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

Contents lists available at ScienceDirect

Computer Networks journal homepage: www.elsevier.com/locate/comnet

Balancing message delivery latency and network lifetime through an integrated 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 2010 Received in revised form 21 February 2011 Accepted 25 May 2011 Available online 14 June 2011 Responsible Editor: I.F. Akyildiz Keywords: Wireless Sensor Networks Delay-tolerant Sensor Networks Message delivery latency Energy efficiency

a b s t r a c t One common approach to extend Wireless Sensors Networks (WSN) lifetime is to use mobile sinks to gather sensed information through the network, avoiding that sensor nodes spend 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 is widely recognized that the optimization of any Quality of Service parameter in WSN, message delivery latency included, must always be conducted bearing in mind the implied impact in the network lifetime. In this paper, we introduce a network model to seek for a good solution for this inherent multi-objective optimization problem. In our approach, optimization algorithms are used to define optimal (or near-optimal) density control policies, sensors clustering and sink routes to collect sensed data. We deal with the multiobjective nature of the design in WSN by explicitly minimizing message delivery latency and by imposing topology constraints that help to reduce energy consumption. Our proposal differs from most studies in the literature by the integrated way in which we tackle clustering and routing decisions. Various metaheuristic based heuristics that solve the integrated problem were incorporated into a dynamic simulation environment. Through extensive simulation experiments, we compared our approach to others in the literature, in terms of Quality of Service parameters. Our results indicate that the integrated model proposed here compares favorably to other approaches, allowing a good balance among conflicting parameters like message delivery latency, network lifetime and rate of messages received.  2011 Elsevier B.V. All rights reserved.

1. Introduction Wireless Sensor Networks (WSN) are a kind of ad hoc network based on the collaborative effort of autonomous tiny multi-functional entities called sensor nodes, each one being equipped with a sensing device, a low computational capacity processor, a short-range wireless transmit⇑ Corresponding author. E-mail addresses: aioffi@dcc.ufmg.br (W.M. Aioffi), [email protected] (C.A. Valle), [email protected] (G.R. Mateus), [email protected] (A.S. da Cunha). 1 Geraldo Robson Mateus was partially funded by CNPq Grant 55.0790/ 2007-1 and FAPEMIG Grant CEX-APQ-01201-09. 2 Alexandre Salles da Cunha was partially funded by CNPq Grant 302276/ 2009-2. 1389-1286/$ - see front matter  2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comnet.2011.05.023

ter–receiver and a limited battery-supplied energy. A special node with unlimited (rechargeable) energy availability and processing capabilities, called sink, plays an important role in WSN. Through a wireless protocol, it is responsible for receiving and/or disseminating information and managing the network behavior. WSN distinguish from other types of networks in many ways. First, sensor nodes are highly constrained in terms of processing capacity and energy availability. To overcome the hardware limitations and to perform complex tasks, sensors operate in a cooperative and distributed fashion and WSN are typically very dense. Consequently, the coverage in WSN tends to be highly redundant, i.e., some areas of the sensing field can be sensed by many sensor nodes at the same time. That suggests that many nodes could be

2804

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

turned off without implying coverage losses. It may be possible then to improve the network lifetime by choosing a (preferably small) subset of nodes to be kept active during a certain time period while maintaining others idle (with their communication radios turned off). The problem of defining such subset of nodes to be kept active in order to minimize energy consumption is referred here as the Density Control Problem (DCP). Together with other strategies like defining an appropriate network topology, embedding the network with density control algorithms allows substantial gains in energy efficiency and, consequently, in network lifetime. Choosing a network topology involves, for example, to define whether the sinks will be fixed or allowed to move and to establish how information will be disseminated from (to) nodes to (from) sink [15]. These issues strongly influence the complexity of data routing and processing, as well as important Quality of Service (QoS) parameters in WSN like connectivity, energy consumption and message delivery latency (i.e., the elapsed time between the moment the message was generated and the moment it reached the sink). In many cases, the communication topology can be a rather simple structure like a tree where nodes much farther from a fixed sink must send their sensed information to other nodes, until it reaches the sink, the root of the tree. With such tree-like structures involving (possibly) multiple hops in the path between a sensor node and the fixed sink, it is possible to achieve the best message delivery latency in WSN [24]. One drawback of such structures is that sensor nodes located near the sink suffer from the sinkneighborhood problem [37]. Not only such nodes spend energy to communicate their own data to the sink, but also for relaying to it the data from several other nodes of the network. Since among the three primary functions of a sensor node (sensing, communication and data processing), data communication is where energy is mostly spent [18], they deplete their batteries very quickly and the sink may get isolated from the rest of the network, leading to a premature disconnection of the network [37,21]. Mobile-sink based networks, on the other hand, allow a more balanced energy consumption among the nodes [38]. Sink mobility not only is a way to reduce energy expenditures and to extend network lifetime, but also allows sparse networks to be connected. However, these gains do not come for free. Since the sink speed is much smaller than the message transmission speed between nodes, allowing the sink to move to collect messages throughout the network substantially increases message delivery latency. This seems to be the major performance bottleneck of WSN with mobile sinks, since increasing their speed will lead to much higher manufacturing costs and power consumption [8]. For delay-tolerant applications, the mobile sink can upload data from every sensor node, following a path that spans every single sensor node in the network. Contrarily to the fixed-sink case, this type of data collection offers the best possible energy efficiency [24], since data need not to be routed with multiple hops. The design of other network structures where the sink is neither fixed nor visits every single sensor (and thus some kind of clustering 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 should be designed seeking a trade-off between these two design issues [24]. 1.1. Our contribution As it could be appreciated from the previous discussion, complex optimization problems exhibiting conflicting objectives abound in WSN. It is widely recognized that the optimization of any QoS parameter in WSN, message delivery latency included, must always be conducted bearing in mind the implied impact in the network lifetime. In this paper, we introduce a network model to seek for a good solution for this inherent multi-objective optimization problem. In our approach, optimization algorithms are used to define optimal (or near-optimal) density control policies, sensors clustering and sink routes to collect sensed data. In doing so, our aim is to reduce message latency and to achieve, at the same time, a good trade-off in network lifetime. We deal with the multi-objective nature of the design of WSN by explicitly minimizing message delivery latency and by imposing topology constraints that help to reduce energy consumption. One aspect that distinguishes our work from most studies in the literature is that, in spite of first defining which sensor nodes should be visited (i.e., solving a clustering problem) and only then defining the sink routes (solving the 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 sink in a route or else are close enough to one of them. The problem of jointly finding a set of cluster heads and routing them is named here as the Integrated Clustering and Routing Problem (ICRP). In order to achieve low message delivery latency, we model ICRP as a version of the Vehicle Routing Problem (VRP) [10], where the fleet size is fixed, the goal is to minimize the length of the longest sink route and not all sensors need to be visited. To solve ICRP, we implemented the heuristics in [3] and proposed a new algorithm. Once the set of cluster heads is obtained after ICRP is solved, we seek for a solution of the resulting Density Control Problem. To that aim, we implemented the methods proposed in a previous paper by our research group [40]. The resolution of these two optimization problems (ICRP and DCP) was embedded into a realistic model of the network dynamics over the time, allowing the proposed model for sink mobility, clustering and density control to be validated through simulation. In our view, the main contributions of this work are twofold: (1) The way we formulate the clustering and the routing problems in WSN, through a single integrated optimization problem, resulting in a Min–max Selective Vehicle Routing Problem [5]. The integrated model was chosen in order to achieve a good balance between energy consumption and message delivery latency. Although other approaches (see [8], for instance) also have dealt with these two problems

