Balancing message delivery latency and network lifetime through an integrated model for clustering and routing in Wireless Sensor Networks

Computer Networks 55 (2011) 2803–2820

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Computer Networks

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Balancing message delivery latency and network lifetime through anintegrated model for clustering and routing in Wireless Sensor Networks

Wagner Moro Aioffi, Cristiano Arbex Valle, Geraldo R. Mateus 1, Alexandre Salles da Cunha ⇑,2

Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil

a r t i c l e i n f o

Article history:Received 29 April 2010Received in revised form 21 February 2011Accepted 25 May 2011Available online 14 June 2011Responsible Editor: I.F. Akyildiz

Keywords:Wireless Sensor NetworksDelay-tolerant Sensor NetworksMessage delivery latencyEnergy efficiency

1389-1286/$ - see front matter � 2011 Elsevier B.Vdoi:10.1016/j.comnet.2011.05.023

⇑ Corresponding author.E-mail addresses: [email protected] (W.M. Aioffi

(C.A. Valle), [email protected] (G.R. Mateus), acunda Cunha).

1 Geraldo Robson Mateus was partially funded by2007-1 and FAPEMIG Grant CEX-APQ-01201-09.

2 Alexandre Salles da Cunha was partially funded by2009-2.

a b s t r a c t

One common approach to extend Wireless Sensors Networks (WSN) lifetime is to usemobile sinks to gather sensed information through the network, avoiding that sensor nodesspend their limited energy in relaying other nodes’ messages to the sinks. Such approach,however, tends to significantly increase message delivery latency. On the other hand, it iswidely recognized that the optimization of any Quality of Service parameter in WSN, mes-sage delivery latency included, must always be conducted bearing in mind the impliedimpact in the network lifetime. In this paper, we introduce a network model to seek fora good solution for this inherent multi-objective optimization problem. In our approach,optimization algorithms are used to define optimal (or near-optimal) density control pol-icies, sensors clustering and sink routes to collect sensed data. We deal with the multi-objective nature of the design in WSN by explicitly minimizing message delivery latencyand by imposing topology constraints that help to reduce energy consumption. Our pro-posal differs from most studies in the literature by the integrated way in which we tackleclustering and routing decisions. Various metaheuristic based heuristics that solve the inte-grated problem were incorporated into a dynamic simulation environment. Throughextensive simulation experiments, we compared our approach to others in the literature,in terms of Quality of Service parameters. Our results indicate that the integrated modelproposed here compares favorably to other approaches, allowing a good balance amongconflicting parameters like message delivery latency, network lifetime and rate of mes-sages received.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Wireless Sensor Networks (WSN) are a kind of ad hocnetwork based on the collaborative effort of autonomoustiny multi-functional entities called sensor nodes, eachone being equipped with a sensing device, a low computa-tional capacity processor, a short-range wireless transmit-

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), [email protected]@dcc.ufmg.br (A.S.

CNPq Grant 55.0790/

CNPq Grant 302276/

ter–receiver and a limited battery-supplied energy. Aspecial node with unlimited (rechargeable) energy avail-ability and processing capabilities, called sink, plays animportant role in WSN. Through a wireless protocol, it isresponsible for receiving and/or disseminating informationand managing the network behavior.

WSN distinguish from other types of networks in manyways. First, sensor nodes are highly constrained in terms ofprocessing capacity and energy availability. To overcomethe hardware limitations and to perform complex tasks,sensors operate in a cooperative and distributed fashionand WSN are typically very dense. Consequently, the cov-erage in WSN tends to be highly redundant, i.e., some areasof the sensing field can be sensed by many sensor nodes atthe same time. That suggests that many nodes could be

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2804 W.M. Aioffi et al. / Computer Networks 55 (2011) 2803–2820

turned off without implying coverage losses. It may be pos-sible then to improve the network lifetime by choosing a(preferably small) subset of nodes to be kept active duringa certain time period while maintaining others idle (withtheir communication radios turned off). The problem ofdefining such subset of nodes to be kept active in orderto minimize energy consumption is referred here as theDensity Control Problem (DCP). Together with other strat-egies like defining an appropriate network topology,embedding the network with density control algorithmsallows substantial gains in energy efficiency and, conse-quently, in network lifetime.

Choosing a network topology involves, for example, todefine whether the sinks will be fixed or allowed to moveand to establish how information will be disseminatedfrom (to) nodes to (from) sink [15]. These issues stronglyinfluence the complexity of data routing and processing,as well as important Quality of Service (QoS) parametersin WSN like connectivity, energy consumption and mes-sage delivery latency (i.e., the elapsed time between themoment the message was generated and the moment itreached the sink).

In many cases, the communication topology can be arather simple structure like a tree where nodes much far-ther from a fixed sink must send their sensed informationto other nodes, until it reaches the sink, the root of the tree.With such tree-like structures involving (possibly) multi-ple hops in the path between a sensor node and the fixedsink, it is possible to achieve the best message delivery la-tency in WSN [24]. One drawback of such structures is thatsensor nodes located near the sink suffer from the sink-neighborhood problem [37]. Not only such nodes spend en-ergy to communicate their own data to the sink, but alsofor relaying to it the data from several other nodes of thenetwork. Since among the three primary functions of asensor node (sensing, communication and data process-ing), data communication is where energy is mostly spent[18], they deplete their batteries very quickly and the sinkmay get isolated from the rest of the network, leading to apremature disconnection of the network [37,21].

Mobile-sink based networks, on the other hand, allow amore balanced energy consumption among the nodes [38].Sink mobility not only is a way to reduce energy expendi-tures and to extend network lifetime, but also allowssparse networks to be connected. However, these gainsdo not come for free. Since the sink speed is much smallerthan the message transmission speed between nodes,allowing the sink to move to collect messages throughoutthe network substantially increases message delivery la-tency. This seems to be the major performance bottleneckof WSN with mobile sinks, since increasing their speed willlead to much higher manufacturing costs and power con-sumption [8]. For delay-tolerant applications, the mobilesink can upload data from every sensor node, following apath that spans every single sensor node in the network.Contrarily to the fixed-sink case, this type of data collec-tion offers the best possible energy efficiency [24], sincedata need not to be routed with multiple hops. The designof other network structures where the sink is neither fixednor visits every single sensor (and thus some kind of clus-tering procedure is applied) allows to achieve a balance be-

tween message delivery latency and network lifetime[22,4]. Indeed, the trajectory followed by the sinks shouldbe designed seeking a trade-off between these two designissues [24].

1.1. Our contribution

As it could be appreciated from the previous discussion,complex optimization problems exhibiting conflictingobjectives abound in WSN. It is widely recognized thatthe optimization of any QoS parameter in WSN, messagedelivery latency included, must always be conducted bear-ing in mind the implied impact in the network lifetime. Inthis paper, we introduce a network model to seek for agood solution for this inherent multi-objective optimiza-tion problem. In our approach, optimization algorithmsare used to define optimal (or near-optimal) density con-trol policies, sensors clustering and sink routes to collectsensed data. In doing so, our aim is to reduce message la-tency and to achieve, at the same time, a good trade-offin network lifetime. We deal with the multi-objective nat-ure of the design of WSN by explicitly minimizing messagedelivery latency and by imposing topology constraints thathelp to reduce energy consumption.

One aspect that distinguishes our work from most stud-ies in the literature is that, in spite of first defining whichsensor nodes should be visited (i.e., solving a clusteringproblem) and only then defining the sink routes (solvingthe routing problem), we address both problems together.This is accomplished by the way we search for the routes,imposing that all sensor nodes are either visited by a sinkin a route or else are close enough to one of them. The prob-lem of jointly finding a set of cluster heads and routingthem is named here as the Integrated Clustering and Rout-ing Problem (ICRP). In order to achieve low message deliv-ery latency, we model ICRP as a version of the VehicleRouting Problem (VRP) [10], where the fleet size is fixed,the goal is to minimize the length of the longest sink routeand not all sensors need to be visited. To solve ICRP, weimplemented the heuristics in [3] and proposed a newalgorithm.

Once the set of cluster heads is obtained after ICRP issolved, we seek for a solution of the resulting Density Con-trol Problem. To that aim, we implemented the methodsproposed in a previous paper by our research group [40].The resolution of these two optimization problems (ICRPand DCP) was embedded into a realistic model of the net-work dynamics over the time, allowing the proposed mod-el for sink mobility, clustering and density control to bevalidated through simulation.

In our view, the main contributions of this work aretwofold:

(1) The way we formulate the clustering and the routingproblems in WSN, through a single integrated opti-mization problem, resulting in a Min–max SelectiveVehicle Routing Problem [5]. The integrated modelwas chosen in order to achieve a good balancebetween energy consumption and message deliverylatency. Although other approaches (see [8], forinstance) also have dealt with these two problems

W.M. Aioffi et al. / Computer Networks 55 (2011) 2803–2820 2805

jointly, our approach differs from them since we alsoconsider the resolution of DCP and by the way routesare chosen here, aiming to explicitly minimizelatency. Reductions in energy consumption areachieved by the resolution of DCP and by imposingsingle-hop communication between sinks andsensors.

