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Research ArticleCombinatorial Optimization-Based Clustering Algorithm forWireless Sensor Networks

Yuxiao Cao 1 and Zhen Wang 2

1School of Computer Engineering Nanjing Institute of Technology Nanjing Jiangsu 211167 China2School of Information Science and Technology Huizhou University Huizhou Guangdong 516007 China

Correspondence should be addressed to Zhen Wang wangzhenhzueducn

Received 16 October 2019 Revised 26 May 2020 Accepted 11 June 2020 Published 3 July 2020

Academic Editor Mariano Torrisi

Copyright copy 2020YuxiaoCao and ZhenWangis is an open access article distributed under theCreative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

As node energy of wireless sensor networks (WSN) is limited and cannot be supplemented after exhaustion clustering algorithmis frequently taken as an effective method to prolong the lifetime of WSN However the existing clustering algorithms have somedrawbacks either consuming excessive energy as a result of exchanging too much controlling information between nodes orlacking a comprehensive perspective in terms of the balance among several conflicting objectives In order to overcome theseshortcomings a novel combinatorial optimization-based clustering algorithm (COCA) for WSN is proposed in this paperDifferent from the above mentioned algorithms which take clustering as a continuous optimization problem COCA solves theclustering problem from the perspective of combinatorial optimization Firstly the clustering of WSN is abstracted into acombinatorial optimization problem en the binary particle coding scheme of cluster head is proposed which is based on thecorresponding relationship between nodes and particle position vectors and the fitness function is designed according to theparameters used in the process of cluster formation Finally the binary particle swarm optimization algorithm is applied toimplement the clustering COCA is validated under different scenarios compared with three other clustering algorithms esimulation results show that COCA has better performance than its comparable algorithms

1 Introduction

As a key part of the Internet of ings (IOT) [1 2] wirelesssensor network (WSN) has been widely utilized in manyfields such as industry agriculture military environmentalmonitoring transportation smart home and so on [3ndash8]WSN is composed of a large number of sensor nodes whichare deployed in the surveillance area Each sensor nodewith limited computing storage and communication ca-pabilities is usually powered by batteries In most cases it isdifficult to replace the batteries after node deploymentOnce the battery power is exhausted the sensor node willdie and the network lifetime will be over after a largenumber of nodes died To overcome the shortcomingsresearch on the schemes of saving node energy and pro-longing network lifetime becomes a key issue in the field ofWSN [9 10]

e clustering technology can reduce the energy con-sumption of nodes and prolong the lifetime of networks[11 12] A WSN network can be divided into several subsetswhich are called clusters by using the technology of clus-tering e nodes in the same cluster are adjacent to eachother geographically In each cluster one node is selected asthe cluster head (CH) and other nodes act as themembers ofthe cluster Instead of communicating with the base station(BS) directly the members send their sensed data to the CHsin which the data is aggregated and sent to the BS [13 14]e earliest proposed WSN clustering algorithm is low-energy adaptive clustering hierarchy (LEACH) [15] Com-pared with the previous planar routing algorithms LEACHcan make the network lifetime longer [16 17] HoweverLEACH selects the CHs only according to the result of thecomparison of a random number generated by the node anda predefined fixed threshold which makes the number of

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 6139704 13 pageshttpsdoiorg10115520206139704

clusters and the election of CHs very random LEACH doesnot guarantee the best clustering scheme from the point ofview of the energy balance of the whole network

Since the emergence of LEACH a lot of WSN clusteringalgorithms have been proposed ere are several kinds ofclustering algorithms based on different clustering criteriasuch as network structure communication model topologyand reliable routing In this paper we classify clusteringalgorithms into two categories ie independent and co-operative according to whether the BS participates in theprocess of clustering Independent clustering algorithms runon network nodes without the BSrsquos participation andcontrol information is exchanged among nodes Indepen-dent clustering algorithms include HEED [18] PEGASIS[19] EECS [20] EEMC [21] TEEN [22] ECO-LEACH [23]NR-LEACH [24] and ECCR [25] etc In cooperative al-gorithms the BS participates in the process of clustering andall or part work of clustering is done by the BS A smallamount of control information is exchanged between the BSand network nodes e cooperative algorithms includeLEACH-C [26] PDOPR [27] UC-GA and KC-GA [28]PSO-ECHS [33] approaches in [34ndash36] etc e above-mentioned two kinds of clustering algorithms both prolongthe lifetime of the network to some extent but there are stillsome shortcomings in terms of the working mechanismIndependent algorithms run on each node and a largeamount of control information needs to be exchangedamong nodes which leads to additional energy consump-tion Although the cooperative algorithms reduce the energyconsumption of control information exchange they stillcannot get the best clustering result from the perspective ofthe whole network because there are multiple parametersaffecting the clustering and these parameters are mutuallyconflicting In particular with the development of evolvednature inspired algorithms some clustering approachesemploy them to improve clustering performance in recentyears [33ndash36]

To reduce the node energy consumption and prolongthe network lifetime we propose a combinatorial opti-mization-based clustering algorithm (COCA) which runson the BS for WSN from the point view of combinatorialoptimization in this paper We abstract WSN clusteringinto a combinatorial optimization problem and employbinary particle swarm optimization (BPSO) algorithm tosolve it In [33ndash36] continuous particle swarm optimi-zation (PSO) is employed for WSN clustering the positioncomponent of the particle is a real number in a certaininterval and the corresponding relationship betweenparticle position and CHs is established by using atransforming formula In contrast COCA applies binaryPSO for clustering in which the position component of theparticle is either 0 or 1 in binary space FurthermoreCOCA directly determined that whether the node is a CHbased on the value of the particle position component ifthe value is 1 the node corresponding to the component iselected as a CH contrastively if the component value is 0the corresponding node is selected as a member of acluster

e main contributions of this paper are as follows

(1) Based on the objective and procedure the clusteringof WSN is abstracted into a combinatorial optimi-zation problem

(2) A novel binary particle coding scheme is designed topresent the selection of CHs

(3) After the CHs are elected the constraints betweenparameters which affect clustering are consideredcomprehensively en the fitness function isdesigned and the clustering process is implementedby using BPSO

As the main innovation and contribution COCA es-tablishes a direct correspondence relationship between thebinary value of particle components and the role of whethernodes act as a CH After determining how to use binarycoding to represent whether a node is a CH COCA can beimplemented not only by using BPSO but also by applyingother swarm intelligence algorithms discrete version Be-cause BPSO has the advantages of a few parameters simpleimplementation and fast convergence we employ BPSO tosolve the WSN clustering problem based on combinatorialoptimization

e rest of this paper is organized as follows In Section2 related works are discussed In Section 3 the concept ofcombinatorial optimization and BPSO is presented firstlythen the network and energy consumption model of WSNare introduced Section 4 describes the proposed algorithmCOCA in detail In Section 5 the simulation results areshown to demonstrate the effectiveness of COCA Finallyconclusions are drawn in Section 6

2 Related Work

In order to elaborate the principle of COCA clearly theclassical LEACH and other representative WSN clusteringalgorithms proposed in recent years are summarized brieflyas follows

In LEACH [15] the lifespan of WSN is divided into anumber of periods called rounds Each round consists of twophases cluster setup phase and stable phase In the clustersetup phase each node generates a random number r in theinterval [0 1] and compares r with a threshold T(n) ecalculation of T(n) is shown in the following equation

T(n)

p

1 minus p rmodpminus1( 1113857 n isin G

0

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)

where p represents the percentage of CHs in the network r

stands for the number of the current round n denotes asensor node and G is the set of nodes that never acted as CHin the last pminus1 rounds

If r is less than T(n) the node will take the role of CHOtherwise it will be a member node After being electedeach CH broadcasts its own packet information to thenetwork When other nodes receive the broadcast infor-mation from CHs they decide to join a cluster according tothe received signal strength Subsequently the member node