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

jointly, our approach differs from them since we also consider the resolution of DCP and by the way routes are chosen here, aiming to explicitly minimize latency. Reductions in energy consumption are achieved by the resolution of DCP and by imposing single-hop communication between sinks and sensors. (2) The integration of the optimization algorithms to solve ICRP and DCP into a dynamic simulation environment, where the network and the sensor properties change over the time. Although our network model and optimization algorithms are grounded on assumptions that may be considered too strong to allow their use in practice (they are centralized, sinks should be aware of the sensors’ energy state and spatial location), the optimization-simulation tool offered here allows the network designer to bound important QoS parameters over the time. Additionally, we extend the algorithms and results presented in a preliminary version of this paper [3]. We now introduce an improved metaheuristic to solve ICRP and we evaluate the impact of the quality of the ICRP optimization algorithms on QoS parameters. Although much about the optimization procedures to solve ICRP is not new (most procedures were proposed in [3] and later incorporated into more elaborate exact and heuristic algorithms for ICRP in [5]), to our knowledge, the impact of the quality of the optimization algorithms used to solve the clustering and routing problems on QoS parameters has never been conducted before. With this evaluation, we confirmed that the better the optimization algorithm is (in terms of solution quality obtained under a constrained time limit) the better the WSN performs. Furthermore, in the current study, we compare ICRP not only to the method it derived from (the Single Hop Strategy in [40]) but also to the Centralized Spatial Partitioning algorithm, proposed by Chatzigiannakis et al. [17]. Through extended simulation experiments, we conducted a deeper investigation about the compromise of some QoS parameters, for each method evaluated in our study. In this regard, our simulation results indicate that, compared to the model it derived from, ICRP allowed significant reductions in message delivery latency. Albeit being less efficient than the Single Hop Strategy in [40] in terms of overall energy expenditures, thanks to a more frequent implementation of density control policies, ICRP also provided higher network coverage and network lifetime. Compared to the Centralized Spatial Partitioning in [17], ICRP provided much longer network lifetime, coverage and rate of messages received. In our testings, for a sensing area of fixed size, Centralized Spatial Partitioning performed better than ICRP in terms of message delivery latency, when the number of sinks increase. This happens because the proportion of the communication radius to the sensing area assigned to a sink increases and, in practice, the sink almost does not need to move to collect sensed information. The rest of this paper is organized as follows. In Section 2, we review important contributions on sink mobility and sensors clustering techniques in the literature. We also

2805

present ICRP as an optimization problem in graphs and discuss how our approach differs from previous works. In Section 3, we describe the optimization algorithms implemented to solve ICRP. In Section 4, we show, through simulation, how the QoS parameters are improved when the optimization algorithms proposed here are used. We finish the paper in Section 5, offering some concluding remarks and directions for future work. 2. Sensors clustering and sink routing in Wireless Sensor Networks Mobility and routing in ad hoc networks have been studied extensively. However, results and protocols obtained for ad hoc networks cannot be directly applied to WSN, since sensor nodes are highly constrained devices. In this section, we review important contributions that have addressed these issues in the specific domain of WSN 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 where dominating sets of low cardinality are repeatedly calculated throughout the network lifetime. In such approaches, every sensor node is either a dominating set node (a node that represents a whole cluster and is responsible for collecting sensed data from other nodes in its cluster) or is assigned to a dominating node. Within the cluster, only single hop communication is used. Within the set of dominating nodes and the fixed sink, multiple hop paths are allowed. From time to time, dominating sets are updated to avoid draining the energy of the same few nodes. In a recent study, Albath et al. [19] proposed an enhancement over other clustering approaches based on dominating sets. Instead of attempting to find a dominating set of minimum cardinality, in [19], sensors to be included in the dominating set must also have a minimum residual energy. To solve the associated energy-constrained dominating set problem, the authors have proposed an approximation polynomial time algorithm. Aiming the same goals, Gandham et al. [38] proposed a protocol where multiple base stations (sinks) are deployed and their locations in the network change at certain moments in time. The network lifetime is divided into equal periods of time (rounds), during which the location of the base stations is fixed and multi-hop communication protocols are used to forward sensed information to them. At the end of a round, a Linear Integer Program is solved to define new locations for the base stations as well as new communication trees to ensure energy efficient routing during each round. In other approaches [1,16,36], authors have employed sinks that gather sensed information by changing their positions continuously, during the entire network lifetime, and not only at certain time intervals. An important aspect that has to be considered in the design of WSN based on sink mobility is that sensor nodes have to buffer the information sensed during two consecutive visits of the sink.