(2) The integration of the optimization algorithms tosolve ICRP and DCP into a dynamic simulation envi-ronment, where the network and the sensor proper-ties change over the time. Although our networkmodel and optimization algorithms are groundedon assumptions that may be considered too strongto allow their use in practice (they are centralized,sinks should be aware of the sensors’ energy stateand spatial location), the optimization-simulationtool offered here allows the network designer tobound important QoS parameters over the time.

Additionally, we extend the algorithms and results pre-sented in a preliminary version of this paper [3]. We nowintroduce an improved metaheuristic to solve ICRP andwe evaluate the impact of the quality of the ICRP optimiza-tion algorithms on QoS parameters. Although much aboutthe optimization procedures to solve ICRP is not new (mostprocedures were proposed in [3] and later incorporatedinto more elaborate exact and heuristic algorithms for ICRPin [5]), to our knowledge, the impact of the quality of theoptimization algorithms used to solve the clustering androuting problems on QoS parameters has never been con-ducted before. With this evaluation, we confirmed thatthe better the optimization algorithm is (in terms of solu-tion quality obtained under a constrained time limit) thebetter the WSN performs. Furthermore, in the currentstudy, we compare ICRP not only to the method it derivedfrom (the Single Hop Strategy in [40]) but also to the Cen-tralized Spatial Partitioning algorithm, proposed by Chatz-igiannakis et al. [17]. Through extended simulationexperiments, we conducted a deeper investigation aboutthe compromise of some QoS parameters, for each methodevaluated in our study.

In this regard, our simulation results indicate that, com-pared to the model it derived from, ICRP allowed signifi-cant reductions in message delivery latency. Albeit beingless efficient than the Single Hop Strategy in [40] in termsof overall energy expenditures, thanks to a more frequentimplementation of density control policies, ICRP also pro-vided higher network coverage and network lifetime. Com-pared to the Centralized Spatial Partitioning in [17], ICRPprovided much longer network lifetime, coverage and rateof messages received. In our testings, for a sensing area offixed size, Centralized Spatial Partitioning performed bet-ter than ICRP in terms of message delivery latency, whenthe number of sinks increase. This happens because theproportion of the communication radius to the sensingarea assigned to a sink increases and, in practice, the sinkalmost does not need to move to collect sensedinformation.

The rest of this paper is organized as follows. In Section2, we review important contributions on sink mobility andsensors clustering techniques in the literature. We also

present ICRP as an optimization problem in graphs and dis-cuss how our approach differs from previous works. InSection 3, we describe the optimization algorithms imple-mented to solve ICRP. In Section 4, we show, through sim-ulation, how the QoS parameters are improved when theoptimization algorithms proposed here are used. We finishthe paper in Section 5, offering some concluding remarksand directions for future work.

2. Sensors clustering and sink routing in WirelessSensor Networks

Mobility and routing in ad hoc networks have beenstudied extensively. However, results and protocols ob-tained for ad hoc networks cannot be directly applied toWSN, since sensor nodes are highly constrained devices.In this section, we review important contributions thathave addressed these issues in the specific domain ofWSN and, at the end, we present ICRP more formally.

2.1. Related works

In order to go around the sink-neighborhood problem,authors [25,19] have proposed clustering schemes wheredominating sets of low cardinality are repeatedly calcu-lated throughout the network lifetime. In such approaches,every sensor node is either a dominating set node (a nodethat represents a whole cluster and is responsible for col-lecting sensed data from other nodes in its cluster) or is as-signed to a dominating node. Within the cluster, onlysingle hop communication is used. Within the set of dom-inating nodes and the fixed sink, multiple hop paths are al-lowed. From time to time, dominating sets are updated toavoid draining the energy of the same few nodes. In a re-cent study, Albath et al. [19] proposed an enhancementover other clustering approaches based on dominatingsets. Instead of attempting to find a dominating set of min-imum cardinality, in [19], sensors to be included in thedominating set must also have a minimum residual energy.To solve the associated energy-constrained dominating setproblem, the authors have proposed an approximationpolynomial time algorithm.

Aiming the same goals, Gandham et al. [38] proposed aprotocol where multiple base stations (sinks) are deployedand their locations in the network change at certain mo-ments in time. The network lifetime is divided into equalperiods of time (rounds), during which the location of thebase stations is fixed and multi-hop communication proto-cols are used to forward sensed information to them. At theend of a round, a Linear Integer Program is solved to definenew locations for the base stations as well as new commu-nication trees to ensure energy efficient routing duringeach round.

In other approaches [1,16,36], authors have employedsinks that gather sensed information by changing theirpositions continuously, during the entire network lifetime,and not only at certain time intervals. An important aspectthat has to be considered in the design of WSN based onsink mobility is that sensor nodes have to buffer the infor-mation sensed during two consecutive visits of the sink.


Since sensors’ memory capabilities are often very limited,if the sinks stay long periods without visiting a node, datalosses are likely to occur. Somasundara et al. [1] investi-gated routing strategies in a scenario where different sam-pling rates are assigned to sensor nodes and, thus, some ofthem are given preference to be visited more frequently.The scheduling problem addressed in [1] seeks a routingstrategy where a node may need to be visited multipletimes before all other nodes are visited. In addition, as soonas a node is visited, the time before which it should berevisited is updated.

Another important issue in WSN is to avoid that two ormore sinks visit some sensor nodes simultaneously, leav-ing other nodes un-visited for long periods. Chatzigianna-kis et al. [16] suggested a clever distributed approach foravoiding the overlapping in the trajectories of mobilesinks, under the assumption that sinks do not need toknow the geographical position of sensor nodes. To accom-plish that goal, sinks leave an imprint (a trail of their move-ment) that, if detected by another sink, allows it to changeits trajectory, giving preference to collect data from un-vis-ited areas. In doing so, message delivery latency is signifi-cantly reduced.

In another contribution, Chatzigiannakis et al. [17] sug-gested a centralized method, named Centralized SpatialPartitioning (CSP), for coordinating the movement of sev-eral mobile sinks. In a first step, the area to be sensed is di-vided in non-overlapping regions (rectangles) and onedifferent mobile sink is made responsible for sensing eachof them. To collect data from the sensors belonging to itsassigned rectangle, each mobile sink repeatedly imple-ments a snake-like movement over the rectangle (see[17] for details on how the movement is controlled). Indoing so, CSP first assigns sensor nodes to regions and onlythen decides the trajectory of mobile sinks in each of them.

Saad et al. [6] and Nakayama et al. [14] also proposedapproaches that, like CSP, suffer from the lack of integra-tion between the resolution of the clustering and the rout-ing problems. Aiming to achieve an even distribution forthe traffic load among cluster heads and prolong networklifetime, the approach in [6] also consists in first defininga set of clusters to be routed later. In the methods in [6],an implementation of the Bee’s algorithm is used to definethe routes that visit the centroids of each cluster. As inother methods, the communication topology is chosen toguarantee that every cluster head will be at most onehop away from one mobile sink path.

The method introduced in [14] (named KAT in thatstudy) is quite similar to the method in [6] and to theSHS method in [40] (to be described, later, in detail). Afterclustering the sensor nodes using a scheme named K-means, a route spanning all cluster heads is found by aTraveling Salesman Problem (TSP) local search heuristic.One interesting feature of the KAT model is that the sinkmay vary its velocity, avoiding predictability of its move-ment and, thus, being safer with respect to externalattacks.

Basagni et al. [37] also proposed strategies for deter-mining sink mobility. One centralized approach introducedin [37] is based on Linear Integer Programming techniquesto determine optimal (with respect to network lifetime)

sink movements and soujorn times at cluster heads. TheInteger Programming approach in Basagni et al. [37] canbe viewed as an improvement over a previous study [43]by the same research group. This happens since, in the lat-ter, the scheduling part of the problem (the order in whichnodes should be visited by the mobile sink) was not ad-dressed. In [43], the output of the model was only the nec-essary amount of time the sink should rest close to eachnode in order to collect and pass messages from/to thenetwork.

Since approaches based on Integer Programming Tech-niques are usually quite time consuming, Basagni et al.[37] also introduced a distributed heuristic, named GreedyMaximum Residual Energy (GMRE). In such method, sinksdefine their own trajectories giving preference to visit en-ergy-rich areas. More precisely, the sink keeps monitoringsurrounding areas in order to identify sensor nodes withhigher energy. Once such nodes are found, the sink greed-ily moves to that direction to collect data.

