 8. Number of clusters vs. network nodes in case of WCA, CLPSO, and

.2.1. Number of clusters vs. transmission rangeWe conduct the experiments to find the number of clusters

gainst the transmission range varying from 10 m to 60 m by fixinghe number of nodes. We obtain four different solutions by fixinghe number of nodes to 30, 40, 50, and 60, using the grid size as00 m × 100 m. Results are also produced by varying the grid sizerom 100 m × 100 m to 400 m × 400 m.

We use average number of clusters as the performance metric.s can be seen in Fig. 4, our proposed algorithm based on MOPSOnds a range of solutions against each transmission range to coverhe whole network as compared to WCA and CLPSO in the samenvironment, i.e., 100 m × 100 m.

The numbers of clusters are less than WCA and CLPSO. We con-uct the experiments by varying the nodes from 30 to 60. In mostf the cases, MOPSO finds minimum number of clusters as com-ared to WCA. The MOPSO also gives a diversity of solutions at eachoint, which gives a choice to select the solution that performs bestccording to the situation of the network.

Now we change the network area from 100 m × 100 m to00 m × 200 m. The results are shown in Fig. 5; we can see thathe CLPSO and WCA provide almost same number of solutions inll cases. It is to be noted that when the transmission range is very
mall the numbers of solutions are same and in many cases only oneolution is available. The reason behind this scenario is that withinimum transmission range all the nodes are almost isolated from
ach other, so every node is a cluster-head in that case.

SO in 100 m × 100 m area with transmission range fixing from 10 to 40.

As the transmission range increases the numbers of solutionsincrease in case of MOPSO. In this case MOPSO also performs betterthan the other two algorithms in all cases with a variety of solutions.

Now we change the network area to 300 m × 300 m. If we seeFig. 6(a) and (b), the number of clusters are almost same up totransmission range 25.

It is because the network area is very large and the number ofnodes is relatively small. So we can say that a direct relation isavailable between the network area and the number of solutionswhen we fix the transmission range. It is also found that the numberof solutions increases as transmission range increases. MOPSO stillperforms better than other two algorithms when the network areaincreases to 300 m × 300 m.

Now we change the network area to 400 m × 400 m. In Fig. 7(a)the number of clusters are almost same up to the transmissionrange 50.

Whereas, in Fig. 7(b–d), the MOPSO algorithm performs bet-ter because we increase the number of nodes, so there are manycluster-heads that have their neighbours in the network.

6.2.2. Number of clusters vs. network nodes
We conduct the experiments to find the number of clusters
against the number of nodes in a network varying from 20 to60, by fixing the transmission range. We obtain four differentsolutions by fixing the transmission range as 10, 20, 30, and 40.


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Fig. 9. Number of clusters vs. network nodes in case of WCA, CLPSO, and

esults are produced by varying the grid size from 100 m × 100 mo 400 m × 400 m.

We evaluate the performance of the three algorithms by keep-ng the transmission range constant and increasing the number ofodes. Fig. 8 shows that the proposed algorithm works better thanhe other two algorithms in terms of producing number of solu-ions and the average number of clusters. This shows the flexibilitynd robustness of the algorithm in terms of the parameters setting.he results in Fig. 8 are produced by fixing the transmission ranges 10, 20, 30, and 40 and the grid size as 100 m × 100 m. Figure alsohows that as the transmission range increases the MOPSO per-ormance also increases. So, we can say that the MOPSO performs

uch better in case of dense networks.Fig. 9 shows the results of number of clusters against network

odes when the grid size increases to 200 m × 200 m, and fixing theransmission range to 10, 20, 30, and 40. If we compare Figs. 8 and 9,e observe that as the grid size increases, the number of clusters

lso increases, which shows the direct relation of the network sizeith the number of clusters.

Fig. 10 shows the relation of number of clusters against the net-ork nodes. These results are obtained by fixing the grid size to

00 m × 300 m and transmission range to 10, 20, 30 and 40. As weimit the degree of cluster-heads, the number of clusters increases


as the number of nodes increases. In some cases the numbers ofclusters are less when we increase the transmission range, whichis due to increase in the degree of the cluster-head.

If we see Fig. 10(a) and (b), we find that all algorithms producealmost equal number of clusters because at transmission ranges 10and 20 different nodes made isolated groups. As the transmissionrange increases, MOPSO performs better than the other algorithms.If we observe the number of clusters when the transmission range is40 and nodes in the network are 60, we find that MOPSO produces((26 − 20)/26) × 100 = 23% less number of clusters than the otheralgorithms. MOPSO also performs better in all cases.