2806

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

Since sensors’ memory capabilities are often very limited, if the sinks stay long periods without visiting a node, data losses are likely to occur. Somasundara et al. [1] investigated routing strategies in a scenario where different sampling rates are assigned to sensor nodes and, thus, some of them are given preference to be visited more frequently. The scheduling problem addressed in [1] seeks a routing strategy where a node may need to be visited multiple times before all other nodes are visited. In addition, as soon as a node is visited, the time before which it should be revisited is updated. Another important issue in WSN is to avoid that two or more sinks visit some sensor nodes simultaneously, leaving other nodes un-visited for long periods. Chatzigiannakis et al. [16] suggested a clever distributed approach for avoiding the overlapping in the trajectories of mobile sinks, under the assumption that sinks do not need to know the geographical position of sensor nodes. To accomplish that goal, sinks leave an imprint (a trail of their movement) that, if detected by another sink, allows it to change its trajectory, giving preference to collect data from un-visited areas. In doing so, message delivery latency is significantly reduced. In another contribution, Chatzigiannakis et al. [17] suggested a centralized method, named Centralized Spatial Partitioning (CSP), for coordinating the movement of several mobile sinks. In a first step, the area to be sensed is divided in non-overlapping regions (rectangles) and one different mobile sink is made responsible for sensing each of them. To collect data from the sensors belonging to its assigned rectangle, each mobile sink repeatedly implements a snake-like movement over the rectangle (see [17] for details on how the movement is controlled). In doing so, CSP first assigns sensor nodes to regions and only then decides the trajectory of mobile sinks in each of them. Saad et al. [6] and Nakayama et al. [14] also proposed approaches that, like CSP, suffer from the lack of integration between the resolution of the clustering and the routing problems. Aiming to achieve an even distribution for the traffic load among cluster heads and prolong network lifetime, the approach in [6] also consists in first defining a set of clusters to be routed later. In the methods in [6], an implementation of the Bee’s algorithm is used to define the routes that visit the centroids of each cluster. As in other methods, the communication topology is chosen to guarantee that every cluster head will be at most one hop away from one mobile sink path. The method introduced in [14] (named KAT in that study) is quite similar to the method in [6] and to the SHS method in [40] (to be described, later, in detail). After clustering the sensor nodes using a scheme named Kmeans, a route spanning all cluster heads is found by a Traveling Salesman Problem (TSP) local search heuristic. One interesting feature of the KAT model is that the sink may vary its velocity, avoiding predictability of its movement and, thus, being safer with respect to external attacks. Basagni et al. [37] also proposed strategies for determining sink mobility. One centralized approach introduced in [37] is based on Linear Integer Programming techniques to determine optimal (with respect to network lifetime)

sink movements and soujorn times at cluster heads. The Integer Programming approach in Basagni et al. [37] can be viewed as an improvement over a previous study [43] by the same research group. This happens since, in the latter, the scheduling part of the problem (the order in which nodes should be visited by the mobile sink) was not addressed. In [43], the output of the model was only the necessary amount of time the sink should rest close to each node in order to collect and pass messages from/to the network. Since approaches based on Integer Programming Techniques are usually quite time consuming, Basagni et al. [37] also introduced a distributed heuristic, named Greedy Maximum Residual Energy (GMRE). In such method, sinks define their own trajectories giving preference to visit energy-rich areas. More precisely, the sink keeps monitoring surrounding areas in order to identify sensor nodes with higher energy. Once such nodes are found, the sink greedily moves to that direction to collect data. To our knowledge, only the ICRP approach introduced here and the methods proposed by Xing et al. [8] do integrate the resolution of the clustering and the routing problems in WSN. The approach in [8] is aimed at minimizing the energy consumption by a centralized network model, where message delivery latency is controlled by explicitly imposing constraints that guarantee that sink routes longer than a design parameter must be avoided. Xing et al. [8] stated the problem of defining a route for the sink as follows: Given a set of source (sensor) nodes, find a tour (that starts and returns to the same gateway point) no longer than a parameter L and a set of trees that are rooted at the vertices in the tour, such that the cost of the edges in the trees (which represent the Euclidean distance between the edge endpoints) is minimized. To solve such problem, Xing et al. proposed an approximation algorithm based on Minimal Steiner Trees, that jointly provides the cluster heads (the roots of the trees) and a tour (of length at most L) spanning them. Differently from the model in [8], ICRP explicitly minimizes message delivery latency while trying to keep low energy consumption by imposing one-hop communication protocols and implementing density control algorithms. In this sense, ICRP differ from the method in [8] by the way the multi-objective nature of WSN is addressed and by implementing DCP algorithms. One key difference among the approaches found in the WSN literature to address mobility and clustering issues is related to the amount of network information required to implement them. Clearly, the more information and data processing is needed, the less applicable the protocol is in 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 applicable in practice than other approaches. ICRP is indeed grounded on more restrictive assumptions than CSP, for example. This seems to be true since ICRP requires that each mobile sink knows the geographical position of each sensor node, while CSP does not. On the other hand, CSP cannot implement density control algorithms like those implemented by ICRP. Compared to the distributed algorithms in [16,37], CSP, ICRP, KAT and the Single Hop Strategy (SHS) introduced in

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

[40] are more restrictive to be implemented in practice. Nevertheless, more intensive information approaches like those outlined above may be quite important for the theoretical evaluation of WSN, to bound QoS parameters. Bearing in mind the differences on their applicability as well as the goals aimed by each method, distributed approaches are not going to be compared with ICRP. Instead, for benchmarking our method, we will compare results obtained by approaches that are more suitable for the off-line design of WSN: ICRP, CSP and SHS. Since KAT is very similar to SHS (their difference rely mostly on the clustering technique and on the TSP heuristic used to route the sink) and ICRP improves on SHS, the latter is described next, in detail. Aioffi et al. [40] proposed the Single Hop Strategy to establish a model for data dissemination, reception and transmission in WSN. In SHS, the sink communicates directly to every fixed sensor node; direct communication between sensor nodes is not considered. A single mobile sink is used to collect the sensed information and it is assumed that all sensor nodes locations are known by the sink. Only when the sink arrives at a certain cluster center (which in this case represents a cluster head), the communication between the sink and all the nodes covered by that cluster takes place. In the SHS method in [40], a two-step method was proposed 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 (a parameter that depends on the hardware being used) between the sink and the sensor nodes as its maximum radius. Once the clusters are defined, the second step follows by calculating the shortest Hamiltonian circuit spanning all cluster geometrical centers. In [40], the minimal number of clusters was found by solving an inverse pCenters problem [35]. Since the clustering and routing problems are not solved jointly, a minimal number of clusters does not necessarily imply minimal length routes. Additional gains in terms of message delivery latency could be attained, for example, by tackling the clustering and 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 multiple mobile sinks and hundreds of randomly deployed sensor nodes. The sensing area, modeled by a large square in the Euclidean plane, comprises discretized sets of small squares with uniform sensing requirements. It is assumed that the sinks know the geographical location of sensor nodes after their deployment in the sensing field. Aiming to cut down energy consumption, communication between sensor nodes is not allowed in the model (communication only takes place between sensor nodes and the sinks). Aiming to cut down message delivery latency, instead of visiting each sensor node, only a small set of them, called cluster heads, are visited. In addition, attempting to improve our previous results [3], we allow sinks to communicate with sensor nodes, while they move through the network, as follows. During its movement, at every one second, each sink broadcasts a message to in-