2 Mathematical Problems in Engineering

sends the request packet to the CH to which they belong Ifthe request is agreed by the CH the time division multipleaddress (TDMA) slice is allocated to the member node toprevent communication conflicts between nodes in the samecluster After the clustering is completed the stable phasebegins In the stable phase the member node sends thesensed data to its CH and the CH aggregates the receiveddata and transmits them to the BS e core idea of LEACHis to select different nodes as CHs in a random way so thatthe energy consumption can be spread over different nodesas much as possible to prolong the network lifetimeHowever LEACH uses a random algorithm to select CHwithout considering the residual energy of nodes In theprocess of clustering LEACH only takes the distance be-tween member nodes and CH into account and does notconsider the size of clusters and the distance between CHsand the BS Consequently some CHs will die early becauseof overload which reduces the networkrsquos lifetime

In [24] a node ranked-LEACH (NR-LEACH) for WSNwas presented by Al-Baz and Sayed In NR-LEACH theclustering is divided into two stages cluster setup and stablecommunication Node rank (NR) algorithm is used to selectthe CHs in the setup stage e NR algorithm calculates therank of each node through a number of iterations based onthe received signal strength residual energy and the numberof connections with other nodes After all nodes calculatedthe rank the node that has the highest rank is selected as theCH NR-LEACH considers the influence of more than onefactor on clustering when CHs are selected However whenmember nodes choose different clusters to join NR-LEACHdoes not consider the influence of different attributes ofmember nodes on clustering

In [25] Hosen and Cho proposed an energy centriccluster-based routing protocol for WSN (ECCR) ECCRdivides the whole network into several static grids and allnodes in each grid constitute a cluster Each node calculatesits rank according to the residual energy and the averagedistance to other nodes in the cluster In the first round eachnode broadcasts its rank value and residual energy infor-mation to other nodes in the same cluster e node whichhas the largest rank value is elected as the CH If the rank ofsome nodes is equal to the rank of other nodes the node withthe largest residual energy is selected as the CH From thesecond round the CH of the current round selects the nodewith the largest rank as the CH of the next round In theclustering procedure the residual energy of nodes and theaverage distance to other nodes are taken into accountwhich makes the lifetime of the selected CHs longerHowever the nodes number and membership of clustersremains unchanged throughout the whole lifetime of thenetwork which will lead to the premature death of someclusters and affect the overall performance of the network

In [29] Hai et al put forward a novel fuzzy clusteringscheme for 3D WSN called FCM-3 WSN In FCM-3 WSNfirstly the authors established a mathematical model ofclustering in 3DWSN which takes into account the networkenergy consumption communication constraints and thecharacteristics of the 3D network en the Lagrangemultiplier method is utilized to calculate the cluster centers

and the membership matrix of the model which is used tocluster the network

In [30] Shen et al proposed a new energy efficientcentroid-based routing protocol (EECRP) for WSN InEECRP the conception of ldquoenergy centroidrdquo is introducedAt the beginning of clustering all nodes send their locationand energy information directly to the BS e BS calculatesthe average energy and the maximum communicationdistance of the whole network en according to the givenproportion some nodes are randomly selected as CHs andCHsrsquo ID are sent back to the network On the basis of in-formation from the BS all nodes know who is CH in thenetworke remaining nodes join a cluster whose CH is thenearest to them At the end of each round the CH calculatesthe energy centroid of the cluster and selects the membernode whose distance is the closest to the energy centroid andthe remaining energy is above the average energy of thecluster as the CH of the next round e EECRP utilizes theposition changing of the energy centroid to balance theenergy consumption of nodes in a cluster and prolongs thelifetime of the network However the nodes (including theCH and cluster members) of a cluster remain unchangedthroughout the whole network lifetime When the CH isrotated some nodes will probably die prematurely becausethe energy consumption of nodes in different clusters cannotbe balanced while it is balanced in a single cluster

In [31] Zhang et al presented an improved LEACHalgorithm for WSN to optimize the election of CH In theinitialization stage the BS broadcasts the initializationmessage to the whole network After receiving the initiali-zation message all nodes estimate the distance fromthemselves to the BS according to the received signalstrength and then save the information of adjacent nodes ina table In the setup phase the nodes located in the com-munication radius of the BS communicate with the BS di-rectly while others are clustered for effective datatransmission When the CH is being elected the formulawhich is used to calculate the threshold in the originalLEACH is modified to make the residual energy of nodesthe average energy of networks the distance between nodesand the BS play an important role in the calculation of thethreshold In the stable phase of clustering single-hop andmulti-hop communication are both utilized to transmit datafrom CHs to the BS If the distance between a CH and the BSexceeds the communication radius the CH chooses anotherCH which is closer to the BS as the relay node Although theimproved LEACH considers the energy and distance of thenode it still relies on a completely random mechanism toselect the CH It is not guaranteed to select the most suitablenode as the CH from more than one node that meets thequalification

In [32] a new energy efficient multihop routing tech-nique (MR) is put forward by Alnawafa and Marghescu InMR nodes are divided into three categories CHs membernodes and independent nodes (IN) INs are the nodes thatcommunicate directly with the BS without joining anycluster e round of MR is composed of four phases initialannouncement tables preparation and routing In the initialphase the clustering process is completed In tables

Mathematical Problems in Engineering 3

preparation phase member nodes calculate their level basedon the distance to corresponding CHs and the CHs judgetheir level according to their distance to the BS Each clustermember that is located at the second level CHs and INswhich are located at the second or more level establish theirown routing table respectively In the routing phasemember nodes in the second level communicate with CHand CHs communicate with the BS according to theirrouting table respectively In MR an accurate routingmechanism is proposed which greatly reduces the energyconsumption of sensed data transmission However MRalgorithm does not consider the size of the cluster area andthe distance from the CHs to the BS and MR sets thenumber of members the same in different clusters so thatthe energy consumption of different clusters is unbalancedand some nodes are prone to die prematurely

In [33] Rao et al proposed a PSO-based energy efficientcluster head selection algorithm for WSN (PSO-ECHS) InPSO-ECHS the following parameters are taken into ac-count the distance from the nodes to the CH the distancefrom the CHs to the sink and the influence of the residualenergy on the clustering performance and a linear com-bination of these parameters are used as the fitness functionof particles Furthermore PSO-ECHS takes the coordinatesof the candidate CH as the position vector of the particlesHowever after updating the position of the particles theposition component cannot correspond to the coordinatesof the nodes precisely erefore PSO-ECHS selects thenode which is the nearest to the position component of aparticle which has the global optimal value as the CH isapproximate approach cannot enable the final clusteringscheme to the optimal

In [34] Azharuddin and Jana presented a PSO-basedapproach for energy-efficient and energy-balanced routingand clustering inWSN In the routing algorithm the authorsbuild a tradeoff between energy efficiency and energy bal-ance In the clustering algorithm the energy consumption ofCHs and cluster member nodes are both taken into accountWhen applying PSO to cluster the WSN the coding schemeof particles is as follows the dimension of particles is thesame as the number of network nodes and the positioncomponent of each dimension of particles is a randomnumber r which obeys the uniform distribution in the in-terval (0 1] An integer k is obtained from r through atransformation formula and k is taken as the ID of a CH towhich the node corresponding to the particle positioncomponent belongs In addition a fitness function isdesigned to minimize the energy consumption of datatransmission and balance the residual energy in the trans-mission path

In [35] Kuila and Jana put forward energy efficientclustering and routing algorithms for wireless sensornetworks particle swarm optimization approach In thisapproach the particle encoding scheme for clustering isthe same as that of [34] but the objective of the fitnessfunction is to make the CH have the longest life and thecluster members have the shortest average distance to theCH