To our knowledge, only the ICRP approach introducedhere and the methods proposed by Xing et al. [8] do inte-grate the resolution of the clustering and the routing prob-lems in WSN. The approach in [8] is aimed at minimizingthe energy consumption by a centralized network model,where message delivery latency is controlled by explicitlyimposing constraints that guarantee that sink routes long-er than a design parameter must be avoided. Xing et al. [8]stated the problem of defining a route for the sink as fol-lows: Given a set of source (sensor) nodes, find a tour (thatstarts and returns to the same gateway point) no longer thana parameter L and a set of trees that are rooted at the verticesin the tour, such that the cost of the edges in the trees (whichrepresent the Euclidean distance between the edge endpoints)is minimized. To solve such problem, Xing et al. proposed anapproximation algorithm based on Minimal Steiner Trees,that jointly provides the cluster heads (the roots of thetrees) and a tour (of length at most L) spanning them. Dif-ferently from the model in [8], ICRP explicitly minimizesmessage delivery latency while trying to keep low energyconsumption by imposing one-hop communication proto-cols and implementing density control algorithms. In thissense, ICRP differ from the method in [8] by the way themulti-objective nature of WSN is addressed and by imple-menting DCP algorithms.

One key difference among the approaches found in theWSN literature to address mobility and clustering issues isrelated to the amount of network information required toimplement them. Clearly, the more information and dataprocessing is needed, the less applicable the protocol isin practice. In this sense, ICRP (as well as the KAT method[14], the Linear Integer Programming schemes in [37,1]and the integrated method in [8]) seems to be less applica-ble in practice than other approaches. ICRP is indeedgrounded on more restrictive assumptions than CSP, forexample. This seems to be true since ICRP requires thateach mobile sink knows the geographical position of eachsensor node, while CSP does not. On the other hand, CSPcannot implement density control algorithms like thoseimplemented by ICRP.

Compared to the distributed algorithms in [16,37], CSP,ICRP, KAT and the Single Hop Strategy (SHS) introduced in


[40] are more restrictive to be implemented in practice.Nevertheless, more intensive information approaches likethose outlined above may be quite important for the theo-retical evaluation of WSN, to bound QoS parameters. Bear-ing in mind the differences on their applicability as well asthe goals aimed by each method, distributed approachesare not going to be compared with ICRP. Instead, for bench-marking our method, we will compare results obtained byapproaches that are more suitable for the off-line design ofWSN: ICRP, CSP and SHS. Since KAT is very similar to SHS(their difference rely mostly on the clustering techniqueand on the TSP heuristic used to route the sink) and ICRPimproves on SHS, the latter is described next, in detail.

Aioffi et al. [40] proposed the Single Hop Strategy toestablish a model for data dissemination, reception andtransmission in WSN. In SHS, the sink communicates di-rectly to every fixed sensor node; direct communicationbetween sensor nodes is not considered. A single mobilesink is used to collect the sensed information and it is as-sumed that all sensor nodes locations are known by thesink. Only when the sink arrives at a certain cluster center(which in this case represents a cluster head), the commu-nication between the sink and all the nodes covered bythat cluster takes place.

In the SHS method in [40], a two-step method was pro-posed to define a route for the mobile sink. In the first step,the network is divided into a minimal number of clusters,each one having the maximum communication range R (aparameter that depends on the hardware being used) be-tween the sink and the sensor nodes as its maximum ra-dius. Once the clusters are defined, the second stepfollows by calculating the shortest Hamiltonian circuitspanning all cluster geometrical centers. In [40], the mini-mal number of clusters was found by solving an inverse p-Centers problem [35]. Since the clustering and routingproblems are not solved jointly, a minimal number of clus-ters does not necessarily imply minimal length routes.Additional gains in terms of message delivery latencycould be attained, for example, by tackling the clusteringand routing problems as one single integrated problem,as proposed here.

2.2. Our model: the Integrated Clustering and Routing Problem

The network considered in our study involves multiplemobile sinks and hundreds of randomly deployed sensornodes. The sensing area, modeled by a large square in theEuclidean plane, comprises discretized sets of smallsquares with uniform sensing requirements. It is assumedthat the sinks know the geographical location of sensornodes after their deployment in the sensing field.

Aiming to cut down energy consumption, communica-tion between sensor nodes is not allowed in the model(communication only takes place between sensor nodesand the sinks). Aiming to cut down message delivery la-tency, instead of visiting each sensor node, only a smallset of them, called cluster heads, are visited. In addition,attempting to improve our previous results [3], we allowsinks to communicate with sensor nodes, while they movethrough the network, as follows. During its movement, atevery one second, each sink broadcasts a message to in-

form sensor nodes nearby that the sink is close and readyto receive their messages. Every sensor that gets the mes-sage and have stored data, starts transmitting its data tothe sink. In this process, when the sensor actually sendsthe message, the sink may be already too far away andthe message may be lost. This process is interrupted whenthe sink arrives at a cluster head, to avoid too much mes-sage collisions. Differently, when the sink is placed in acluster head, it schedules a time interval for each sensornode within that cluster to send its data.

ICRP can be described as follows. Given a setV = {1, . . . ,n} of sensor nodes (active or idle, never dead)in the Euclidean plane and a set K ¼ f1; . . . ;Kg of mobilesinks, the problem we want to solve consists in findingK 2 Zþ routes, one for each mobile sink. Each route mustspan some sensor nodes, the cluster heads, in such a waythat every sensor node in the network is either spannedby a route (the node is itself a cluster head) or lies withina distance no greater than R from a cluster head in one ofthe possible K routes. Note that the term cluster head hasa slightly different meaning here. In [40], it was used to de-fine the clusters geometrical centers which were the loca-tions to be visited by the sink. Here, it defines a sensornode that will be visited by one of the sinks. Although inICRP cluster heads are those nodes that are actually visitedby the sinks, they are not assigned any special function inthe network, when compared to non-cluster-head nodes.

In order to attain improved message delivery latency,we try to find K routes such that the length of the longestone is minimized. As K increases, the average messagedelivery latency is expected to decrease. Minimizing thelongest route helps in balancing their lengths, so every sinkwill take more or less the same time to collect the informa-tion from the sensor nodes assigned to its route.

An important assumption in the ICRP model is that theK different sinks start their movement at the same time,i.e., they are synchronized. If this were not the case, thenetwork could be unbalanced, since a sensor node spannedby a shorter route would communicate more often with itssink than other nodes spanned by much longer routes.Therefore, the first sink that arrives at the initial spot mustwait all the others in order to start a new cycle (a full walkof all sinks over their designed route).

Although mobile sinks are ideally assumed to haveplenty of energy, memory and processing capabilities, inpractice, from time to time, they must return to a sharedbase station (a network gateway) to download data andto recharge their batteries. In our network model, we as-sume that a single gateway or depot is shared by all mobilesinks. It should be pointed out that this assumption impliesno loss of generality in the proposed methods since if moredepots were available, the optimization algorithms imple-mented here would still be valid for reducing messagedelivery latency. Under the knowledge of which sinks areassigned to which depots, the algorithms could be used tosolve specific ICRP problems defined over smaller parts ofthe sensed region, like the CSP method in [17]. The differ-ences between CSP and ICRP in that case would remainthe same: an integrated resolution process for the cluster-ing and routing problems would still be aimed in ICRP (withone sink for each smaller region that defines the sensing


field) while in CSP, the trajectories of the sinks would not bedetermined by optimization methods. If each sink were as-signed to a region of the sensing field and if sinks did notshare the same depot, ICPR could be viewed, in some as-pects, as an improvement over CSP since it defines theroutes by means of optimization techniques that take intoaccount the clustering and density control policies.

2.2.1. A graph-theoretic model for ICRPTo present a graph-theoretic model for ICRP, we will

make use a digraph D = (V,A) with set of vertices V (definedpreviously) and arcs A. For that purpose, assume that,initially, all mobile sinks are located at a central station(the depot), represented by vertex 1 2 V. Arc set A :¼{(i, j), (j, i) :"i, j 2 V, i – j} represents the set of all possibletranslations of the mobile sinks, moving from one clusterhead to another. A cost dij P 0, proportional to the Euclid-ean distance between i and j, is assigned to every arc(i, j) 2 A. Let us also define that dii = 0, "i 2 V. Finally, letx(i) :¼ {j 2 V :dij 6 R} (note that i 2x(i)).

A solution to ICRP in D is a collection of constrained Kroutes. Each route k starts in 1, spans a set Skn{1} of se-lected vertices and ends back at 1. We refer to the sub-graph of D implied by each route k as Hk = (Sk,Ak).Accordingly, H ¼

SKk¼1ðSk;AkÞ denotes the subgraph associ-

ated to the whole set of K routes. In what follows, we saythat i– 2

SKk¼1Sk is covered by j if there exists k 2 K such

that j 2 Sk and i 2x(j). Whenever this is the case, we alsosay that j is spanned by route k. If we define f ðHkÞ ¼Pði;jÞ2Ak

dij as the length of the k-route, the cost of a feasiblesolution H to ICRP is given by f(H) = max {f(Hk) :k = 1, . . . ,K}.We can now state ICRP as:

min f ðHÞ : H ¼[K

k¼1

ðSk;AkÞ; ð1Þ

such that 8k 2 K : Ak induces a Hamiltoniancircuit spanning Sk; ð2Þ

Si \ Sj ¼ f1g; 8i; j 2 K; i–j; ð3Þ

8i 2 V : either i 2[K

k¼1

Sk or

9j 2 V n fig : j 2[K

k¼1

Sk; i 2 xðjÞ: ð4Þ

Note that (2) imposes that the depot is the only commonvertex spanned by any pair of routes and that (3) guaran-tees that each vertex is either a cluster head or it is coveredby one cluster head.