2807

form sensor nodes nearby that the sink is close and ready to receive their messages. Every sensor that gets the message and have stored data, starts transmitting its data to the sink. In this process, when the sensor actually sends the message, the sink may be already too far away and the message may be lost. This process is interrupted when the sink arrives at a cluster head, to avoid too much message collisions. Differently, when the sink is placed in a cluster head, it schedules a time interval for each sensor node within that cluster to send its data. ICRP can be described as follows. Given a set V = {1, . . . , n} of sensor nodes (active or idle, never dead) in the Euclidean plane and a set K ¼ f1; . . . ; Kg of mobile sinks, the problem we want to solve consists in finding K 2 Zþ routes, one for each mobile sink. Each route must span some sensor nodes, the cluster heads, in such a way that every sensor node in the network is either spanned by a route (the node is itself a cluster head) or lies within a distance no greater than R from a cluster head in one of the possible K routes. Note that the term cluster head has a slightly different meaning here. In [40], it was used to define the clusters geometrical centers which were the locations to be visited by the sink. Here, it defines a sensor node that will be visited by one of the sinks. Although in ICRP cluster heads are those nodes that are actually visited by the sinks, they are not assigned any special function in the 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 longest one is minimized. As K increases, the average message delivery latency is expected to decrease. Minimizing the longest route helps in balancing their lengths, so every sink will take more or less the same time to collect the information from the sensor nodes assigned to its route. An important assumption in the ICRP model is that the K different sinks start their movement at the same time, i.e., they are synchronized. If this were not the case, the network could be unbalanced, since a sensor node spanned by a shorter route would communicate more often with its sink than other nodes spanned by much longer routes. Therefore, the first sink that arrives at the initial spot must wait all the others in order to start a new cycle (a full walk of all sinks over their designed route). Although mobile sinks are ideally assumed to have plenty of energy, memory and processing capabilities, in practice, from time to time, they must return to a shared base station (a network gateway) to download data and to recharge their batteries. In our network model, we assume that a single gateway or depot is shared by all mobile sinks. It should be pointed out that this assumption implies no loss of generality in the proposed methods since if more depots were available, the optimization algorithms implemented here would still be valid for reducing message delivery latency. Under the knowledge of which sinks are assigned to which depots, the algorithms could be used to solve specific ICRP problems defined over smaller parts of the sensed region, like the CSP method in [17]. The differences between CSP and ICRP in that case would remain the same: an integrated resolution process for the clustering and routing problems would still be aimed in ICRP (with one sink for each smaller region that defines the sensing

2808

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

field) while in CSP, the trajectories of the sinks would not be determined by optimization methods. If each sink were assigned to a region of the sensing field and if sinks did not share the same depot, ICPR could be viewed, in some aspects, as an improvement over CSP since it defines the routes by means of optimization techniques that take into account the clustering and density control policies. 2.2.1. A graph-theoretic model for ICRP To present a graph-theoretic model for ICRP, we will make use a digraph D = (V, A) with set of vertices V (defined previously) 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 possible translations of the mobile sinks, moving from one cluster head to another. A cost dij P 0, proportional to the Euclidean 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, let x(i) :¼ {j 2 V : dij 6 R} (note that i 2 x(i)). A solution to ICRP in D is a collection of constrained K routes. Each route k starts in 1, spans a set Skn{1} of selected vertices and ends back at 1. We refer to the subgraph of D implied by each route k as Hk = (Sk, Ak). S Accordingly, H ¼ Kk¼1 ðSk ; Ak Þ denotes the subgraph associated to the whole set of K routes. In what follows, we say S that i– 2 Kk¼1 Sk is covered by j if there exists k 2 K such that j 2 Sk and i 2 x(j). Whenever this is the case, we also say that j is spanned by route k. If we define f ðHk Þ ¼ P ði;jÞ2Ak dij as the length of the k-route, the cost of a feasible solution 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 [

ðSk ; Ak Þ;

ð1Þ

k¼1

such that 8k 2 K : Ak induces a Hamiltonian circuit spanning Sk ; Si \ Sj ¼ f1g;

8i; j 2 K; i–j;

8i 2 V : either i 2

K [

ð2Þ ð3Þ

Sk or

k¼1

9j 2 V n fig : j 2

K [

Sk ; i 2 xðjÞ:

ð4Þ

k¼1

Note that (2) imposes that the depot is the only common vertex spanned by any pair of routes and that (3) guarantees that each vertex is either a cluster head or it is covered by one cluster head. ICRP is clearly NP-Complete, since the Traveling Salesman Problem [9,31] is one of its special cases, when K = 1 and x(i) = {i}, "i 2 V. To the best of our knowledge, the VRP variant closest to ICRP is that discussed by Glaab [12]. In that reference, the author introduces a Vehicle Routing Problem that arises in the design of a semi-automatic system for cutting leather skins. As in ICRP, one has to minimize the longest route length and the fleet size is fixed. However, ICRP differs from that VRP variant in two aspects: in [12] all customers need to be visited and each vehicle starts its route from a different depot. Lower bounds in that application were

obtained by replacing the min–max objective function by the average route length to later formulate and solve combinatorial relaxations based on matchings and one-trees. Due to its selective nature, other Combinatorial Optimization Problems that also relate to ICRP are the Covering Tour Problem [30] (CTP) and the Generalized Traveling Salesman Problem [29] (GTSP). Contrarily to ICRP which involves multiple vehicles, GTSP and CTP seek optimal routes for a single vehicle. In CTP, there are two sets of vertices: those that must be visited (covered) by any feasible tour and those that may be visited in order to lower the cost of connecting the former set. In GTSP, on the other hand, the vertices of the graph are previously partitioned into clusters. The problem seeks a tour that visits exactly one vertex of each cluster, at minimal cost. In [30,29], Linear Integer Programming formulations, Branch-and-cut algorithms and heuristics were proposed for CTP and GTSP, respectively. 3. Metaheuristic based heuristics for ICRP In a recent paper [5], we have provided two exact solution approaches (a Branch-and-cut algorithm [33] and a Local Branching method [28]) for ICRP, based on Linear Integer Programming techniques. According to the findings in [5], ICRP is indeed very difficult to solve to proven optimality, mainly when K and n increase. Although the network model introduced here is aimed at the off-line evaluation of WSN, we do not use the exact solution approaches in [5] to solve ICRP. The sizes of the instances we plan to investigate here (with up to 600 sensor nodes) are out of reach for the exact solution procedures introduced in [5]. Our choice to resort to heuristics is motivated by the fact that the huge time requirements for finding reasonably good solutions to ICRP by the exact methods in [5] preclude their use in a simulation environment for WSN, where several rounds of routing and clustering decisions should be taken and the simulation clock is not stopped to run optimization algorithms. The optimization algorithms implemented here are hybrid implementations of GRASP [39] and of Iterated Local Search (ILS). They combine a constructive phase and three main operators: two Local Search procedures and a diversification mechanism. Depending on how these methods are combined and controlled, different metaheuristics with varying levels of intensification and diversification, better suited for WSN applications with a single or multiple mobile sinks, arise. Some GRASP implementations discussed here were combined into a sophisticated (and more time consuming) 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 of completeness, in the sequence, we review the main ingredients of the metaheuristics. 3.1. Constructive heuristic The constructive heuristic designed here is based on the Cheapest Insertion Algorithm (CIA) [2] proposed for the Euclidean Traveling Salesman Problem. For the sake of clarity, let us first describe how CIA operates for the TSP