Fig. 11 shows the results in case of grid size 400 m × 400 m andtaking the value of transmission range as 10, 20, 30 and 40. There isa direct relation between the distances of the nodes from each otherand the grid size. As the grid size increases, the distance betweenthe nodes also increases which leads to the isolation of nodes fromeach other. If all the nodes are isolated from each other then all thealgorithms must produce the same number of clusters.

If we see Fig. 11, almost all the algorithms are producing the
same number of clusters because with grid size 400 m × 400 m andtransmission ranges up to 60 all the nodes are isolated. The networkof Fig. 11(d) is more dense than Fig. 11(a–c), so the MOPSO algo-rithm performs better than other algorithms. We can easily claim


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argwiautm

6

iFfn

o

Fig. 10. Number of clusters vs. network nodes in case of WCA, CLPSO, an

hat MOPSO is better than the other algorithms for our clusteringroblem.

.2.3. Number of clusters vs. grid sizeFig. 12 shows the relation between the number of clusters

nd the grid size by fixing the network nodes and transmissionange. As we can see the number of clusters increases as therid size increases due to increase of distance between nodes,hich isolate the nodes from each other. Fig. 12(a–d) shows that

ncrease in transmission range decreases the number of clusterst each grid size. The MOPSO decreases the number of clustersp to 30%, which leads to efficient clustering. Fig. 12 also showshat the MOPSO performs better in the case of dense environ-

ent.

.2.4. Number of clusters vs. displacementFig. 13 shows the different variations of network nodes and max-

mum displacement. The transmission range is kept constant as 30.ig. 13 shows that the number of cluster-heads is almost the same
or different values of displacement particularly for larger values ofumbers of nodes.
This is because, mobility of nodes just changes the configurationf clusters but the cluster size remains the same. Moreover, the pro-


posed MOPSO algorithm provides multiple solutions in each casethat shows its significance.

6.2.5. Energy consumptionIn our experiments, we use the radio model as discussed in Ref.

[20], which is the first order radio model. To run the transmitterand receiver circuitry, this model uses Eelec = 50 nJ/bit and for ampli-fier it uses Eamp = 100 pJ/bit/m2. These power levels are suitable forEb/No. The energy loss of the node is proportional to r2 (where ris distance between the transmitter and receiver nodes). Thus, totransmit a n-bit message the total energy consumed is calculatedas follows:

The energy required at receiver node = energy consumed incircuitry + energy consumed to transmit a n-bit message from trans-mitter to receiver

ET (n, d) = ETx(n, d) + ERx(n, d) (3)

where

E (n, d) = E × n + E × n × d2 (4)
Tx elec amp
and

ERx(n, d) = Eelec × n (5)


MOP

uat

a(o

ar3ionowct

fMit

Fig. 11. Number of clusters vs network nodes in case of WCA, CLPSO, and

If we see Eqs. (4) and (5), the total energy consumption dependspon the distance between the transmitter and the receiver nodess well as the number of operations required to transmit and receivehe massage.

To evaluate the performance, we vary the nodes from 30 to 60 inplay field of size 100 m × 100 m. The receiver is located at position

50, 110). We assume the program stops running when the numberf iterations is 150.

Fig. 14 shows the energy consumed in case of WCA, CLPSO,nd MOPSO when grid size is 100 m × 100 m and the transmissionange varies from 10 to 60 while fixing the number of nodes to0, 40, 50 and 60. The results show that as the transmission range

ncreases, energy consumption also increases because the numberf clusters decreases. The maximum energy consumed is when theumbers of clusters are equal to the numbers of nodes or there isnly one cluster. So we must find the optimum number of clusters,hich consume less energy to perform their functions. The energy

onsumed by the different algorithms is shown in the followingables.

Tables 2 and 3 show the total energy saving of the best algorithm
rom the 2nd best algorithm in percentage (%). Table 2 shows that
OPSO consumed less energy 10 out of 11 times and energy savings up to 13%. Table 3 shows that when the number of nodes are 40he MOPSO performs better 8 out of 11 times and the energy saving

SO in 400 m × 400 m area with transmission range varying from 10 to 40.

is up to 27%. So, we can easily say that MOPSO performs better thanthe other single-objective algorithms for clustering in an ad hocnetwork.