ICRP is clearly NP-Complete, since the Traveling Sales-man Problem [9,31] is one of its special cases, when K = 1and x(i) = {i}, "i 2 V.

To the best of our knowledge, the VRP variant closest toICRP is that discussed by Glaab [12]. In that reference, theauthor introduces a Vehicle Routing Problem that arises inthe design of a semi-automatic system for cutting leatherskins. As in ICRP, one has to minimize the longest routelength and the fleet size is fixed. However, ICRP differsfrom that VRP variant in two aspects: in [12] all customersneed to be visited and each vehicle starts its route from adifferent depot. Lower bounds in that application were

obtained by replacing the min–max objective function bythe average route length to later formulate and solve com-binatorial relaxations based on matchings and one-trees.

Due to its selective nature, other Combinatorial Optimi-zation Problems that also relate to ICRP are the CoveringTour Problem [30] (CTP) and the Generalized TravelingSalesman Problem [29] (GTSP). Contrarily to ICRP which in-volves multiple vehicles, GTSP and CTP seek optimal routesfor a single vehicle. In CTP, there are two sets of vertices:those that must be visited (covered) by any feasible tourand those that may be visited in order to lower the cost ofconnecting the former set. In GTSP, on the other hand, thevertices of the graph are previously partitioned into clusters.The problem seeks a tour that visits exactly one vertex ofeach cluster, at minimal cost. In [30,29], Linear Integer Pro-gramming formulations, Branch-and-cut algorithms andheuristics were proposed for CTP and GTSP, respectively.

3. Metaheuristic based heuristics for ICRP

In a recent paper [5], we have provided two exact solu-tion approaches (a Branch-and-cut algorithm [33] and aLocal Branching method [28]) for ICRP, based on LinearInteger Programming techniques. According to the findingsin [5], ICRP is indeed very difficult to solve to proven opti-mality, mainly when K and n increase.

Although the network model introduced here is aimedat the off-line evaluation of WSN, we do not use the exactsolution approaches in [5] to solve ICRP. The sizes of the in-stances we plan to investigate here (with up to 600 sensornodes) are out of reach for the exact solution proceduresintroduced in [5]. Our choice to resort to heuristics is moti-vated by the fact that the huge time requirements for find-ing reasonably good solutions to ICRP by the exactmethods in [5] preclude their use in a simulation environ-ment for WSN, where several rounds of routing and clus-tering decisions should be taken and the simulation clockis not stopped to run optimization algorithms.

The optimization algorithms implemented here are hy-brid implementations of GRASP [39] and of Iterated LocalSearch (ILS). They combine a constructive phase and threemain operators: two Local Search procedures and a diver-sification mechanism. Depending on how these methodsare combined and controlled, different metaheuristics withvarying levels of intensification and diversification, bettersuited for WSN applications with a single or multiple mo-bile sinks, arise. Some GRASP implementations discussedhere were combined into a sophisticated (and more timeconsuming) Column Generation Heuristic for ICRP in [5].A new GRASP hybridization scheme (named GRASP-ILS/

VND) is introduced in the current study. For the sake ofcompleteness, in the sequence, we review the main ingre-dients of the metaheuristics.

3.1. Constructive heuristic

The constructive heuristic designed here is based on theCheapest Insertion Algorithm (CIA) [2] proposed for theEuclidean Traveling Salesman Problem. For the sake ofclarity, let us first describe how CIA operates for the TSP


defined on a set of n vertices and distance matrix d. Themain idea in CIA is to iteratively construct a tour spanningthe n vertices, in a process that builds a tour involving r 6 nvertices from a previous one that includes only r � 1. Moreprecisely, at any given CIA iteration, let S; S respectively bethe set of nodes spanned by the tour in hands and its com-plement in V. Assume that p 2 V is visited right after i 2 V inthe current tour. The selection policy that chooses a nodeto be inserted into the partial solution is based on thecheapest insertion rule. For any j 2 S, let Dj

ip :¼ dijþdjp � dip denote the cost of inserting j between i and p.Accordingly, let Dj :¼minfDj

ip : i; p 2 S; p is visited rightafter ig denote the minimum increment cost of inserting jin S, considering all possible insertion positions. The in-serted vertex is actually z 2 arg minfDj : j 2 Sg. Ties arebroken arbitrarily. The algorithm then inserts z betweenthe vertices i and p for which the optimal value Dz was at-tained and removes z from S. This process goes on untilS ¼ ;.

The adaptation of this constructive procedure to ICRP,resulting into algorithm CIA_ICRP, is straightforward. Tounderstand how this is carried out when K = 1, let us firstredefine S as the set of cluster heads and S as the set of ver-tices that are not covered by any vertex in S, i.e.S ¼ V n

Si2SxðiÞ. For the ICRP case, we keep on adding

new cluster heads, one at time, until S becomes empty.To address the K P 2 case, minor modifications are neces-sary. In such situation, our algorithm constructs K P 2routes simultaneously, adding one cluster head at a timeto one of them. Since the goal is to build a set of routeswhere the length of the longest one is minimized, we al-ways insert a new cluster head in the route that has theshortest length. The insertion policy and the stopping cri-teria are the same whenever K = 1 or K P 2.

3.2. Main operators

In order to improve the initial solutions obtained by ourconstructive heuristic, two Local Search (LS) procedures(2-OPT [7] and 2-SWAP [41]) and a diversification mecha-nism (the Nodes Reinsertion Algorithm, NRA [11]) wereimplemented and tested.

Given a feasible solution to ICRP, 2-OPT is always ap-plied to the longest of the K routes. It works by removingtwo arcs from the route and then trying to reconnect theresulting two paths using less expensive arcs. If the lengthof the route becomes smaller than the length of any otherroute in the solution, the search switches to the new lon-gest one. 2-OPT implemented here makes use of the Don’tLook Bits neighborhood reduction [20] to cut down CPUrunning times.

In 2-SWAP, we try to improve the solution by swappingnodes from their routes. Assuming that two cluster headsp 2 Sk1 and q 2 Sk2 are given, one replaces p by q and q byp. Note that after swapping the two vertices, only two setsof cluster heads change: Sk1 becomes ðSk1 n fpgÞ [ fqg andSk2 becomes ðSk2 n fqgÞ [ fpg. In case k1 = k2, only the visit-ing order of p and q is changed.

One weakness of the previous search procedures is thatthe whole set of cluster heads is preserved after their appli-cation; no clusters heads are added or removed from the

whole set of cluster heads, although due to 2-SWAP, theymay swap routes. To overcome this weakness, we alsomake use of the Nodes Reinsertion Algorithm [11]. In orderto explore a broader solution space, our implementation ofNRA has two phases. In the first one, we attempt to removeone cluster head a time from each route, according to a gi-ven probability. Whenever a cluster head p 2 Sk (togetherwith its incident arcs) is removed from route k, the twoneighbors of p in the route are joined by an arc, in orderto establish a Hamiltonian circuit spanning the remainingset of cluster heads Skn{p}. After the last removal operation,the second phase starts. Since the set of routes obtainedafter the first phase is not necessarily feasible (S may benot empty), we apply CIA_ICRP to recover feasibility. Indoing so, cluster heads different from those that were re-moved in the preceding phase will be possibly added, gen-erating a new feasible solution.

3.3. GRASP and Iterated Local Search

In this Section, it is shown how the constructive proce-dure and the main operators presented previously areembedded in various algorithmic frameworks in order toimprove their performance and robustness. Depending onhow the procedures described in Sections 3.1 and 3.2 areguided to explore the solution space, different Metaheuris-tic based heuristics for the ICRP arise: three hybrid GRASP[39] implementations and an Iterated Local Search method[13].

GRASP (Greedy Randomized Adaptive Search Proce-dure) is a class of stochastic search algorithms that usesrandomized greedy constructive search heuristics to gen-erate a large number of different candidate solutions. Ineach GRASP iteration, the solution obtained with the ran-domized constructive phase is submitted to a local searchprocedure [13]. This two-phase process is iterated until atermination criterion is satisfied; usually, after a maximumnumber of iterations are performed.