In [36] Wang et al suggested an improved routingscheme with special clustering using the PSO algorithmfor heterogeneous WSN (EC-PSO) In the first stage ofEC-PSO CHs are elected according to geographical lo-cation When the network is running for a period and theenergy of nodes is not equal to each other EC-PSO isapplied to cluster the WSN again EC-PSO employs PSOto find the energy center of the network and the node nearthe energy center is selected as the CH In addition EC-PSO uses a protection mechanism to prevent low-energynodes from becoming CHs In EC-PSO the encodingscheme of the particle is that the dimension of the particleis equal to the number of CHs and the position com-ponent of particles is a 2-tuple which contains the co-ordinates of the energy center During the iteration thenode that is the nearest to the energy center is elected asthe CH e particle position components in EC-PSO arealso continuous real numbers

3 Preliminaries and System Model

A lot of algorithms are proposed to solve combinatorialoptimization problems [37] such as simulated anneal-ing tabu search greedy randomized adaptive searchprocedure (GRASP) variable neighborhood search(VNS) and BPSO [39] As BPSO has the characteristicsof a few parameters quick convergence and easy toimplement we employ BPSO to cluster the WSN In thissection a brief introduction to combinatorial optimi-zation and BPSO is given firstly and then the networkmodel and energy consumption model of WSN aredescribed

31 Overview of Combinatorial Optimization Many prob-lems in engineering can be transformed into optimizationproblemse so-called optimization problem is to select thebest one among a plurality of sets of variables to meet aparticular need Combinatorial optimization is a branch ofoptimization algorithms which is devoted to discovering theoptimal grouping order or arrangement of discrete eventswith mathematical methods

32 Overview of Binary Particle Swarm Optimization AsBPSO is developed from continuous PSO therefore a brieflook at PSO and BPSO is taken respectively as follows PSO[38] is a swarm intelligence algorithm that simulates theforaging behavior of birds For PSO a potential solution toan optimization problem is represented by a particle and thenumber of particles is called population size Each particlehas a position vector Xk

i (Xki1 Xk

i2 XkiN) and a velocity

vector Vki (Vk

i1 Vki2 Vk

iN) in D-dimensional space Inthe D-dimensional space the particles fly to the individualextreme points they have experienced and the global extremepoints that the whole population has experienced and theoptimal solution of the optimization problem is obtained inthis way

When particles fly in a D-dimensional space the d-thdimensional position and velocity vector of the i-th particle


in the k-th iteration can be expressed by using the followingequations respectively

Xkid X

kminus1id + V

kid (2)

Vkid wV

kminus1id + c1r1 PBid minus X

kminus1id1113872 1113873 + c2r2 GBid minus X

kminus1id1113872 1113873 (3)

where w is the inertia factor which is utilized to keep thebalance between the optimal personal and optimal globalfunction value c1 and c2 indicate learning factors which areapplied to represent the summary of the experience of in-dividual particle and whole population r1 and r2 are tworandom numbers between 0 and 1 and PB and GB are theoptimal personal and optimal global fitness function valuerespectively

Continuous PSO is usually used to solve continuousoptimization problems However some problems are finallyabstracted as a combinatorial optimization one HenceKennedy and Eberhart proposed BPSO in 1997 For BPSOthe continuous vector of particle position in continuous PSOis replaced by a discrete vector whose component is either 0or 1 in binary space For BPSO the particle velocity vectorupdating formula is the same as that of the continuous PSOas shown in equation (3) However the position vector isupdated as follows

Xkid

1 r(0 1)lt S Vkid( 1113857

0 otherwise

⎧⎨

⎩ (4)

where S is calculated by using the following equation

S Vkid1113872 1113873

11 + eminusVk

id

(5)

In equation (5) the S function is the commonly usedfuzzy function in neural networks which is called Sigmoid

For BPSO the probability that a particle is set to 0 or 1 isas follows

P Xkid 11113960 1113961 S V

kid1113960 1113961 (6)

33NetworkModel We assume the network model of WSNused in this paper has the following properties

(1) e nodes are randomly deployed in a square area ofLlowast L e initial energy of nodes is equal to eachother and the nodes cannot move after deployment

(2) e BS is located at the center of one edge of theWSN area with infinite energy e BS knows thelocation and initial energy of nodes COCA runs onthe BS

(3) e BS can calculate the residual energy of thenetwork node according to the number of the datapackets sent by the node

(4) e member nodes of a cluster can adjust theirtransmission power according to their distance to theCH

(5) After a cluster is constructed the CH uses TDMA toallocate time slots to member nodes for transmittingdata

(6) Single-hop communication is utilized

34 Energy Consumption Model To calculate the energyconsumption of a single node as well as the whole networkwe make use of the energy consumption model in [15] eenergy consumption of a node sending l bits is as follows

ETx(l d) llowastEElec + llowast εfs lowast d2 dlt d0( 1113857

llowastEElec + llowast εmp lowastd4 d ge d0( 1113857

⎧⎨

⎩ (7)

where l is the number of bytes sent by a node (CH ormember) d denotes the distance of data transmission EElecindicates the energy consumed by the sensor circuit toprocess one-bit data εfs represents the energy consumptioncoefficient of the wireless channel in free space transmissionmodel εmp stands for the energy consumption coefficient ofthe wireless channel in multipath attenuation transmissionmodel and d0 is a threshold which is expressed as follows

d0

εfsεmp

1113971

(8)

e energy consumption of a node (CH or member)receiving l bits is expressed in the following equation

ERx(l) llowastEElec (9)

where EElec is the energy consumed by the sensor circuit toprocess one-bit data

4 Combinatorial Optimization-BasedClustering Algorithm

In this section COCA is described in detail Firstly themathematical model of clustering is established and clus-tering is abstracted into a combinatorial optimizationproblem en the binary coding scheme of particles ispresented and the fitness function is designed Finally theimplementation procedure of COCA is described in detail

41 Mathematical Model of Clustering e following issuesneed to be settled when aWSN is clustered (1) selecting CHsfrom all nodes and (2) member nodes joining differentclusters e purpose of clustering WSN is to reduce theenergy consumption of a single node and to balance theenergy consumption of different nodes so as to prolong thelifetime of the whole network as much as possible Here weanalyze the clustering problem from the perspective ofcombinatorial optimization

Let there be N nodes in a WSN that are divided into Kclusters ere are Mi( 1 le i leK) members in the i-thcluster e number of CHs and the number of members ineach cluster should satisfy the following constraints


1 leMi leN + 2 minus 2K ( 1 le i leK)

1113944

K

i1Mi + K N

⎧⎪⎪⎨

⎪⎪⎩(10)

According to equation (10) the total number of allpossible clustering schemes is as follows

NUM CKNC

M1NminusKC

M2NminusKminusM1minus1 C

MK

NminusKminusM1minusM2minusminusMKminus1minusK+1

(11)

where CKN denotes K combinations of N elements and

Mi (1le i leK) is the number of members of the i-th clusterand should satisfy the constraint in equation (10)

Clustering WSN means that under the constraintexpressed by equation (10) one approximately optimalscheme S is selected from the NUM schemes expressed byequation (11) For the selected scheme S the objectivefunction expressed by the following equation should beminimized

f w1f1 + w2f2 + w3f3 + w4f4 (12)

In equation (12) the subobjective function f1 rep-resents the sum of the energy consumed by all membernodes in all clusters during the whole network lifetime f2denotes the sum of the standard deviations of energyconsumed by all members of all clusters f3 stands for thesum of the energy consumed by all CHs f4 is the sum ofthe standard deviations of the energy consumed by allCHs and w1 w2 w3 w4 are the weights of each sub-objective function and they should satisfy the followingconstraints

w1 + w2 + w3 + w4 1 wi gt 0 1 le ile 4( 1113857 (13)