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

defined on a set of n vertices and distance matrix d. The main idea in CIA is to iteratively construct a tour spanning the n vertices, in a process that builds a tour involving r 6 n vertices from a previous one that includes only r  1. More precisely, at any given CIA iteration, let S; S respectively be the set of nodes spanned by the tour in hands and its complement in V. Assume that p 2 V is visited right after i 2 V in the current tour. The selection policy that chooses a node to be inserted into the partial solution is based on the cheapest insertion rule. For any j 2 S, let Djip :¼ dij þ djp  dip denote the cost of inserting j between i and p. Accordingly, let Dj :¼ minfDjip : i; p 2 S; p is visited right after ig denote the minimum increment cost of inserting j in S, considering all possible insertion positions. The inserted vertex is actually z 2 arg minfDj : j 2 Sg. Ties are broken arbitrarily. The algorithm then inserts z between the vertices i and p for which the optimal value Dz was attained and removes z from S. This process goes on until S ¼ ;. The adaptation of this constructive procedure to ICRP, resulting into algorithm CIA_ICRP, is straightforward. To understand how this is carried out when K = 1, let us first redefine S as the set of cluster heads and S as the set of vertices that are not covered by any vertex in S, i.e. S S ¼ V n i2S xðiÞ. 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 necessary. In such situation, our algorithm constructs K P 2 routes simultaneously, adding one cluster head at a time to one of them. Since the goal is to build a set of routes where the length of the longest one is minimized, we always insert a new cluster head in the route that has the shortest length. The insertion policy and the stopping criteria are the same whenever K = 1 or K P 2. 3.2. Main operators In order to improve the initial solutions obtained by our constructive heuristic, two Local Search (LS) procedures (2-OPT [7] and 2-SWAP [41]) and a diversification mechanism (the Nodes Reinsertion Algorithm, NRA [11]) were implemented and tested. Given a feasible solution to ICRP, 2-OPT is always applied to the longest of the K routes. It works by removing two arcs from the route and then trying to reconnect the resulting two paths using less expensive arcs. If the length of the route becomes smaller than the length of any other route in the solution, the search switches to the new longest one. 2-OPT implemented here makes use of the Don’t Look Bits neighborhood reduction [20] to cut down CPU running times. In 2-SWAP, we try to improve the solution by swapping nodes from their routes. Assuming that two cluster heads p 2 Sk1 and q 2 Sk2 are given, one replaces p by q and q by p. Note that after swapping the two vertices, only two sets of cluster heads change: Sk1 becomes ðSk1 n fpgÞ [ fqg and Sk2 becomes ðSk2 n fqgÞ [ fpg. In case k1 = k2, only the visiting order of p and q is changed. One weakness of the previous search procedures is that the whole set of cluster heads is preserved after their application; no clusters heads are added or removed from the

2809

whole set of cluster heads, although due to 2-SWAP, they may swap routes. To overcome this weakness, we also make use of the Nodes Reinsertion Algorithm [11]. In order to explore a broader solution space, our implementation of NRA has two phases. In the first one, we attempt to remove one cluster head a time from each route, according to a given probability. Whenever a cluster head p 2 Sk (together with its incident arcs) is removed from route k, the two neighbors of p in the route are joined by an arc, in order to establish a Hamiltonian circuit spanning the remaining set of cluster heads Skn{p}. After the last removal operation, the second phase starts. Since the set of routes obtained after the first phase is not necessarily feasible (S may be not empty), we apply CIA_ICRP to recover feasibility. In doing so, cluster heads different from those that were removed in the preceding phase will be possibly added, generating a new feasible solution. 3.3. GRASP and Iterated Local Search In this Section, it is shown how the constructive procedure and the main operators presented previously are embedded in various algorithmic frameworks in order to improve their performance and robustness. Depending on how the procedures described in Sections 3.1 and 3.2 are guided to explore the solution space, different Metaheuristic based heuristics for the ICRP arise: three hybrid GRASP [39] implementations and an Iterated Local Search method [13]. GRASP (Greedy Randomized Adaptive Search Procedure) is a class of stochastic search algorithms that uses randomized greedy constructive search heuristics to generate a large number of different candidate solutions. In each GRASP iteration, the solution obtained with the randomized constructive phase is submitted to a local search procedure [13]. This two-phase process is iterated until a termination criterion is satisfied; usually, after a maximum number of iterations are performed. All three hybrid GRASP proposed here share the same randomized implementation of CIA_ICRP, followed by 2-OPT. In each iteration, after a local optimum within the 2-OPT neighborhood is found, another Metaheuristic is applied to that solution. Therefore, depending on which Metaheuristics are called after 2-OPT, different hybrid versions of GRASP appear. The algorithm outlined in Fig. 1 indicates the main steps of our hybrid approach. All differ only in step 7 in Fig. 1. Before describing how GRASP was hybridized, let us first discuss how its constructive phase works. To that  ðjÞj : j 2 Sg as the minimum aim, define D ¼ minfDj  kjx cost of adding a new cluster head to the route in hands. Instead of choosing the vertex s for which D is attained to add to the route, in the randomized version of CIA_ICRP, one randomly chooses any sensor node j 2 S whose corre ðjÞj lies in the interval [D, sponding value of Dj  kjx (1 + a)D], where parameter a P 0 controls the level of randomization of the procedure. Actually, since a is not kept constant during all GRASP iterations, our procedure is a reactive GRASP (see [32] for details). In our implementation, at the first GRASP iteration, a is randomly chosen from the set {0.05, 0.10, . . . , 0.50} with uniform probability.

2810

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

perturbation phase in ILS. The ILS implementation used in this hybrid version also differs from that used in GRASP-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 given by CIA_ICRP. The perturbation step and the Local Search procedures used are NRA and 2-OPT, respectively. 3.4. Optimization results Fig. 1. Algorithm outline of the hybrid GRASP.