All three hybrid GRASP proposed here share the samerandomized implementation of CIA_ICRP, followed by2-OPT. In each iteration, after a local optimum withinthe 2-OPT neighborhood is found, another Metaheuristicis applied to that solution. Therefore, depending on whichMetaheuristics are called after 2-OPT, different hybrid ver-sions of GRASP appear. The algorithm outlined in Fig. 1indicates the main steps of our hybrid approach. All differonly in step 7 in Fig. 1.

Before describing how GRASP was hybridized, let usfirst discuss how its constructive phase works. To thataim, define D ¼minfDj � kj �xðjÞj : j 2 Sg as the minimumcost of adding a new cluster head to the route in hands. In-stead of choosing the vertex s for which D is attained toadd to the route, in the randomized version of CIA_ICRP,one randomly chooses any sensor node j 2 S whose corre-sponding value of Dj � kj �xðjÞj lies in the interval [D,(1 + a)D], where parameter a P 0 controls the level of ran-domization of the procedure. Actually, since a is not keptconstant during all GRASP iterations, our procedure is areactive GRASP (see [32] for details). In our implementa-tion, at the first GRASP iteration, a is randomly chosenfrom the set {0.05,0.10, . . . ,0.50} with uniform probability.

Fig. 1. Algorithm outline of the hybrid GRASP.


As the algorithm evolves, higher probabilities are assignedto those values of a that result in higher quality solutions.

In our first GRASP procedure, named GRASP-ILS, anIterated Local Search Method is implemented in step 7 ofFig. 1. The main idea of ILS is to use perturbations to allowescaping from local optimum solutions. Briefly, ILS is a ran-domized algorithm that, first, applies a Local Search proce-dure to a feasible solution to the problem being solved. Inthe sequel, the local optimum is submitted to a perturba-tion procedure, originating a new intermediate solution.Then a Local Search step takes place once again: the LS pro-cedures are applied to this intermediate solution, obtaininga (possibly) new local optimum. This process of alternatingLS and perturbation steps goes on until a satisfaction crite-rion is met. In our case, 2-SWAP is used as the perturbationphase and 2-OPT is the inner LS method. This two-stepprocedure runs until a certain number of iterations areconducted without improving the best solution found.

GRASP-VND, the second hybrid procedure proposedhere, implements a Variable Neighborhood Descent (VND)[34]. Roughly speaking, VND is a local search method basedon the idea of iteratively switching neighborhoods duringthe course of the algorithm. The neighborhood structuresare ordered according to their size (complexity): smaller(cheaper) neighborhoods precede larger (more expensive)neighborhoods. Accordingly, one first performs a LocalSearch algorithm exploring a cheaper neighborhood. Oncea local minimum (w.r.t. the current neighborhood) is found,a Local Search algorithm based on the next larger neighbor-hood starts. In this process, whenever an improved solutionis found, the search restarts from the simplest neighbor-hood. The two neighborhoods explored in our GRASP-VNDalgorithm are 2-OPT and 2-SWAP. Accordingly, after step6 in Fig. 1, we apply 2-SWAP. If a better solution is found,we resort back to 2-OPT and the procedure goes on, untilthe best solution in hands is found to be a local minimumin both neighborhoods. Although the two previous hybrid-ized versions make use of the same operators, GRASP-VND,unlike GRASP-ILS, performs a full scan over the analyzedneighborhoods. Due to this reason, typical iterations ofGRASP-ILS are performed faster than GRASP-VND counter-parts. Consequently, more initial solutions are generated byGRASP-ILS, while deeper searches on less solutions areperformed by the second hybrid GRASP variant.

In the third and last GRASP algorithm, GRASP-ILS/VND,we use both ILS and VND approaches to hybridize themethod. This is accomplished by using the NRA as the

perturbation phase in ILS. The ILS implementation usedin this hybrid version also differs from that used inGRASP-ILS on the choice of the Local Search algorithm.Here, the VND method described earlier replaces 2-OPT

used in GRASP-ILS.The last method proposed here, ILS, implements a pure

ILS. In this approach, an initial solution to the method is gi-ven by CIA_ICRP. The perturbation step and the LocalSearch procedures used are NRA and 2-OPT, respectively.

3.4. Optimization results

In this Section, we report on our computational experi-ence with the Metaheuristics presented previously. Ourpurpose here is to validate one or more algorithms to beused in a dynamic context, for example, in a simulationframework to WSN. All computational testings were con-ducted on an AMD Dual Core machine running at 1.9 GHz,with 3 Gb of RAM memory, under Linux operating system.

In order to evaluate the proposed algorithms, several in-stances (each one representing an initial WSN configura-tion) were generated. The instances considered here haven varying from 50 to 600 sensor nodes, randomly spreadover a sensing area represented by a square in the plane.In order to test dense and sparse networks, we kept thearea and the communication range R respectively fixed to40,000m2 and 30 m. For each value of n and K 2 {1,2,3,4},33 different instances were randomly generated. There-fore, computational results presented for a given pair of nand K are average values attained for 33 instances. All algo-rithms proposed here, CIA_ICRP, GRASP-ILS, GRASP-VND,GRASP-ILS/VND and ILS, were run with the same set of33 instances for each pair n, K.

In order to address the quality of the solutions providedby the Metaheuristics, these algorithms were comparedagainst the basic constructive procedure proposed here,CIA_ICRP.

To establish a fair comparison between the heuristics,for each pair n,K, we allowed CIA_ICRP to run n � 1 times,each one initializing one route with the depot and a differ-ent sensor node. We also imposed the same CPU time limitof 60 s on all procedures running times. Therefore, one canjudge the merits of each algorithm only in terms of solu-tion quality. When deciding for this parameter, we consid-ered a realistic situation where the sink may have a timelimit of 60 s (no matter the network size) to find the bestpossible solution to the problem.

In Table 1, we present the main computational resultsattained by each heuristic. In the first two columns of Table1, we respectively indicate the number of mobile sinks andthe network size. In the next column (under headingsCIA_ICRP), we present �f , the average (over 33 instancesfor each pair n, K) shortest longest route length obtainedfor the n � 1 different runs of CIA_ICRP. In the next col-umns, we present average results attained by each Meta-heuristic. For each one (GRASP-ILS, GRASP-VND, GRASP-ILS/VND and ILS), two entries are given: the averagelength �f of the longest route and the implied reduction in�f when compared to the solution found by CIA_ICRP. Forexample, for K = 1, n = 50, the longest routes found byGRASP-ILS/VND are, on the average, 5.9% shorter than

Table 1Average longest route lengths.

Instance CIA_ICRP Grasp-ILS Grasp-VND Grasp-ILS/VND ILS

K n �f �f Gain �f Gain �f Gain �f Gain

1 50 793.3 757.3 4.5% 756.0 4.7% 746.2 5.9% 763.0 3.8%100 878.9 831.0 5.4% 821.4 6.5% 803.4 8.6% 832.5 5.3%150 914.8 869.9 4.9% 859.9 6.0% 837.6 8.4% 848.6 7.2%200 914.3 869.8 4.9% 866.4 5.2% 840.6 8.1% 851.6 6.9%250 939.8 899.5 4.3% 895.6 4.7% 875.3 6.9% 864.2 8.0%300 939.2 903.6 3.8% 901.5 4.0% 885.8 5.7% 869.3 7.4%350 953.8 921.2 3.4% 925.2 3.0% 904.3 5.2% 887.6 6.9%400 960.6 928.1 3.4% 939.4 2.2% 917.0 4.5% 890.8 7.3%450 961.7 935.3 2.7% 945.8 1.7% 923.2 4.0% 887.0 7.8%500 968.6 942.2 2.7% 947.8 2.2% 926.0 4.4% 894.7 7.6%550 972.1 948.7 2.4% 962.5 1.0% 939.5 3.3% 902.4 7.2%600 994.8 963.1 3.2% 977.7 1.7% 954.7 4.0% 912.5 8.3%

Average rate 3.8% 3.6% 5.8% 7.0%

2 50 516.2 467.6 9.4% 464.5 10.0% 460.7 10.8% 485.8 5.9%100 561.3 512.2 8.7% 506.2 9.8% 495.5 11.7% 520.1 7.3%150 573.6 521.2 9.1% 512.8 10.6% 499.6 12.9% 523.1 8.8%200 568.3 521.3 8.3% 511.7 10.0% 498.2 12.3% 520.9 8.4%250 590.4 541.7 8.3% 532.3 9.8% 513.5 13.0% 536.1 9.2%300 589.5 544.7 7.6% 535.6 9.2% 518.7 12.0% 538.4 8.7%350 595.9 557.8 6.4% 549.5 7.8% 528.3 11.4% 544.0 8.7%400 599.8 562.8 6.2% 554.2 7.6% 537.4 10.4% 547.2 8.8%450 598.0 566.3 5.3% 558.8 6.6% 539.4 9.8% 548.0 8.4%500 614.2 576.0 6.2% 565.4 7.9% 541.8 11.8% 555.4 9.6%550 607.9 578.6 4.8% 568.9 6.4% 545.9 10.2% 554.7 8.7%600 619.8 594.8 4.0% 578.2 6.7% 558.1 9.9% 565.9 8.7%