6.2.6. Load balance factorLoad balance factor is used to quantify how well a cluster-head

is balanced. In an ideal case every cluster-head must handle equalnumber of nodes, but it is very difficult to maintain a perfectlyload-balanced system at all times. The main reason is the frequentdetachment and attachment of neighbours from the cluster-heads.The cardinality of the cluster size represents the load of a cluster-head.

In Ref. [4], the LBF is defined as the inverse of the variance of thecardinality of the clusters. Thus,

LBF = nc∑

i(xi − �)2(6)

where nc is the number of cluster-heads, xi is the cardinality ofcluster i, and � = N − nc/nc is the average number of neighbours
of a cluster-head (being the total number of nodes in the system). Inthis equation it is clear that a higher value of LBF signifies a betterload distribution and it tends to infinity for a perfectly balancedsystem.


Fig. 12. Number of clusters vs. Grid size in case of WCA, CLPSO, and MOPSO when node = 40 and transmission range varying from 30 to 60.

Fig. 13. Number of clusters vs. displacement in case of WCA, CLPSO, and MOPSO in 100 m × 100 m area when nodes are 40 and 60 while transmission range is 30.


Fig. 14. Energy consumed in case of WCA, CLPSO, and MOPSO in case of 100 m × 100 m area and transmission range varying from 10 to 60 and number of nodes from 30 to60.

Table 2Energy consumed by different algorithms when nodes = 30.

Transmission Range Energy consumed by the network in (J)* Saving in energy consumption (%)

MOPSO CLPSO WCA ((high value − low value)/high value) × 100

10 0.0374 0.0379 0.0373 ((0.0374 − 0.0373)/0.0374) × 100 = 0.2715 0.0365 0.0373 0.0365 ((0.0365 − 0.0365)/0.0365) × 100 = 0.0020 0.0375 0.0385 0.0396 ((0.0385 − 0.0375)/0.0385) × 100 = 2.6025 0.0394 0.0407 0.0434 ((0.0407 − 0.0394)/0.0407) × 100 = 3.2030 0.0403 0.0408 0.0407 ((0.0407 − 0.0403)/0.0407) × 100 = 0.9835 0.0390 0.0421 0.0397 ((0.0397 − 0.0390)/0.0397) × 100 = 1.7640 0.0403 0.0445 0.0428 ((0.0428 − 0.0403)/0.0428) × 100 = 5.8445 0.0365 0.0447 0.0393 ((0.0393 − 0.0365)/0.0393) × 100 = 7.1250 0.0413 0.0435 0.0456 ((0.0435 − 0.0413)/0.0435) × 100 = 5.0655 0.0405 0.0445 0.0410 ((0.0410 − 0.0405)/0.0410) × 100 = 1.22

faa

60 0.0401 0.0471

* The unit of energy is Joule (J).

Eq. (6) is only suitable when we consider just the load balanceactor. But it fails when we want to optimize not only the LBF butlso the number of clusters at the same time. We illustrate this withn example.

Case 1:
Algorithms/objectives Algorithm 1 Algorithm 2
No. of clusters 5 5∑i(xi − �)2 2 3

0.0466 ((0.0466 − 0.0401)/0.0466) × 100 = 13.95

Case 2:Algorithms/objectives Algorithm 1 Algorithm 2

No. of clusters 5 8∑i(xi − �)2 3 3

In case 1, LBF1 = 5/2 = 2.5 and LBF2 = 5/3 = 1.67
So, in this case the algorithm 1 is better than the algorithm 2.
This solution fulfils our requirement because algorithm 1 is morebalanced than algorithm 2 although it has the same number ofsolutions.


Table 3Energy consumed by different algorithms when nodes = 40.

Transmission Range Energy consumed by the network in (J)* Saving in energy consumption (%)