At different stages of network operation for differentnetwork topologies the four weights could be dynamicallychanged based upon equation (13) In this paper in order toquickly verify our approach ie combinatorial optimizationbased clustering the value of w1 w2 w3 w4 in differentsituations are all taken as 025 for simplicity

From the above analysis it can be drawn that clusteringWSN actually can be regarded as a combinatorial optimi-zation problem

42 Particle Coding If PSO is applied to pursue the bestsolution the first step is to encode the particles WhenCOCA is utilized to cluster the WSN the nodes in thenetwork are either CHs or member nodes and there is noother possibility For BPSO a particle represents a possiblesolution to the optimization problem e component valueof each dimension of the particle is either 0 or 1 and no thirdvalue exists erefore a correspondence between theparticle component value of each dimension and the CHselection can be established If the component of a di-mension of the particle takes a value of 1 the node corre-sponding to the dimension is selected as a CH Otherwise ifthe value is 0 the corresponding node acts as a cluster

member e coding scheme of particles is as follows indetail

Let there be a total of N nodes in the network which aredivided into K clusters e population size of particles isMe dimension of each particle and the number of nodes inthe network are both set to be N and the position vector ofthe ith (1le ileM) particle is (Xi1 Xi2 XiN) IfXij 1(1 le j leN) the jth( 1 le jleN) node in the networkis selected as a CH if Xij 0(1 le jleN) the jth( 1 le jleN)

node is treated as a member node For example for a WSNnetwork with 10 nodes if the position vector of a particle is(0 0 1 0 0 0 1 0 1 0) it means that the third seventh andninth nodes are elected as CHs and the remaining nodes areused as member nodes For BPSO the velocity vector of thei-th (1le ileM) particle is Vi (Vi1 Vi2 ViN) and theupdating formula of the velocity vector of the particle is thesame as that of continuous PSO presented in equation (3)

43 Fitness Function Design e second step of applyingBPSO is to design a fitness function e purpose of clus-tering is to reduce the node energy consumption andprolong the network lifetime e goal of COCA is to (1)minimize and balance the energy consumption of nodes in acluster and (2) minimize and balance the energy con-sumption of all CHs To achieve the goal of clustering weutilize the fitness function expressed in equation (12) inSection 41

e definition of function f1 in equation (12) is given asfollows

f1 1113944K

i11113944

Mi

j1εda

iHminusij

1113944

K

i11113944

Mi

j1εfsd

2iHminusij diHminusij lt d01113872 1113873

1113944

K

i11113944

Mi

j1εmpd

4iHminusij ddiHminusij ge d01113872 1113873

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)

where diHminusij is the distance from the j-th member to the CHin the i-th clusterMi indicates the number of member nodesin the i-th cluster and K is the number of clusters emeaning and value of εfs and εmp are the same as that inequation (7) and if diHminusij is less than the threshold d0 theexponent a equals 2 otherwise 4 It can be seen fromequations (7) and (14) that the value of f1 is proportional toand can be used to describe the energy consumption of allmember nodes in all clusterse smaller the value of f1 thesmaller the member nodes energy consumption

e definition of function f2 is as follows

f2 1113944K

i1

1Mi

1113944

Mi

j1diHminus ij minus di1113872 1113873

2

11139741113972

(15)

where diHminusij is the distance from the j-th member node tothe CH in the i-th cluster Mi denotes the number ofmember nodes in the i-th cluster and di is the averagedistance from all member nodes to their CH in the i-thcluster and can be expressed as follows


di 1

Mi

1113944

Mi

j1dj (16)

where dj means the distance from the j-th member to theCH e function f2 represents the sum of mean squareerror (MSE) of the distance from all members to their CHe smaller the value of f2 the closer the distance from themembers to the CH so that the energy consumption ofmember nodes is balanced

e definition of the function f3 is as follows

f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd

2BSminusiH dBSminusiH lt d0( 1113857

1113944

K

i1εmpd

4BSminusiH dBSminusiH ge d0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)

where dBSminusiH denotes the distance from the i-th CH to theBS the values of εfs and εmp are the same as those inequations (7) and (14) It can be seen from equation (17) thatthe value of f3 is proportional to the energy consumption ofall CHs e smaller is the value of f3 the less is the energyconsumption of all CHs


f4

1K

dBSminus iH minus d1113872 11138732

1113970

(18)

where K is the number of clusters dBSminusiH stands for thedistance from the i-th CH to the BS and d is expressed asfollows

d 1K

1113944

K

i1di (19)

where di is the distance from the ith CH to the BS e valueof the function f4 is the sum of the MSE of the distancebetween all CHs and the BS e smaller the value of f4 isthe closer the distance between different CHs and the BS isso that the remaining energy of CHs is basically balanced inthe process of network operation

It can be seen from the definitions of ff1f2f3 and f4that if f has the minimum value it means that the CH andthe member nodes in the network consume the least amountof energy and the energy consumption is also balanced atthe same time

44 Procedure of COCA Similar to most clustering algo-rithms COCA is also divided into two phases setup phaseand stable phase e process of the COCA setup phase isexpressed as Algorithm 1 and 2

At the beginning of the clustering the parameters ofWSN and BPSO are initialized respectively e parametersof WSN include the size of the area where the network islocated the location of nodes and the BS the initial energy ofnodes the proportion of CHs etc e parameters of BPSOinclude population size individual learning factor globallearning factor and inertia factor

After parameters initialization the velocity vector ofeach particle is initialized by using equation (3) and theposition vector of each particle is initialized by usingequations (4) and (5) According to the particle encodingscheme proposed in Section 42 the node corresponding toeach particle position component with value 1 acts as theCH After the CH is elected the BS calculates the distancebetween each member node and all CHs and makes thenode join the cluster in which the nearest CH is located

After the initial clustering the individual optimal valueof each particle is calculated with equations (12)ndash(19) andthe minimum individual optimal value of all particles istreated as the global optimal value of the whole populationus the initialization of the particle swarm is completed

During the iteration process the velocity and positionvectors of all particles are updated according to equations(3)ndash(6) e individual optimum value of each particle and theglobal optimum value of the whole population are calculatedafter the velocity and position update is completed

When the number of iteration reaches the pre-determined value the CH selection scheme correspondingto the particle which has the global optimal value is selectedas the final clustering scheme After the completion ofclustering the ID of CHs cluster members and clusters isbroadcasted to the whole network so that each node knowsits clustering information After clustering the CH assignseach member a TDMA slot and broadcasts it to the cluster

It can be seen from the clustering process that COCAhas anadvantage over other clustering algorithms in terms of the se-lection of CH On the basis of the binary particle coding schemeCOCA keeps iterating to obtain the optimal clustering schemeby taking advantage of BPSO evolutionary optimization

5 Algorithm Performance Evaluation

In order to verify the performance of COCA we simulatedCOCA using Matlab 2016a and compared the simulationresults with three other clustering algorithms ie LEACHECCR and PSO-ECHS e simulation results showed thatCOCA has better performance than other algorithms interms of network lifetime average residual energy of nodesand network throughput e reason for choosing LEACHas the comparison algorithm is that LEACH as the firsthierarchical clustering algorithm has been widely used as abenchmark to evaluate the performance of other algorithmse other two algorithms are chosen for comparison becauseECCR and PSO-ECHS are the representatives of indepen-dent and cooperative algorithms respectively