Average rate 7.0% 8.5% 11.4% 8.4%

3 50 451.7 397.2 12.1% 395.3 12.5% 393.7 12.8% 419.6 7.1%100 480.8 429.4 10.7% 422.9 12.0% 417.1 13.3% 445.5 7.3%150 483.1 431.5 10.7% 420.9 12.9% 410.6 15.0% 442.7 8.4%200 483.9 433.5 10.4% 422.8 12.6% 410.5 15.2% 446.5 7.7%250 505.9 452.6 10.5% 435.1 14.0% 422.3 16.5% 456.2 9.8%300 495.5 452.3 8.7% 435.8 12.0% 423.1 14.6% 454.0 8.4%350 507.5 467.1 8.0% 449.8 11.4% 433.4 14.6% 465.5 8.3%400 512.0 467.6 8.7% 451.4 11.8% 436.6 14.7% 464.9 9.2%450 515.2 473.0 8.2% 455.6 11.6% 437.5 15.1% 472.5 8.3%500 513.8 474.3 7.7% 452.7 11.9% 435.7 15.2% 468.3 8.8%550 513.8 474.7 7.6% 456.2 11.2% 432.0 15.9% 471.5 8.2%600 529.5 491.5 7.2% 469.7 11.3% 449.7 15.1% 479.6 9.4%

Average rate 9.2% 12.1% 14.8% 8.4%

4 50 412.5 366.8 11.1% 364.8 11.6% 364.4 11.7% 391.4 5.1%100 441.7 396.3 10.3% 391.7 11.3% 388.0 12.1% 420.5 4.8%150 436.7 390.1 10.7% 382.6 12.4% 376.1 13.9% 406.1 7.0%200 438.5 394.3 10.1% 386.0 12.0% 377.1 14.0% 411.5 6.2%250 461.5 411.4 10.9% 395.6 14.3% 386.5 16.2% 420.0 9.0%300 450.5 407.6 9.5% 393.9 12.6% 383.4 14.9% 415.4 7.8%350 468.9 420.0 10.4% 405.2 13.6% 392.6 16.3% 435.3 7.2%400 466.6 423.3 9.3% 406.0 13.0% 391.5 16.1% 431.7 7.5%450 467.7 426.5 8.8% 407.6 12.8% 392.7 16.0% 429.8 8.1%500 473.7 425.1 10.3% 407.3 14.0% 389.7 17.7% 434.5 8.3%550 457.3 420.4 8.1% 395.3 13.6% 379.3 17.1% 421.8 7.8%600 478.0 438.9 8.2% 419.6 12.2% 402.9 15.7% 439.8 8.0%

Average rate 9.8% 12.8% 15.1% 7.2%


the average shortest longest route found when CIA_ICRPis used alone.

Results in Table 1 indicate that the best improvementsover the solutions found by CIA_ICRP were attained byILS, when K = 1, and by GRASP-ILS/VND, when K P 2.As K increases from 1 to 4, all other solution approacheswork much better than ILS. An important difference be-tween ILS and GRASP is that ILS works always on the sameinitial solution, while GRASP generate new solutions at

each iteration. When K = 1, ILS seems to achieve a goodbalance between intensification and diversification, thanksto NRA. Apparently, when more sinks are used, NRA alonewas not able to provide enough diversification. In suchcases, it seems that the diversification provided by themulti-start structure of GRASP, allowed better routes tobe found. Nevertheless, one can infer that NRA had aremarkable importance on the gains attained for ILS andGRASP-ILS/VND over the other Metaheuristics. This


seems to be true since the best algorithms for each case(K = 1 and K P 2) implement NRA, while none of the othersdoes.

Based on the results reported above, ILS and GRASP-

ILS/VND were the chosen algorithms (respectively, forK = 1 and K P 2) to solve ICRP in a simulation frameworkfor WSN.

4. WSN simulation

In many complex dynamic systems, like in WSN, it isvery difficult to exactly capture the relationships and inter-actions of the system entities in strict mathematical equa-tions. Therefore, a Discrete Event Simulator was the tool ofour choice to evaluate how ICRP compares to other ap-proaches in the literature (CSP in [17] and SHS in [40]),in terms of message delivery latency, network lifetime,coverage and rate of messages received. To that aim, wedeveloped a WSN framework built over the JIST/SWANSsimulator [26]. The transmission, energy, sensing and stor-age protocols are already built-in the SWANS procedure.Apart from that, in the hope of improving the overallbehavior of the network, we incorporated other importantfeatures into the framework: algorithms to address bothICRP and DCP (see [40] for details on how DCP is modeledand solved). Results obtained for SHS and ICRP presentedhere differ from results respectively reported in [40,3]since in this paper, for both methods, we allowed sinks

Fig. 2. Simulator fl

to communicate to sensor nodes while they move throughthe network (communication is not restricted to take placewhen the sink arrives and stops at a cluster head).

The simulation model we present for WSN comprises aset of cyclic operations performed by each sink. In Fig. 2, aflowchart of the simulation process is depicted. The firstsimulation cycle starts with the ICRP resolution, right afterthe sensor nodes deployment. After the design of the firstset of routes, DCP is solved. Each sink then starts its move-ment throughout the network. Using recent technologiesand supported protocols for the MAC layer [23,27], sensornodes can be kept in very low power levels (idle state),where no sensing functions are performed, but being ableto turn into a full operating state, whenever an appropriatestimulus from the outside environment is received. There-fore, during their movement throughout the network,sinks collect sensed information and also deactivate andactivate some sensor nodes, according to the density con-trol policies. In this process, the sinks become aware ofthe energy state of all nodes in their routes.

When all sinks have returned to the depot, the energystate of all nodes is available. If any sensor node died dur-ing the previous cycle, another solution to the new result-ing ICRP is searched. The rationale to recompute the routesis to try to shorten the longest one since new dead nodesno longer need to communicate to the sinks. The newlyfound set of routes, however, are implemented only if thenew longest route is shorter than the previous one. Given

ow diagram.

Table 2Main simulation parameters.

Parameter Value Parameter Value

Sensor energy 50 mA h Transmissionpower

8.9 mA

Sensing range 15 m Reception power 7 mAData acquisition

board5 mA Radio idle power 7 lmA

Sink speed 1 m/s Processor power 8 mACommunication

range30m Sensed area 40,000m2

Bandwidth 250 kbps


the energy state of the network in hands, no matter if ICRPwas solved again or not, we solve DCP once again, and an-other simulation cycle takes place. Since the routes werecomputed before the density control algorithms are called,one weakness of our approach is that sensor nodes that re-main idle in two consecutive simulation cycles keep beingvisited by the set of routes. On the one hand, visiting sen-sor nodes that remain idle during two or more consecutivecycles unnecessarily increases route lengths. On the otherhand, it allows us to have a full appreciation of the energystate in the network. Accordingly, better density controlpolicies can be implemented if one has more realistic en-ergy information in hands. This is the reason why we solveICRP before DCP.

The downside of the use of synchronized mobile sinks isthat it may impose higher average message delivery latencyrates. On the positive side, it allows an easy centralizedimplementation of the density control policies that may re-sult in benefits for the overall behavior of WSN. In our mod-el, after one of the K sinks solves both ICRP and DCP, allother sinks become aware of their routes as well as theset of vertices they should activate or deactivate duringthe next cycle. This is another reason why the resolutionof ICRP must take place before the resolution of DCP.

Another factor that may increase message delivery la-tency is the time taken to run the optimization algorithmsthemselves, since the simulation clock does not stop whilethey are executed. Therefore, in order to limit from abovethe impact of the time taken to solve ICRP, in the first cycle,the optimization algorithm is allowed to run for only 60 s.Whenever there is the need to run it again (if new sensornodes become dead), a tighter time limit of 2 s is imposed.

One might consider that the 60 s necessary to calculatethe route at the first cycle will affect negatively the averagemessage delivery latency. However, since this calculationtakes place only once, its impact on the first cycle (whichcannot be neglected) will be diluted through the next cy-cles. As our computational results demonstrate, the gainobtained when using our optimization algorithms in cut-ting down average message delivery latency during the en-tire simulation time more than makes up for this initialoverhead.

The simulation parameters chosen in our study were setaccording to the commercially available Mica2 nodes [42](see Table 2). For the particular application described here,it was assumed that sensor nodes periodically collect infor-mation encoded using 32 bits, at a constant rate of 1/20 Hz.Since their memory board can store up to 4 Kbytes, sensorshave autonomy of 14 h of data collection. The MAC layer isthe IEEE 802.11 available in SWANS simulator, as theMica2 nodes implements a CSMA/CA protocol. All methodsimplemented and tested in our study, namely ICRP, SHSand CSP, make use of IEEE 802.11.