MOPSO CLPSO WCA ((high value − low value)/high value) × 100

10 0.0560 0.0573 0.0564 ((0.0564 − 0.0560)/0.0564) × 100 = 0.7115 0.0560 0.0590 0.0568 ((0.0568 − 0.0560)/0.0568) × 100 = 1.4120 0.0590 0.0614 0.0576 ((0.0590 − 0.0576)/0.0590) × 100 = 2.3725 0.0595 0.0630 0.0606 ((0.0606 − 0.0595)/0.0606) × 100 = 1.8130 0.0556 0.0625 0.0632 ((0.0625 − 0.0556)/0.0625) × 100 = 11.0435 0.0553 0.0608 0.0569 ((0.0569 − 0.0553)/0.0569) × 100 = 2.8140 0.0581 0.0629 0.0569 ((0.0581 − 0.0569)/0.0581) × 100 = 2.0645 0.0648 0.0668 0.0663 ((0.0663 − 0.0648)/0.0663) × 100 = 2.2650 0.0571 0.0709 0.0743 ((0.0709 − 0.0571)/0.0709) × 100 = 19.4655 0.0750 0.0777 0.0742 ((0.0750 − 0.0742)/0.0750) × 100 = 1.0660 0.0537 0.0779 0.0741 ((0.0741 − 0.0537)/0.0741) × 100 = 27.53

* The unit of energy is Joule (J).

F 100 m3

Bit

wlL

L

Tbs

ram

C1b

ig. 15. Load Balance Factor in case of WCA, CLPSO, and MOPSO when grid size is0–40.

In case 2, LBF1 = 5/3 = 1.67 and LBF2 = 8/3 = 2.67This shows that the algorithm 2 is better than the algorithm 1.

ut actually the algorithm 1 is better than the algorithm 2, becauset has less number of clusters. So algorithm 1 is more optimizedhan algorithm 2.

The above discussion clearly shows that Eq. (3) is not suitablehen we want to optimize both the number of clusters and the

oad balance factor. To overcome this problem we modify Eq. (6) ofBF as:

BF = 1

nc ×∑

i(xi − �)2(7)

Now we calculate the LBF of above cases according to Eq. (7).In case 1, LBF1 = 1/(5 × 2) = 0.01 and LBF2 = 1/(5 × 3) = 0.067So, in this case the algorithm 1 is better than the algorithm 2.

his solution fulfils our requirement because algorithm 1 is morealanced than algorithm 2 although it has the same number ofolutions.

In case 2, LBF1 = 1/(5 × 3) = 0.067 and LBF2 = 1/(8 × 3) = 0.042This now shows that the algorithm 1 is better than the algo-

ithm 2, which confirms the desired results. It is clear from thebove results that Eq. (7) is more suitable than Eq. (6) in case ofulti-objective criteria optimization.
Load balance factor is shown in Fig. 15 in case of WCA,
LPSO, and MOPSO. The LBF is calculated when the grid size is00 m × 100 m, transmission range varying from 10 to 60, and num-er of nodes are 30 and 40. The MOPSO gives more balanced clusters

× 100 m and transmission range varying from 10 to 60 and number of nodes are

than the WCA and CLPSO as we increase the transmission range aswell as it gives a variety of solutions.

Both graphs show that MOPSO is more effective as the numberof neighbours reaches the threshold value and performs better thanWCA and CLPSO in terms of balancing the load in the network.

7. Conclusion and future work

In this paper, we have presented a multi-objective particleswarm optimization algorithm for energy-efficient clustering inmobile ad hoc networks (MANETs). One of the main constraints ofthese networks is the limited battery power. The major challengefor the researchers is to make these networks energy-efficient asmuch as possible. In the proposed approach we have used clus-tering for providing the energy-efficient solution. Moreover, theproposed approach has the ability to find out multiple optimalsolutions, which provides the flexibility of the solutions. The userscan choose a solution according to their needs. By minimizing thenumber of clusters we can reduce the routing cost of a packet. Italso makes the routing energy-efficient because less number ofnodes are involved for routing a packet. The evolutionary capa-bility of the algorithm allows it to search large search space. Italso has the advantage of dynamically adjusting objective func-tion values instead of specifying by the user. The simulation resultsshow that it is an effective and flexible approach. We compared the
results with two other well-known clustering algorithms, i.e., WCAand CLPSO-based clustering. The proposed MOPSO-based approachoutperforms these two algorithms in finding optimal number ofclusters as well as providing multiple options for the user.

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[applications in electric power systems, IEEE Transactions on Evolutionary Com-

928 H. Ali et al. / Applied Soft C

In future we will try to optimize the different parameters usedn the algorithm. Further, more objectives can be added in thelgorithm. We can also change our environment by making theumber of nodes dynamic. Another future direction is to use otherulti-objective evolutionary techniques and make a comprehen-

ive comparison among them.

cknowledgements

The authors thank the Higher Education Commission (HEC)akistan for supporting this work through the Indigenous PhD Fel-owship Program. The authors are also thankful to the anonymouseviewers for their valuable suggestions and feedback.

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