51 Simulation Parameters and Evaluation Metrics In thesimulation the nodes are randomly distributed in a squarearea and the nodes do not move after deployment e BS islocated in the center of the edge of the network area and thepercentage of CHs is 10 A randomly generated networkstructure is shown in Figure 1 In the simulation the totalnumber of nodes in the network varies from100 to 300 and theinitial energy of each node is equal to each other e specificnetwork parameters are listed in Table 1 and the BPSO


parameters are listed in Table 2 For Table 1 the parametersnetwork size BS coordinates control packet size datapacket size and data packet number per round are definedby us 10 as the percentage of CHs is the best valueobtained through many experiments and other parameterson energy are the same as parameters in [15 24 25 29ndash36]For Table 2 the number of the parameters of particles andthe number of iterations are defined by us and otherparameters are the optimal values obtained through manyexperiments

In order to evaluate the performance of different clus-tering algorithms the metrics are as follows the number oflive nodes in the network the total residual energy of thenetwork and the number of packets received by the BS

52 Network Lifetime Network lifetime is the most im-portant metrics to measure the performance of clusteringalgorithms In this paper the network lifetime is defined asthe number of rounds when all nodes are dead ie all nodes

CH Cluster headPB Personal best valueGB Global best valueFFV Fitness function valueInitialize WSN and BPSO parametersInitialize every particlersquos position and velocity vectorSet PB and GB to infinityfor each (particle)Clustering

end forwhile iteration numberltMax numberfor each (particle)

Update position vectorUpdate velocity vectorClustering

end forend whilee last result is the clustering scheme corresponding to GB

ALGORITHM 1 COCA process

CH Cluster headPB Personal best valueGB Global best valueFFV Fitness function valueUpdate velocity vectorif random numberlt value of Sigmoid functionNode is elected as CH

elseNode acts as member

end ifUpdate position vectorfor each (member node)Calculate distance to every CHJoin the nearest CHrsquos cluster

end forCalculate FFVif FFVltPB thenPB⟵ FFV

end ifif PBltGB thenGB⟵ PB

end ifGet best position vector according to GB

ALGORITHM 2 Clustering process


exhausted their energy Figure 2 depicts the number ofrounds of four algorithms when the last node died in threescenarios Figures 3ndash5 shows the relationship between thenumber of living nodes and the number of rounds of

0 20

Red circle BS black circle member nodes

40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200

Figure 1 Network nodes deployment

Table 1 Network parameters

Parameters ValuesNetwork size (m) 200lowast 200BS coordinates (100 200)Nodes number 100ndash300e percentage of CHs 10Initial energy (J) 05EElec 50 nJbitεfs 10 pJbitm2

εmp 00013 pJbitm4

Control packet size (bits) 200Data packet size (bits) 6400Data packet number per round 10

Table 2 BPSO parameters

Parameters ValuesNumber of particles 20Number of iterations 200w 08c1 2c2 2r1 Random number in [0 1]r2 Random number in [0 1]

530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000

100 nodes 200 nodes 300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS

Figure 2 e lifetime of four algorithms versus different nodenumbers

0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS

Figure 3 Alive nodes number versus the rounds number (totalnumber of nodes is 100)

0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS



COCA LEACH ECCR and PSO-ECHS It can be seen fromFigure 2 that with increasing the number of rounds nodesbegin to die in four algorithms (when the remaining energyof one node is 0 the node is considered dead) However thefirst dead node in COCA appears later than the other threealgorithms and COCA has the most alive nodes when thenumber of rounds is equal In four algorithms LEACH hasthe earliest dead node However COCA has the latest deadnode In the same network environment LEACH has theshortest lifetime and COCA has the longest lifespan elifetime of the other two algorithms is between the lifetime ofCOCA and LEACH

Figures 6ndash8 reveal the number of rounds when the firsthalf and last node of the four clustering algorithms die inthree scenarios It can be seen from Figures 6ndash8 that thenumber of rounds of the first half and last nodes of COCAis later than that of the other three comparison algorithmsand the trend of node death of COCA is more gradual ereason that COCA has a longer lifetime is that clustermembers and CHs of COCA consume less energy than theother three algorithms during data transmission

53 Residual Energy Nodes need to consume energy forsensing and transmitting data e more is the residual energyof the whole network the longer is the lifetime ereforeclustering algorithms should minimize the energy consump-tion of the entire network Figures 9ndash11 show the relationshipbetween the total residual energy and the number of rounds ofthe four algorithms in three scenarios From Figures 9ndash11 itcan be seen that with the increase in the number of rounds thetotal residual energy of the four algorithms is all decreasingHowever the residual energy of COCA is decreasing slowerthan the other three algorithms and the trend of energy re-duction of COCA is gentle than the compared algorithms Ascan be seen from Figures 9ndash11 LEACH has the fastest energyconsumption rate COCA has the slowest rate and the othertwo algorithms energy consumption rate is in the middle ereason why COCA consumes the least energy is that whenCOCA selects the CHs and cluster members it comprehen-sively considers the influence of several factors that restrict eachother on the cluster formation

0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS

The round number of the first node dead

Figure 6 e round number of the first node dead versus differentnode numbers

134173

282

43 51 764985

181

85 98

242

0

100

200

300

100 nodes 200 nodes 300 nodesN

umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS

The round number of half nodes dead

Figure 7 e round number of half nodes dead versus differentnode numbers

530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes

e round number of all nodes dead

300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS

Figure 8 e round number of all nodes dead versus differentnode numbers

0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

Figure 9 Total nodes residual energy versus the rounds number(total number of nodes is 100)


54 Network roughput Two metrics are considered toevaluate network throughput ie the number of packetsreceived by the BS and the number of packets received by allCHs Obviously the more data packets received by the BSthe better the performance of the clustering algorithm

Figure 12 shows the total number of packets received byall CHs using four algorithms in three network scenariosFigure 13 depicts the total number of packets received bythe BS of the four algorithms in three network scenariosFigure 14 displays the sum of data packets received by the BSand all CHs of four algorithms in three network scenarios Itcan be seen from Figures 12ndash14 that in all scenarios COCAalgorithm receives the most data packets in terms of whetherthe BS or CHs which shows that COCA has the mostnetwork throughput

From the above description we can conclude that COCAhas excellent performance than the other three algorithms interms of network lifetime residual energy and throughput

6 Conclusion

To save the nodes energy and prolong the network lifetime aclustering algorithm based on combinatorial optimizationfor WSN ie COCA is proposed in this paper From thepoint of view of combinatorial optimization COCA ab-stracts the selection of CHs and the formation of clustersinto a combinatorial optimization problem Due to the largescale of feasible solutions of the combinatorial optimizationproblem an approximation algorithm is generally adoptedto solve such a problem erefore the BPSO which has afew parameters and is easy to implement is utilized tocluster theWSN In order to apply BPSO to cluster theWSNa novel particle binary coding scheme for selecting CHs isproposed For the coding scheme the dimension of particlesis equal to the number of nodes in the network If theposition component of particles in a certain dimension is 1the node corresponding to this dimension is selected as CHIf the position component of particles in a dimension is 0the node corresponding to this dimension is regarded as acluster member After the CH is elected the fitness functionis designed according to the principle that the energyconsumption of the whole network is minimum and bal-anced After a number of iterations the WSN clustering isimplemented by BPSO Because the fitness function takesinto account the influence of different factors on clustering

100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes

e number of data packets received by all CHs

300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS

Figure 12 e number of data packets received by all CHs versusdifferent node numbers (unit of the packet number is 1000)

114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes

The number of data packets received by the BS

300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS

Figure 13 e number of data packets received by the BSversus different node numbers (unit of the packet number is1000)

259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS

Figure 14 e throughput versus different node numbers (unit ofthe packet number is 1000)


performance and the constraints between these factors itensures that the clustering result is optimal

Experiments showed that compared with existingclustering algorithms COCA has the best performance interms of network lifetime residual energy of nodes and thenetwork throughput COCA extended the lifetime of thenetwork greatly and caused the death of the first node half ofthe nodes and all nodes to be significantly delayed It can beseen from the experiments that COCA makes the BS receivemore data from the member nodes