4.1. Simulation results

Based on the results presented in Section 3.4, ILS andGRASP-ILS/VND are the algorithms of our choice to solveICRP in the simulation framework, respectively, when K = 1and K P 2.

In the sequel, we evaluate how the WSN operating un-der the ICRP model compares to the SHS approach [40] andto the CSP method [17]. As we pointed out before, ICRP (aswell as SHS and CSP) are not going to be compared to dis-tributed approaches, for example, like those proposed in[16].

The comparisons are conducted by measuring fourimportant network parameters: the message delivery la-tency, the network coverage and lifetime and, finally, theratio of messages received. For comparing SHS and ICRP,K was considered in the set {1,2,3,4}. CSP was not simu-lated for K = 3 since, in [16], no guidelines were given onhow to divide the sensing field into rectangles whenK P 2 and K is odd.

For evaluating the message delivery latency, the ratio ofmessages received and the network lifetime, the maximumsimulation time was set to 15 h. For evaluating the net-work coverage, on the other hand, this parameter was ex-tended to 25 h. Longer simulation times were used in thiscase because we found that after 15 h, the coverage wasstill very high for SHS and ICRP. Similar behavior was notobserved by CSP since, contrarily to SHS and ICRP, it doesnot implement density control algorithms.

4.1.1. Message delivery latency and the ratio of messagesreceived

In applications where the sensed information is gener-ated almost on a regular basis or else at high rates (noton demand, nor on an event basis), message delivery la-tency must be low, in order to avoid loss of data due tothe limited storage capacity of sensor nodes.

In Fig. 3, we indicate how the message delivery latencybehave as a function of the number of sensor nodes. Eightcurves are presented in Fig. 3: one for the SHS approach(which considers only one mobile sink), one curve for eachvalue of K 2 {1,2,3,4} for model ICRP and one curve foreach value of K 2 {1,2,4} for model CSP.

By comparing the SHS results against those attained byICRP when K = 1, we observe that the latter attained betterresults. As one can appreciate from the figure, the rate inwhich the message delivery latency increases as n growsis lower for ICRP. When n = 50, both approaches have sim-ilar average latency rates. However, as n grows up to 600,the average latency attained by ICRP grows less than whatis observed in method SHS. As one could expect, usingmore mobile sinks also helps reducing the average latencyrates. Significant reductions were attained when multiplemobile sinks were used.

0

50

100

150

200

250

300

350

400

100 200 300 400 500 600

Mes

sage

del

iver

y la

tenc

y (s

econ

ds)

Number of sensors

ICRP/K=1ICRP/K=2ICRP/K=3ICRP/K=4

SHSCSP/K=1CSP/K=2CSP/K=4

Fig. 3. Average message delivery latency for SHS, ICRP/K and CSP/K.


ICRP was capable of providing lower rates of messagedelivery latency than CSP for K = 1 and for K = 2 whenn 6 400. For K = 2,n > 400 ICRP and CSP obtained compara-ble message delivery latency rates. However, higher rateswere attained for ICRP when K = 4. The advantage of CSPover ICRP for K = 4 is strongly influenced by the shape ofthe sensing area, which is represented by a square of200 � 200 meters. With K = 4, each sink in model CSP isin charge of sensing a square of 100 � 100 m. Since thecommunication radio is 30 m, the entire sensing region isalmost covered if the sink is placed in the midle of thesquare. Based on the fact that ICRP/K = 1 obtained smallermessage delivery latency rates than CSP/K = 1, the advan-tage of CSP over ICRP should vanish if sensors are notplaced uniformly over the sensing region or when the com-munication radius is not so large compared to the side ofeach square in CSP model.

Worse results in terms of message delivery latency whenK = 4 can be explained by an additional aspect: ICRP, con-trarily to CSP, makes use of a single depot (in ICRP, it is al-ways chosen to be vertex 1 2 V, irrespective to anyproperty of the region being sensed-a position in the midleof the region would imply better message delivery latency).Since ICRP performed better than CSP when K = 1, it seemsreasonable to conjecture that if the ICRP/K = 1 model wereapplied to each one of the four squares that (together) repre-sent the sensing field in the CSP model when K = 4, better re-sults in terms of message delivery latency would be attained.

On the positive side, the proportion of messages thatactually reach the sinks is much greater for ICRP (as wellas for SHS), compared to CSP. In Fig. 4, we depict for eachmodel, the ratio of messages received, i.e., the number ofmessages that reached one mobile sink divided by the totalnumber of messages generated at the end of a given simu-lation time. This is a consequence of the fact that, in ICRP,when the sink is at a cluster head, sensor nodes send theirdata in scheduled time intervals.

Let us now address the impact of the use of better orworse optimization algorithms (w.r.t. the longest routelength) on the message delivery latency. To that aim, wesimulated the network behavior when CIA_ICRP (undersimilar CPU time limit constraints) replaces ILS (whenK = 1) and GRASP-ILS/VND, (when K P 2) as the resolu-tion method to ICRP in the simulator. Results of such com-parisons are depicted in Fig. 5. For each value of K, wedepict two curves: one obtained when the best optimiza-tion algorithm (ILS or GRASP-ILS/VND) was used andthe other when CIA_ICRP was considered. We found thatwhen K = 1, on the average, the use of the best optimiza-tion algorithm tested (ILS) implied a reduction of 10% onthe average message delivery latency. Similar gains around15%, 18% and 15% were achieved when GRASP-ILS/VND

procedure is used instead of CIA_ICRP in the simulationframework, respectively for K = 2,3,4. Note that the laten-cies obtained by GRASP-ILS-/VND with K = 3 were lowerthan those obtained when CIA_ICRP was used with K = 4mobile sinks. As these results suggest, the design of higherquality optimization algorithms to tackle ICRP pays off.

4.1.2. Network coverageThe next QoS parameter studied here is the network

coverage, i.e., the percentage of the monitoring area thatis sensed by at least one sensor node in a given simulationtime. In Fig. 6, we indicate how network coverage changesas the simulation clock goes on (for at most 25 h), for net-works with n = 400.

The use of ICRP with K = 1 allowed an increase of 19% incoverage when compared to SHS (37% of coverage against31%), at the end of the simulation time. The reasoning forthat is related to the frequency in which more up to datedensity control policies are implemented. Since ICRP lon-gest routes are shorter than SHS counterparts, the numberof simulation cycles performed in a certain amount of timetends to be higher for ICRP. More cycles being executed

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Fig. 4. Ratio of messages delivered for SHS, ICRP/K and CSP/K.

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CIA_ICRP/K=1CIA_ICRP/K=2CIA_ICRP/K=3CIA_ICRP/K=4

Fig. 5. The impact of the choice of better/worse optimization algorithms on the message delivery latency.


during the same amount of time allows the density controlalgorithm to be executed more often, being thus moreefficient.

Another aspect that should be raised is that, after 5 sim-ulation hours, the coverage rates for both SHS and ICRPdrop from almost 100% to nearly 90% and then, a littlebit later, increase again. These drops in coverage rates oc-cur when the first set of sensor nodes die. Therefore, cover-age rates remain a bit lower until all sinks return to thebase, DCP is run again and new density control policiesare implemented. Since ICRP routes are shorter, the net-work remains shorter periods of time under lower cover-

age rates. This is confirmed by the figure, since all curvesdrop more or less at the same time, but ICRP with K = 4recovers coverage much faster than other methods. Similarfast falls followed by fast recovers of coverage rates occuragain, after around 11 h of simulation.

Note that in Fig. 6, the coverage rates for the CSP modelis zero, after 5 h of simulation. In practice, after 5 h, all sen-sor nodes were already dead, i.e., all sensor nodes haddepleted their batteries entirely. Significantly higher cov-erage rates were attained by ICRP due to the implementa-tion of the density control algorithm. For the CSP case, theincrease on the number of mobile sinks imply higher cov-

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Fig. 6. Network coverage, n = 400.


erage rates. Contrarily to what one may expect, for the ICRPcase, the use of more mobile sinks does not systematicallyimprove the coverage rates, for longer periods of simula-tion. Explanations for that will be given in the next section,together with the analysis of network lifetime.

4.1.3. Network lifetimeIn the literature, different metrics are used to measure

how efficient the network is in terms of energy consump-tion. According to some authors [38], the best metric to mea-sure the energy efficiency is application dependent. Someevaluation metrics usually considered in the literature are:the network lifetime (the elapsed time until the first nodedies) and the overall energy spent during a defined period

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Fig. 7. Network

of time. In other works, the time required for the total energyto drop below 50% of the initial energy is used.

In this study, the first two of these metrics are evalu-ated. As it will be shown, they have to be considered to-gether, in order to fully appreciate the benefits anddrawbacks of a particular protocol. In Fig. 7, we presenthow the network lifetime varies as a function of n and inFig. 8, we show the percentage of the total initial energythat remains available during the simulation. Fig. 8 wasgenerated for n = 400.