As the algorithm evolves, higher probabilities are assigned to those values of a that result in higher quality solutions. In our first GRASP procedure, named GRASP-ILS, an Iterated Local Search Method is implemented in step 7 of Fig. 1. The main idea of ILS is to use perturbations to allow escaping from local optimum solutions. Briefly, ILS is a randomized algorithm that, first, applies a Local Search procedure to a feasible solution to the problem being solved. In the sequel, the local optimum is submitted to a perturbation procedure, originating a new intermediate solution. Then a Local Search step takes place once again: the LS procedures are applied to this intermediate solution, obtaining a (possibly) new local optimum. This process of alternating LS and perturbation steps goes on until a satisfaction criterion is met. In our case, 2-SWAP is used as the perturbation phase and 2-OPT is the inner LS method. This two-step procedure runs until a certain number of iterations are conducted without improving the best solution found. GRASP-VND, the second hybrid procedure proposed here, implements a Variable Neighborhood Descent (VND) [34]. Roughly speaking, VND is a local search method based on the idea of iteratively switching neighborhoods during the course of the algorithm. The neighborhood structures are ordered according to their size (complexity): smaller (cheaper) neighborhoods precede larger (more expensive) neighborhoods. Accordingly, one first performs a Local Search algorithm exploring a cheaper neighborhood. Once a local minimum (w.r.t. the current neighborhood) is found, a Local Search algorithm based on the next larger neighborhood starts. In this process, whenever an improved solution is found, the search restarts from the simplest neighborhood. The two neighborhoods explored in our GRASP-VND algorithm are 2-OPT and 2-SWAP. Accordingly, after step 6 in Fig. 1, we apply 2-SWAP. If a better solution is found, we resort back to 2-OPT and the procedure goes on, until the best solution in hands is found to be a local minimum in both neighborhoods. Although the two previous hybridized versions make use of the same operators, GRASP-VND, unlike GRASP-ILS, performs a full scan over the analyzed neighborhoods. Due to this reason, typical iterations of GRASP-ILS are performed faster than GRASP-VND counterparts. Consequently, more initial solutions are generated by GRASP-ILS, while deeper searches on less solutions are performed 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 the method. This is accomplished by using the NRA as the

In this Section, we report on our computational experience with the Metaheuristics presented previously. Our purpose here is to validate one or more algorithms to be used in a dynamic context, for example, in a simulation framework to WSN. All computational testings were conducted 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 instances (each one representing an initial WSN configuration) were generated. The instances considered here have n varying from 50 to 600 sensor nodes, randomly spread over a sensing area represented by a square in the plane. In order to test dense and sparse networks, we kept the area and the communication range R respectively fixed to 40,000m2 and 30 m. For each value of n and K 2 {1, 2, 3, 4}, 33 different instances were randomly generated. Therefore, computational results presented for a given pair of n and K are average values attained for 33 instances. All algorithms proposed here, CIA_ICRP, GRASP-ILS, GRASP-VND, GRASP-ILS/VND and ILS, were run with the same set of 33 instances for each pair n, K. In order to address the quality of the solutions provided by the Metaheuristics, these algorithms were compared against 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 different sensor node. We also imposed the same CPU time limit of 60 s on all procedures running times. Therefore, one can judge the merits of each algorithm only in terms of solution quality. When deciding for this parameter, we considered a realistic situation where the sink may have a time limit of 60 s (no matter the network size) to find the best possible solution to the problem. In Table 1, we present the main computational results attained by each heuristic. In the first two columns of Table 1, we respectively indicate the number of mobile sinks and the network size. In the next column (under headings CIA_ICRP), we present f , the average (over 33 instances for each pair n, K) shortest longest route length obtained for the n  1 different runs of CIA_ICRP. In the next columns, we present average results attained by each Metaheuristic. For each one (GRASP-ILS, GRASP-VND, GRASPILS/VND and ILS), two entries are given: the average length f of the longest route and the implied reduction in f when compared to the solution found by CIA_ICRP. For example, for K = 1, n = 50, the longest routes found by GRASP-ILS/VND are, on the average, 5.9% shorter than

2811

W.M. Aioffi et al. / Computer Networks 55 (2011) 2803–2820 Table 1 Average longest route lengths. Instance