However COCA still has some shortcomings to over-come COCA uses single-hop communication rather thanmulti-hop communication When the network size is largethe distance between the node and the CH as well as thedistance from the CHs to the BS is far Compared withmulti-hop communication single-hop communicationconsumes more energy which leads to the premature ex-haustion of energy and the death of CHs In addition thefour coefficients of fitness function need to be adjustedaccording to the changes of the networkerefore in futureresearch we will try to change single-hop communication tomulti-hop communication to reduce the energy consump-tion of data transmission And we need to dynamicallyadjust the coefficients of fitness function according to theoperation of the network to obtain a more accurate clus-tering result

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported in part by the Research Fund of theNanjing Institute of Technology under Grant CKJC201506in part by the Doctoral Research Fund of Huizhou Uni-versity under Grant 2018JB007 and in part by the Blue FirePlan Foundation of China under Grant CXZJHZ201704

References

[1] J Gubbi R Buyya S Marusic and M Palaniswami ldquoInternetof ings (IoT) a vision architectural elements and futuredirectionsrdquo Future Generation Computer Systems vol 29no 7 pp 1645ndash1660 2013

[2] D Miorandi S Sicari F De Pellegrini and I ChlamtacldquoInternet of things vision applications and research chal-lengesrdquo Ad Hoc Networks vol 10 no 7 pp 1497ndash1516 2012

[3] P Radmand ldquoComparison of industrial WSN standardsrdquo inProceedings of the 4th IEEE International Conference onDigital Ecosystems and Technologies IEEE Dubai UAE 2010

[4] M Kassim R Mohd and N Ahmad ldquoWireless sensor net-works and cloud computing integrated architecture for ag-ricultural environment applicationsrdquo in Proceedings of the2017 Eleventh International Conference on Sensing Technology(ICST) IEEE Sydney Australia December 2017

[5] H Mostafaei M U Chowdhury and M S Obaidat ldquoBordersurveillance with WSN systems in a distributed mannerrdquoIEEE Systems Journal vol 12 no 4 pp 3703ndash3712 2018

[6] H Ghayvat S Mukhopadhyay X Gui and N SuryadevaraldquoWSN-and IOT-based smart homes and their extension tosmart buildingsrdquo Sensors vol 15 no 5 pp 10350ndash103792015

[7] J P Muntildeoz-Gea P Manzanares-Lopez J Malgosa-Sanahujaand J Garcia-Haro ldquoDesign and implementation of a P2Pcommunication infrastructure for WSN-based vehiculartraffic control applicationsrdquo Journal of Systems Architecturevol 59 no 10 pp 923ndash930 2013

[8] M Li and H-Ju Lin ldquoDesign and implementation of smarthome control systems based on wireless sensor networks andpower line communicationsrdquo IEEE Transactions on IndustrialElectronics vol 62 no 7 pp 4430ndash4442 2014

[9] WWu N Xiong and CWu ldquoImproved clustering algorithmbased on energy consumption in wireless sensor networksrdquoIet Networks vol 6 no 3 pp 47ndash53 2017

[10] M M Warrier and A Kumar ldquoEnergy efficient routing inwireless sensor networks a surveyrdquo in Proceedings of theInternational Conference on Wireless Communications SignalProcessing and Networking (WiSPNET) IEEE Chennai IndiaDecember 2016

[11] M Khabiri and A Ghaffari ldquoEnergy-aware clustering-basedrouting in wireless sensor networks using cuckoo optimiza-tion algorithmrdquo Wireless Personal Communications vol 98no 3 pp 2473ndash2495 2018

[12] A S Rostami M Badkoobe F Mohanna H keshavarzA A R Hosseinabadi and A K Sangaiah ldquoSurvey onclustering in heterogeneous and homogeneous wireless sensornetworksrdquo e Journal of Supercomputing vol 74 no 1pp 277ndash323 2018

[13] S Arjunan and S Pothula ldquoA survey on unequal clusteringprotocols in Wireless Sensor Networksrdquo Journal of King SaudUniversity-Computer and Information Sciences vol 31 no 3pp 304ndash317 2019

[14] S K Singh P Kumar and J P Singh ldquoA survey on successorsof LEACH protocolrdquo Ieee Access vol 5 pp 4298ndash4328 2017

[15] W R Heinzelman A Chandrakasan and H BalakrishnanldquoEnergy-efficient communication protocol for wirelessmicrosensor networksrdquo in Proceedings of the 33rd AnnualHawaii International Conference on System Sciences IEEEMaui Hawaii January 2000

[16] N A Pantazis S A Nikolidakis and D D Vergados ldquoEn-ergy-efficient routing protocols in wireless sensor networks asurveyrdquo IEEE Communications Surveys amp Tutorials vol 15no 2 pp 551ndash591 2012

[17] R Singh and A K Verma ldquoEnergy efficient cross layer basedadaptive threshold routing protocol for WSNrdquo AEU-Inter-national Journal of Electronics and Communications vol 72pp 166ndash173 2017

[18] O Younis and S Fahmy ldquoHEED a hybrid energy-efficientdistributed clustering approach for ad hoc sensor networksrdquoIEEE Transactions on Mobile Computing vol 3 no 4pp 366ndash379 2004

[19] S Lindsey and C S Raghavendra ldquoPEGASIS power-efficientgathering in sensor information systemsrdquo in Proceedings ofthe IEEE aerospace vol 3 IEEE Big Sky MA USA March2002

[20] M Ye ldquoEECS an energy efficient clustering scheme inwireless sensor networksrdquo in Proceedings of the 24th IEEEInternational Performance Computing and CommunicationsConference IEEE Phoenix AZ USA July 2005


[21] Y Jin L Wang Y Kim and X Yang ldquoEEMC an energy-efficient multi-level clustering algorithm for large-scalewireless sensor networksrdquo Computer Networks vol 52 no 3pp 542ndash562 2008

[22] AManjeshwar andD P Agrawal ldquoTEEN ARouting protocolfor enhanced efficiency in wireless sensor networksrdquo Ipdpsvol 1 2001

[23] M S Bahbahani and E Alsusa ldquoA cooperative clusteringprotocol with duty cycling for energy harvesting enabledwireless sensor networksrdquo IEEE Transactions on WirelessCommunications vol 17 no 1 pp 101ndash111 2017

[24] A Al-Baz and A El-Sayed ldquoA new algorithm for cluster headselection in LEACH protocol for wireless sensor networksrdquoInternational Journal of Communication Systems vol 31no 1 Article ID e3407 2018

[25] A Hosen and G Cho ldquoAn energy centric cluster-basedrouting protocol for wireless sensor networksrdquo Sensorsvol 18 no 5 p 1520 2018

[26] W B Heinzelman A P Chandrakasan and H BalakrishnanldquoAn application-specific protocol architecture for wirelessmicrosensor networksrdquo IEEE Transactions on WirelessCommunications vol 1 no 4 pp 660ndash670 2002

[27] G S Brar S Rani V Chopra R Malhotra H Song andS H Ahmed ldquoEnergy efficient direction-based PDORProuting protocol for WSNrdquo IEEE Access vol 4 pp 3182ndash3194 2016

[28] M Sangeetha and A Sabari ldquoGenetic optimization of hybridclustering algorithm in mobile wireless sensor networksrdquoSensor Review vol 38 no 4 pp 526ndash533 2018

[29] D T Hai L H Son and T L Vinh ldquoNovel fuzzy clusteringscheme for 3D wireless sensor networksrdquo Applied SoftComputing vol 54 pp 141ndash149 2017

[30] J Shen A Wang C Wang P C K Hung and C-F Lai ldquoAnefficient centroid-based routing protocol for energy man-agement in WSN-assisted IoTrdquo IEEE Access vol 5pp 18469ndash18479 2017