As it can be appreciated from Fig. 7, the network life-time remains almost unchanged when the number ofnodes rises up to 400. After that point, for ICRP and SHS,a sharp increase in network lifetime is observed. Consider-

400 500 600f sensors

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Fig. 8. Network Residual Energy, n = 400.


ing the sensing area represented by our instances, net-works with 400 or less nodes are indeed sparse. Therefore,it is very likely that a certain discretized part of the sensingarea is covered by only one sensor node. However, for lar-ger values of n, every discretized part is typically coveredby more than one sensor node. Consequently, the densitycontrol implemented here is more likely to increase thenetwork lifetime. Since for CSP density control algorithmsare not implemented, the network lifetime remains almostconstant for the entire range of network size consideredhere. Because of that, the network lifetime observed forCSP is always much lower than for SHS and for ICRP.

Note that ICRP provides higher lifetime than SHS, for allvalues of n. Therefore, one could possibly argue that, basedon network lifetime alone, ICRP also allowed gains in en-ergy consumption when compared to SHS. To address thisissue properly, two other parameters need to be consid-ered: the fraction of the total initial energy that remainsavailable during the simulation time (see Fig. 8) and thepercentage of dead sensors as a function of time (seeFig. 9). Figs. 8 and 9 indicate that ICRP energy consumptionis indeed higher when compared to SHS. The number ofdead sensors is also higher when ICRP is used.

Higher energy consumption rates occur since shorterICRP routes imply that sensor nodes communicate moreoften with the sinks. Since for the application consideredhere, information is sensed at low rates (32 bits at 1/20 Hz), just a tiny fraction of the sensor memory is actuallyused at each transmission. Therefore, the energy spent pertransmission at the MAC layer is pretty much the same forSHS and ICRP, irrespective of the volume of data beingtransmitted. Since more transmissions take place whenICRP is used, more energy is spent. This also explainswhy coverage levels decrease when more sinks are usedin ICRP. Clearly, these experiments indicate how littlevalue the network lifetime alone has to capture the overallbehavior of WSN in terms of energy efficiency.

We must point out that, however, the advantage of SHSover ICRP in terms of smaller energy expenditures shouldvanish in other applications, where messages are gener-ated at much higher rates and, consequently, node mem-ory becomes a concern. For the particular applicationtreated in this study, thanks to the density control algo-rithms, higher energy expenditure levels of ICPR did notimply worse coverage rates, as it could be expected. Never-theless, ICRP could be easily adapted in order to achieve abetter balance between energy consumption and delayrates. That could be accomplished by imposing that all mo-bile sinks should wait a minimum amount of time at thecentral station, before the beginning of a new simulationcycle.

We must stress that, when message delivery latency isanalyzed together with energy related parameters, thetrade off between energy consumption, message latencyand network lifetime becomes very clear. For networkswith n = 400, the average latency for ICRP with K = 4 isaround 30% of the corresponding SHS figures, whilst only50% of the remaining SHS energy was available for ICRPat the end of the simulation time. Considering that our pri-mary goal was to reduce SHS message delivery latency innetworks with mobile sinks without incurring in excessivecoverage losses, we claim that ICRP allowed us to achievethe goals we aimed for. Compared to CSP, on the otherhand, ICRP performed worse when more mobile sinks(K = 4) were used. However, ICRP is capable to allow thenetwork to operate for much longer periods of time; thisone being, certainly, one of the primary goals of any net-work designer.

One may argue that the advantages of ICRP over CSPfor QoS parameters other than message delivery latencyare due mostly to the implementation of density controlalgorithms. Although ICRP benefits a lot from it, in ourview, advantages of ICRP over CSP cannot be resumedto that. To substantiate this claim, we should point out

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Fig. 9. Percentage of dead sensors, n = 400.


that ICRP is better suited for WSN in which sensor nodesare not deployed uniformly over the area being sensed.Since the resolution of the clustering and routing prob-lems is conducted as a result of an optimization process,ICRP is likely to behave better than CSP for networkswhere the density of sensor nodes varies too much.Being adaptive, ICRP is also likely to behave better whenthe configuration of the network changes, for example,when some sensor nodes die and the network becomessparser. In CSP, clustering is done by dividing the areato be sensed into rectangles having, ideally, the samearea. Routing, on the other hand, is always done in thesame way since mobile sinks always perform a predict-able snake-like movement. Thus, QoS parameters likenetwork coverage and rate of messages received maydeteriorate even further when the whole area to besensed is difficult to be split into rectangles where asnake-like movement can be easily implemented andwhen the density of sensor nodes vary significantly.

5. Concluding remarks and future research

In this paper, we presented optimization algorithmsand a simulation framework for Wireless Sensor Networkswith multiple mobile sinks. Since sink speed is muchslower than communication between sensor nodes, highermessage delivery latency is expected for this type of net-work topology. Traditional approaches to deal with thisundesired feature are the use of clustering (to group setsof sensor nodes) and routing algorithms. In doing so, oneallows the sink to visit just a small subset of the sensornodes and, therefore, to reduce the time needed to collectall sensed information.

As an alternative to other approaches in the literature,we proposed an integrated method that simultaneouslyprovides the sets of sensor nodes that should be visitedby each sink as well as their routes. This was accom-

plished by modeling the clustering and routing problemsjointly, as a variant of the Vehicle Routing Problem,where the fleet size is fixed, not all clients need to bevisited and the goal is to minimize the length of the lon-gest vehicle route. Several metaheuristic based heuristicswere implemented to tackle this VRP variant. After theroutes are found, we implemented a density controlalgorithm, in order to reduce unnecessary energy con-sumption in the network.

Thanks to the good results achieved by the optimiza-tion algorithms introduced here, a simulation frameworkthat predicts the network dynamics over the time wasalso implemented and tested computationally. The opti-mization and simulation results indicate that the pro-posed optimization procedures allowed significantreductions in message delivery latency, for example, withthe Single Hop Strategy in [40] (the method from whichICRP derived). Albeit being less efficient than the strate-gies in [40] in terms of overall energy expenditures,thanks to a more frequent implementation of densitycontrol policies, ICRP also provided higher network cov-erage and lifetime. Compared to the Centralized SpatialPartitioning in [17], ICRP provided smaller messagedelivery latency when few mobile sinks were considered.When more mobile sinks were considered, the approachin [17] provided better rates. However, for all other QoSparameters, ICRP performed better than the CentralizedSpatial Partitioning. In the future, we plan to investigatethe impact of allowing multi-hop communication be-tween sensor nodes and the mobile sinks on the messagedelivery latency.

Acknowledgements

The authors thank four anonymous referees for theircareful reading, for providing additional relevant refer-ences and suggestions that improved this paper.


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Wagner Moro Aioffi received his B.Sc. and M.Sc. degrees in ComputerScience from Federal University of Minas Gerais (UFMG), Brazil, in 2004and 2006, respectively. His research interests include applied Combina-torial Optimization, on-line algorithms and simulation.

Cristiano Arbex Valle is currently undertaking a PhD program in AppliedMathematics at Brunel University, London. He received his Msc., inComputer Science in 2009 from the Federal University of Minas Gerais,Belo Horizonte, Brazil. His research interests include combinatorial opti-mization, mathematical programming and related applications such ascomputer networks and financial problems.

http://www.jist.ece.cornell.edu/

http://www.xbow.com/

http://www.xbow.com/


Geraldo Robson Mateus is Full Professor inComputer Science at Federal University ofMinas Gerais, Belo Horizonte, Brazil. Hereceived his PhD and MS in computer sciencefrom Federal University of Rio de Janeiro,Brazil, in 1980 and 1986, respectively. Hespent 1991 and 1992 at the University ofOttawa, Canada, as a visiting researcher. Hisresearch interests span network optimization,combinatorial optimization, algorithms,logistic, transport and telecommunication. Heis a member of INFORMS, IFORS, SBC, SIAM

and SOBRAPO. He has published over 200 scientific papers, 50 journalpapers and book chapters and two books, and is a leader of several

national and international projects. He has worked as a consultant forsome companies such as Usiminas, CVRD, MBR, Telemig, Telemar, FranceTelecom, Embratel and for the Brazilian government.

Alexandre Salles da Cunha has B.S. and M.Sc. degrees in MechanicalEngineering from Federal University of Minas Gerais, Belo Horizonte,Brazil (1994, 2002). He holds a PhD degree in Systems Engineering andComputing from Federal University of Rio de Janeiro (2006). During 2004-2005, he visited the Center for Operations Research and Econometrics atl’Universithé Catholique de Louvain (Belgium), as part of his doctorateresearch. He currently serves as Associate Professor at the ComputerScience Department of Federal University of Minas Gerais, Brazil. Hisresearch spans Mathematical Programming, Combinatorial Optimizationand their applications in Network Optimization.

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Balancing message delivery latency and network lifetime through an integrated model for clustering and routing in Wireless Sensor Networks