CIA_ICRP

Grasp-ILS

f

f

Gain

f

Gain

f

Gain

f

Gain

1

50 100 150 200 250 300 350 400 450 500 550 600 Average rate

793.3 878.9 914.8 914.3 939.8 939.2 953.8 960.6 961.7 968.6 972.1 994.8

757.3 831.0 869.9 869.8 899.5 903.6 921.2 928.1 935.3 942.2 948.7 963.1

4.5% 5.4% 4.9% 4.9% 4.3% 3.8% 3.4% 3.4% 2.7% 2.7% 2.4% 3.2% 3.8%

756.0 821.4 859.9 866.4 895.6 901.5 925.2 939.4 945.8 947.8 962.5 977.7

4.7% 6.5% 6.0% 5.2% 4.7% 4.0% 3.0% 2.2% 1.7% 2.2% 1.0% 1.7% 3.6%

746.2 803.4 837.6 840.6 875.3 885.8 904.3 917.0 923.2 926.0 939.5 954.7

5.9% 8.6% 8.4% 8.1% 6.9% 5.7% 5.2% 4.5% 4.0% 4.4% 3.3% 4.0% 5.8%

763.0 832.5 848.6 851.6 864.2 869.3 887.6 890.8 887.0 894.7 902.4 912.5

3.8% 5.3% 7.2% 6.9% 8.0% 7.4% 6.9% 7.3% 7.8% 7.6% 7.2% 8.3% 7.0%

2

50 100 150 200 250 300 350 400 450 500 550 600 Average rate

516.2 561.3 573.6 568.3 590.4 589.5 595.9 599.8 598.0 614.2 607.9 619.8

467.6 512.2 521.2 521.3 541.7 544.7 557.8 562.8 566.3 576.0 578.6 594.8

9.4% 8.7% 9.1% 8.3% 8.3% 7.6% 6.4% 6.2% 5.3% 6.2% 4.8% 4.0% 7.0%

464.5 506.2 512.8 511.7 532.3 535.6 549.5 554.2 558.8 565.4 568.9 578.2

10.0% 9.8% 10.6% 10.0% 9.8% 9.2% 7.8% 7.6% 6.6% 7.9% 6.4% 6.7% 8.5%

460.7 495.5 499.6 498.2 513.5 518.7 528.3 537.4 539.4 541.8 545.9 558.1

10.8% 11.7% 12.9% 12.3% 13.0% 12.0% 11.4% 10.4% 9.8% 11.8% 10.2% 9.9% 11.4%

485.8 520.1 523.1 520.9 536.1 538.4 544.0 547.2 548.0 555.4 554.7 565.9

5.9% 7.3% 8.8% 8.4% 9.2% 8.7% 8.7% 8.8% 8.4% 9.6% 8.7% 8.7% 8.4%

3

50 100 150 200 250 300 350 400 450 500 550 600 Average rate

451.7 480.8 483.1 483.9 505.9 495.5 507.5 512.0 515.2 513.8 513.8 529.5

397.2 429.4 431.5 433.5 452.6 452.3 467.1 467.6 473.0 474.3 474.7 491.5

12.1% 10.7% 10.7% 10.4% 10.5% 8.7% 8.0% 8.7% 8.2% 7.7% 7.6% 7.2% 9.2%

395.3 422.9 420.9 422.8 435.1 435.8 449.8 451.4 455.6 452.7 456.2 469.7

12.5% 12.0% 12.9% 12.6% 14.0% 12.0% 11.4% 11.8% 11.6% 11.9% 11.2% 11.3% 12.1%

393.7 417.1 410.6 410.5 422.3 423.1 433.4 436.6 437.5 435.7 432.0 449.7

12.8% 13.3% 15.0% 15.2% 16.5% 14.6% 14.6% 14.7% 15.1% 15.2% 15.9% 15.1% 14.8%

419.6 445.5 442.7 446.5 456.2 454.0 465.5 464.9 472.5 468.3 471.5 479.6

7.1% 7.3% 8.4% 7.7% 9.8% 8.4% 8.3% 9.2% 8.3% 8.8% 8.2% 9.4% 8.4%

4

412.5 441.7 436.7 438.5 461.5 450.5 468.9 466.6 467.7 473.7 457.3 478.0

366.8 396.3 390.1 394.3 411.4 407.6 420.0 423.3 426.5 425.1 420.4 438.9

11.1% 10.3% 10.7% 10.1% 10.9% 9.5% 10.4% 9.3% 8.8% 10.3% 8.1% 8.2% 9.8%

364.8 391.7 382.6 386.0 395.6 393.9 405.2 406.0 407.6 407.3 395.3 419.6

11.6% 11.3% 12.4% 12.0% 14.3% 12.6% 13.6% 13.0% 12.8% 14.0% 13.6% 12.2% 12.8%

364.4 388.0 376.1 377.1 386.5 383.4 392.6 391.5 392.7 389.7 379.3 402.9

11.7% 12.1% 13.9% 14.0% 16.2% 14.9% 16.3% 16.1% 16.0% 17.7% 17.1% 15.7% 15.1%

391.4 420.5 406.1 411.5 420.0 415.4 435.3 431.7 429.8 434.5 421.8 439.8

5.1% 4.8% 7.0% 6.2% 9.0% 7.8% 7.2% 7.5% 8.1% 8.3% 7.8% 8.0% 7.2%

K

n

50 100 150 200 250 300 350 400 450 500 550 600 Average rate

Grasp-VND

the average shortest longest route found when CIA_ICRP is used alone. Results in Table 1 indicate that the best improvements over the solutions found by CIA_ICRP were attained by ILS, when K = 1, and by GRASP-ILS/VND, when K P 2. As K increases from 1 to 4, all other solution approaches work much better than ILS. An important difference between ILS and GRASP is that ILS works always on the same initial solution, while GRASP generate new solutions at

Grasp-ILS/VND

ILS

each iteration. When K = 1, ILS seems to achieve a good balance between intensification and diversification, thanks to NRA. Apparently, when more sinks are used, NRA alone was not able to provide enough diversification. In such cases, it seems that the diversification provided by the multi-start structure of GRASP, allowed better routes to be found. Nevertheless, one can infer that NRA had a remarkable importance on the gains attained for ILS and GRASP-ILS/VND over the other Metaheuristics. This

2812

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

seems to be true since the best algorithms for each case (K = 1 and K P 2) implement NRA, while none of the others does. Based on the results reported above, ILS and GRASPILS/VND were the chosen algorithms (respectively, for K = 1 and K P 2) to solve ICRP in a simulation framework for WSN. 4. WSN simulation In many complex dynamic systems, like in WSN, it is very difficult to exactly capture the relationships and interactions of the system entities in strict mathematical equations. Therefore, a Discrete Event Simulator was the tool of our choice to evaluate how ICRP compares to other approaches 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, we developed a WSN framework built over the JIST/SWANS simulator [26]. The transmission, energy, sensing and storage protocols are already built-in the SWANS procedure. Apart from that, in the hope of improving the overall behavior of the network, we incorporated other important features into the framework: algorithms to address both ICRP and DCP (see [40] for details on how DCP is modeled and solved). Results obtained for SHS and ICRP presented here differ from results respectively reported in [40,3] since in this paper, for both methods, we allowed sinks

to communicate to sensor nodes while they move through the network (communication is not restricted to take place when the sink arrives and stops at a cluster head). The simulation model we present for WSN comprises a set of cyclic operations performed by each sink. In Fig. 2, a flowchart of the simulation process is depicted. The first simulation cycle starts with the ICRP resolution, right after the sensor nodes deployment. After the design of the first set of routes, DCP is solved. Each sink then starts its movement throughout the network. Using recent technologies and supported protocols for the MAC layer [23,27], sensor nodes can be kept in very low power levels (idle state), where no sensing functions are performed, but being able to turn into a full operating state, whenever an appropriate stimulus from the outside environment is received. Therefore, during their movement throughout the network, sinks collect sensed information and also deactivate and activate some sensor nodes, according to the density control policies. In this process, the sinks become aware of the energy state of all nodes in their routes. When all sinks have returned to the depot, the energy state of all nodes is available. If any sensor node died during the previous cycle, another solution to the new resulting ICRP is searched. The rationale to recompute the routes is to try to shorten the longest one since new dead nodes no longer need to communicate to the sinks. The newly found set of routes, however, are implemented only if the new longest route is shorter than the previous one. Given

Fig. 2. Simulator flow diagram.

2813

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

the energy state of the network in hands, no matter if ICRP was solved again or not, we solve DCP once again, and another simulation cycle takes place. Since the routes were computed before the density control algorithms are called, one weakness of our approach is that sensor nodes that remain idle in two consecutive simulation cycles keep being visited by the set of routes. On the one hand, visiting sensor nodes that remain idle during two or more consecutive cycles unnecessarily increases route lengths. On the other hand, it allows us to have a full appreciation of the energy state in the network. Accordingly, better density control policies can be implemented if one has more realistic energy information in hands. This is the reason why we solve ICRP before DCP. The downside of the use of synchronized mobile sinks is that it may impose higher average message delivery latency rates. On the positive side, it allows an easy centralized implementation of the density control policies that may result in benefits for the overall behavior of WSN. In our model, after one of the K sinks solves both ICRP and DCP, all other sinks become aware of their routes as well as the set of vertices they should activate or deactivate during the next cycle. This is another reason why the resolution of ICRP must take place before the resolution of DCP. Another factor that may increase message delivery latency is the time taken to run the optimization algorithms themselves, since the simulation clock does not stop while they are executed. Therefore, in order to limit from above the 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 sensor nodes become dead), a tighter time limit of 2 s is imposed. One might consider that the 60 s necessary to calculate the route at the first cycle will affect negatively the average message delivery latency. However, since this calculation takes place only once, its impact on the first cycle (which cannot be neglected) will be diluted through the next cycles. As our computational results demonstrate, the gain obtained when using our optimization algorithms in cutting down average message delivery latency during the entire simulation time more than makes up for this initial overhead. The simulation parameters chosen in our study were set according to the commercially available Mica2 nodes [42] (see Table 2). For the particular application described here, it was assumed that sensor nodes periodically collect information encoded using 32 bits, at a constant rate of 1/20 Hz. Since their memory board can store up to 4 Kbytes, sensors have autonomy of 14 h of data collection. The MAC layer is the IEEE 802.11 available in SWANS simulator, as the Mica2 nodes implements a CSMA/CA protocol. All methods implemented and tested in our study, namely ICRP, SHS and CSP, make use of IEEE 802.11.