[31] Y Zhang P Li and L Mao ldquoResearch on improved low-energy adaptive clustering hierarchy protocol in wirelesssensor networksrdquo Journal of Shanghai Jiaotong University(Science) vol 23 no 5 pp 613ndash619 2018

[32] E Alnawafa and I Marghescu ldquoNew energy efficient mul-tihop routing techniques for wireless sensor networks staticand dynamic techniquesrdquo Sensors vol 18 no 6 p 1863 2018

[33] P C S Rao P K Jana and H Banka ldquoA particle swarmoptimization based energy efficient cluster head selectionalgorithm for wireless sensor networksrdquo Wireless Networksvol 23 no 7 pp 2005ndash2020 2017

[34] M Azharuddin and P K Jana ldquoPSO-based approach forenergy-efficient and energy-balanced routing and clusteringin wireless sensor networksrdquo Soft Computing vol 21 no 22pp 6825ndash6839 2017

[35] P Kuila and P K Jana ldquoEnergy efficient clustering androuting algorithms for wireless sensor networks particleswarm optimization approachrdquo Engineering Applications ofArtificial Intelligence vol 33 pp 127ndash140 2014

[36] J Wang Y Gao W Liu A Sangaiah and H-J Kim ldquoAnimproved routing schema with special clustering using PSOalgorithm for heterogeneous wireless sensor networkrdquo Sen-sors vol 19 no 3 p 671 2019

[37] C Blum and A Roli ldquoMetaheuristics in combinatorial op-timizationrdquo ACM Computing Surveys vol 35 no 3pp 268ndash308 2003

[38] J Kennedy and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the ICNNrsquo95-International Conference on

Neural Networks vol 4 IEEE Perth Australia December1995

[39] J Kennedy and R C Eberhart ldquoA discrete binary version ofthe particle swarm algorithmrdquo in Proceedings of the 1997 IEEEInternational conference on systems man and cyberneticsComputational cybernetics and simulation vol 5 IEEEWuhan China October 2009


clusters and the election of CHs very random LEACH doesnot guarantee the best clustering scheme from the point ofview of the energy balance of the whole network

Since the emergence of LEACH a lot of WSN clusteringalgorithms have been proposed ere are several kinds ofclustering algorithms based on different clustering criteriasuch as network structure communication model topologyand reliable routing In this paper we classify clusteringalgorithms into two categories ie independent and co-operative according to whether the BS participates in theprocess of clustering Independent clustering algorithms runon network nodes without the BSrsquos participation andcontrol information is exchanged among nodes Indepen-dent clustering algorithms include HEED [18] PEGASIS[19] EECS [20] EEMC [21] TEEN [22] ECO-LEACH [23]NR-LEACH [24] and ECCR [25] etc In cooperative al-gorithms the BS participates in the process of clustering andall or part work of clustering is done by the BS A smallamount of control information is exchanged between the BSand network nodes e cooperative algorithms includeLEACH-C [26] PDOPR [27] UC-GA and KC-GA [28]PSO-ECHS [33] approaches in [34ndash36] etc e above-mentioned two kinds of clustering algorithms both prolongthe lifetime of the network to some extent but there are stillsome shortcomings in terms of the working mechanismIndependent algorithms run on each node and a largeamount of control information needs to be exchangedamong nodes which leads to additional energy consump-tion Although the cooperative algorithms reduce the energyconsumption of control information exchange they stillcannot get the best clustering result from the perspective ofthe whole network because there are multiple parametersaffecting the clustering and these parameters are mutuallyconflicting In particular with the development of evolvednature inspired algorithms some clustering approachesemploy them to improve clustering performance in recentyears [33ndash36]

To reduce the node energy consumption and prolongthe network lifetime we propose a combinatorial opti-mization-based clustering algorithm (COCA) which runson the BS for WSN from the point view of combinatorialoptimization in this paper We abstract WSN clusteringinto a combinatorial optimization problem and employbinary particle swarm optimization (BPSO) algorithm tosolve it In [33ndash36] continuous particle swarm optimi-zation (PSO) is employed for WSN clustering the positioncomponent of the particle is a real number in a certaininterval and the corresponding relationship betweenparticle position and CHs is established by using atransforming formula In contrast COCA applies binaryPSO for clustering in which the position component of theparticle is either 0 or 1 in binary space FurthermoreCOCA directly determined that whether the node is a CHbased on the value of the particle position component ifthe value is 1 the node corresponding to the component iselected as a CH contrastively if the component value is 0the corresponding node is selected as a member of acluster

e main contributions of this paper are as follows

(1) Based on the objective and procedure the clusteringof WSN is abstracted into a combinatorial optimi-zation problem

(2) A novel binary particle coding scheme is designed topresent the selection of CHs

(3) After the CHs are elected the constraints betweenparameters which affect clustering are consideredcomprehensively en the fitness function isdesigned and the clustering process is implementedby using BPSO

As the main innovation and contribution COCA es-tablishes a direct correspondence relationship between thebinary value of particle components and the role of whethernodes act as a CH After determining how to use binarycoding to represent whether a node is a CH COCA can beimplemented not only by using BPSO but also by applyingother swarm intelligence algorithms discrete version Be-cause BPSO has the advantages of a few parameters simpleimplementation and fast convergence we employ BPSO tosolve the WSN clustering problem based on combinatorialoptimization

e rest of this paper is organized as follows In Section2 related works are discussed In Section 3 the concept ofcombinatorial optimization and BPSO is presented firstlythen the network and energy consumption model of WSNare introduced Section 4 describes the proposed algorithmCOCA in detail In Section 5 the simulation results areshown to demonstrate the effectiveness of COCA Finallyconclusions are drawn in Section 6

2 Related Work

In order to elaborate the principle of COCA clearly theclassical LEACH and other representative WSN clusteringalgorithms proposed in recent years are summarized brieflyas follows

In LEACH [15] the lifespan of WSN is divided into anumber of periods called rounds Each round consists of twophases cluster setup phase and stable phase In the clustersetup phase each node generates a random number r in theinterval [0 1] and compares r with a threshold T(n) ecalculation of T(n) is shown in the following equation

T(n)

p

1 minus p rmodpminus1( 1113857 n isin G

0

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(1)

where p represents the percentage of CHs in the network r

stands for the number of the current round n denotes asensor node and G is the set of nodes that never acted as CHin the last pminus1 rounds

If r is less than T(n) the node will take the role of CHOtherwise it will be a member node After being electedeach CH broadcasts its own packet information to thenetwork When other nodes receive the broadcast infor-mation from CHs they decide to join a cluster according tothe received signal strength Subsequently the member node




















i (Xki1 Xk


vector Vki (Vk

i1 Vki2 Vk





Xkid X

kminus1id + V

kid (2)

Vkid wV



kminus1id1113872 1113873 (3)



Xkid

1 r(0 1)lt S Vkid( 1113857

0 otherwise

⎧⎨

⎩ (4)


S Vkid1113872 1113873

11 + eminusVk

id

(5)



P Xkid 11113960 1113961 S V

kid1113960 1113961 (6)











⎧⎨

⎩ (7)


d0

εfsεmp

1113971

(8)










1113944

K

i1Mi + K N

⎧⎪⎪⎨

⎪⎪⎩(10)


NUM CKNC

M1NminusKC


MK


(11)




f w1f1 + w2f2 + w3f3 + w4f4 (12)


w1 + w2 + w3 + w4 1 wi gt 0 1 le ile 4( 1113857 (13)









f1 1113944K

i11113944

Mi

j1εda

iHminusij

1113944

K

i11113944

Mi

j1εfsd


1113944

K

i11113944

Mi

j1εmpd


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)



f2 1113944K

i1

1Mi

1113944

Mi


2

11139741113972

(15)



di 1

Mi

1113944

Mi

j1dj (16)



f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd


1113944

K

i1εmpd


⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)



f4

1K


1113970

(18)


d 1K

1113944

K

i1di (19)































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References





























































i (Xki1 Xk


vector Vki (Vk

i1 Vki2 Vk





Xkid X

kminus1id + V

kid (2)

Vkid wV



kminus1id1113872 1113873 (3)



Xkid

1 r(0 1)lt S Vkid( 1113857

0 otherwise

⎧⎨

⎩ (4)


S Vkid1113872 1113873

11 + eminusVk

id

(5)



P Xkid 11113960 1113961 S V

kid1113960 1113961 (6)











⎧⎨

⎩ (7)


d0

εfsεmp

1113971

(8)










1113944

K

i1Mi + K N

⎧⎪⎪⎨

⎪⎪⎩(10)


NUM CKNC

M1NminusKC


MK


(11)




f w1f1 + w2f2 + w3f3 + w4f4 (12)


w1 + w2 + w3 + w4 1 wi gt 0 1 le ile 4( 1113857 (13)









f1 1113944K

i11113944

Mi

j1εda

iHminusij

1113944

K

i11113944

Mi

j1εfsd


1113944

K

i11113944

Mi

j1εmpd


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)



f2 1113944K

i1

1Mi

1113944

Mi


2

11139741113972

(15)



di 1

Mi

1113944

Mi

j1dj (16)



f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd


1113944

K

i1εmpd


⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)



f4

1K


1113970

(18)


d 1K

1113944

K

i1di (19)































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References




















































i (Xki1 Xk


vector Vki (Vk

i1 Vki2 Vk





Xkid X

kminus1id + V

kid (2)

Vkid wV



kminus1id1113872 1113873 (3)



Xkid

1 r(0 1)lt S Vkid( 1113857

0 otherwise

⎧⎨

⎩ (4)


S Vkid1113872 1113873

11 + eminusVk

id

(5)



P Xkid 11113960 1113961 S V

kid1113960 1113961 (6)











⎧⎨

⎩ (7)


d0

εfsεmp

1113971

(8)










1113944

K

i1Mi + K N

⎧⎪⎪⎨

⎪⎪⎩(10)


NUM CKNC

M1NminusKC


MK


(11)




f w1f1 + w2f2 + w3f3 + w4f4 (12)


w1 + w2 + w3 + w4 1 wi gt 0 1 le ile 4( 1113857 (13)









f1 1113944K

i11113944

Mi

j1εda

iHminusij

1113944

K

i11113944

Mi

j1εfsd


1113944

K

i11113944

Mi

j1εmpd


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)



f2 1113944K

i1

1Mi

1113944

Mi


2

11139741113972

(15)



di 1

Mi

1113944

Mi

j1dj (16)



f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd


1113944

K

i1εmpd


⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)



f4

1K


1113970

(18)


d 1K

1113944

K

i1di (19)































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References












































Xkid X

kminus1id + V

kid (2)

Vkid wV



kminus1id1113872 1113873 (3)



Xkid

1 r(0 1)lt S Vkid( 1113857

0 otherwise

⎧⎨

⎩ (4)


S Vkid1113872 1113873

11 + eminusVk

id

(5)



P Xkid 11113960 1113961 S V

kid1113960 1113961 (6)











⎧⎨

⎩ (7)


d0

εfsεmp

1113971

(8)










1113944

K

i1Mi + K N

⎧⎪⎪⎨

⎪⎪⎩(10)


NUM CKNC

M1NminusKC


MK


(11)




f w1f1 + w2f2 + w3f3 + w4f4 (12)


w1 + w2 + w3 + w4 1 wi gt 0 1 le ile 4( 1113857 (13)









f1 1113944K

i11113944

Mi

j1εda

iHminusij

1113944

K

i11113944

Mi

j1εfsd


1113944

K

i11113944

Mi

j1εmpd


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)



f2 1113944K

i1

1Mi

1113944

Mi


2

11139741113972

(15)



di 1

Mi

1113944

Mi

j1dj (16)



f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd


1113944

K

i1εmpd


⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)



f4

1K


1113970

(18)


d 1K

1113944

K

i1di (19)































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References












































1113944

K

i1Mi + K N

⎧⎪⎪⎨

⎪⎪⎩(10)


NUM CKNC

M1NminusKC


MK


(11)




f w1f1 + w2f2 + w3f3 + w4f4 (12)


w1 + w2 + w3 + w4 1 wi gt 0 1 le ile 4( 1113857 (13)









f1 1113944K

i11113944

Mi

j1εda

iHminusij

1113944

K

i11113944

Mi

j1εfsd


1113944

K

i11113944

Mi

j1εmpd


⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(14)



f2 1113944K

i1

1Mi

1113944

Mi


2

11139741113972

(15)



di 1

Mi

1113944

Mi

j1dj (16)



f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd


1113944

K

i1εmpd


⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)



f4

1K


1113970

(18)


d 1K

1113944

K

i1di (19)































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References











































di 1

Mi

1113944

Mi

j1dj (16)



f3 1113944K

i1εda

BSminusiH

1113944

K

i1εfsd


1113944

K

i1εmpd


⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(17)



f4

1K


1113970

(18)


d 1K

1113944

K

i1di (19)































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References




























































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References












































0 20


40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200




εmp 00013 pJbitm4




530643

797

266399 403

316452 473

372528 551

0

200

400

600

800

1000


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

Num

ber o

f aliv

e nod

es

500450400350300250150100 200

100

80

60

40

20

0

COCALEACH

ECCRPSO-ECHS


0 100 200 300 400 500 600 700

50

150

200

Rounds

Num

ber o

f aliv

e nod

es

100

0

COCALEACH

ECCRPSO-ECHS






0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References














































0

50

100

150

200

250

300

Rounds

Num

ber o

f aliv

e nod

es

8007006005004003002001000

COCALEACH

ECCRPSO-ECHS


36 42

65

4 3 712 15 2117 21 21

0

20

40

60

80


Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS



134173

282

43 51 764985

181

85 98

242

0

100

200

300


umbe

r of r

ound

s

COCALEACH

ECCRPSO-ECHS



530643

797

266399 403316

452 473372

528 551

0200400600800

1000

100 nodes 200 nodes


300 nodes

Num

ber o

f rou

nds

COCALEACH

ECCRPSO-ECHS


0 50Rounds

500450400350300250150100 200

50

30

40

20

10

0

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS






6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References














































6 Conclusion


100

80

60

40

20

0

Rounds

COCALEACH

ECCRPSO-ECHS

7006005004003002001000

Resid

ual e

nerg

y (J

)


Rounds

Resid

ual e

nerg

y (J

)

COCALEACH

ECCRPSO-ECHS

80070060050040030020010000

50

100

150


144

328

553

52 104 178

80 200

326

89 223

398

0100200300400500600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by al

lCH

s (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


114 299

531

45 66 134 61 159 228

72 165

283

0200400600

100 nodes 200 nodes


300 nodesPack

ets r

ecei

ved

by B

S (lowast

1000

)

COCALEACH

ECCRPSO-ECHS


259

628

1084

96 171312

141360

555

161389

681

0200400600800

10001200

100 nodes 200 nodes

e throughput

300 nodes

Pack

ets r

ecei

ved

by al

lCH

s and

BS

(lowast10

00)

COCALEACH

ECCRPSO-ECHS






Data Availability




Acknowledgments


References














































Data Availability




Acknowledgments


References
































































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CombinatorialOptimization-BasedClusteringAlgorithmfor ...downloads.hindawi.com/journals/mpe/2020/6139704.pdf · ResearchArticle CombinatorialOptimization-BasedClusteringAlgorithmfor