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

Table 2 Main simulation parameters. Parameter

Value

Parameter

Value

Sensor energy

50 mA h

8.9 mA

Sensing range Data acquisition board Sink speed Communication range Bandwidth

15 m 5 mA

Transmission power Reception power Radio idle power

1 m/s 30m

Processor power Sensed area

8 mA 40,000m2

7 mA 7 lmA

250 kbps

In the sequel, we evaluate how the WSN operating under the ICRP model compares to the SHS approach [40] and to the CSP method [17]. As we pointed out before, ICRP (as well as SHS and CSP) are not going to be compared to distributed approaches, for example, like those proposed in [16]. The comparisons are conducted by measuring four important network parameters: the message delivery latency, the network coverage and lifetime and, finally, the ratio of messages received. For comparing SHS and ICRP, K was considered in the set {1, 2, 3, 4}. CSP was not simulated for K = 3 since, in [16], no guidelines were given on how to divide the sensing field into rectangles when K P 2 and K is odd. For evaluating the message delivery latency, the ratio of messages received and the network lifetime, the maximum simulation time was set to 15 h. For evaluating the network coverage, on the other hand, this parameter was extended to 25 h. Longer simulation times were used in this case because we found that after 15 h, the coverage was still very high for SHS and ICRP. Similar behavior was not observed by CSP since, contrarily to SHS and ICRP, it does not implement density control algorithms.

4.1.1. Message delivery latency and the ratio of messages received In applications where the sensed information is generated almost on a regular basis or else at high rates (not on demand, nor on an event basis), message delivery latency must be low, in order to avoid loss of data due to the limited storage capacity of sensor nodes. In Fig. 3, we indicate how the message delivery latency behave as a function of the number of sensor nodes. Eight curves are presented in Fig. 3: one for the SHS approach (which considers only one mobile sink), one curve for each value of K 2 {1, 2, 3, 4} for model ICRP and one curve for each value of K 2 {1, 2, 4} for model CSP. By comparing the SHS results against those attained by ICRP when K = 1, we observe that the latter attained better results. As one can appreciate from the figure, the rate in which the message delivery latency increases as n grows is lower for ICRP. When n = 50, both approaches have similar average latency rates. However, as n grows up to 600, the average latency attained by ICRP grows less than what is observed in method SHS. As one could expect, using more mobile sinks also helps reducing the average latency rates. Significant reductions were attained when multiple mobile sinks were used.

2814

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

400

Message delivery latency (seconds)

350 ICRP/K=1 ICRP/K=2 ICRP/K=3 ICRP/K=4 SHS CSP/K=1 CSP/K=2 CSP/K=4

300

250

200

150

100

50

0

100

200

300

400

500

600

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

ICRP was capable of providing lower rates of message delivery latency than CSP for K = 1 and for K = 2 when n 6 400. For K = 2,n > 400 ICRP and CSP obtained comparable message delivery latency rates. However, higher rates were attained for ICRP when K = 4. The advantage of CSP over ICRP for K = 4 is strongly influenced by the shape of the sensing area, which is represented by a square of 200  200 meters. With K = 4, each sink in model CSP is in charge of sensing a square of 100  100 m. Since the communication radio is 30 m, the entire sensing region is almost covered if the sink is placed in the midle of the square. Based on the fact that ICRP/K = 1 obtained smaller message delivery latency rates than CSP/K = 1, the advantage of CSP over ICRP should vanish if sensors are not placed uniformly over the sensing region or when the communication radius is not so large compared to the side of each square in CSP model. Worse results in terms of message delivery latency when K = 4 can be explained by an additional aspect: ICRP, contrarily to CSP, makes use of a single depot (in ICRP, it is always chosen to be vertex 1 2 V, irrespective to any property of the region being sensed-a position in the midle of the region would imply better message delivery latency). Since ICRP performed better than CSP when K = 1, it seems reasonable to conjecture that if the ICRP/K = 1 model were applied to each one of the four squares that (together) represent the sensing field in the CSP model when K = 4, better results in terms of message delivery latency would be attained. On the positive side, the proportion of messages that actually reach the sinks is much greater for ICRP (as well as for SHS), compared to CSP. In Fig. 4, we depict for each model, the ratio of messages received, i.e., the number of messages that reached one mobile sink divided by the total number of messages generated at the end of a given simulation time. This is a consequence of the fact that, in ICRP, when the sink is at a cluster head, sensor nodes send their data in scheduled time intervals.

Let us now address the impact of the use of better or worse optimization algorithms (w.r.t. the longest route length) on the message delivery latency. To that aim, we simulated the network behavior when CIA_ICRP (under similar CPU time limit constraints) replaces ILS (when K = 1) and GRASP-ILS/VND, (when K P 2) as the resolution method to ICRP in the simulator. Results of such comparisons are depicted in Fig. 5. For each value of K, we depict two curves: one obtained when the best optimization algorithm (ILS or GRASP-ILS/VND) was used and the other when CIA_ICRP was considered. We found that when K = 1, on the average, the use of the best optimization algorithm tested (ILS) implied a reduction of 10% on the average message delivery latency. Similar gains around 15%, 18% and 15% were achieved when GRASP-ILS/VND procedure is used instead of CIA_ICRP in the simulation framework, respectively for K = 2, 3, 4. Note that the latencies obtained by GRASP-ILS-/VND with K = 3 were lower than those obtained when CIA_ICRP was used with K = 4 mobile sinks. As these results suggest, the design of higher quality optimization algorithms to tackle ICRP pays off. 4.1.2. Network coverage The next QoS parameter studied here is the network coverage, i.e., the percentage of the monitoring area that is sensed by at least one sensor node in a given simulation time. In Fig. 6, we indicate how network coverage changes as the simulation clock goes on (for at most 25 h), for networks with n = 400. The use of ICRP with K = 1 allowed an increase of 19% in coverage when compared to SHS (37% of coverage against 31%), at the end of the simulation time. The reasoning for that is related to the frequency in which more up to date density control policies are implemented. Since ICRP longest routes are shorter than SHS counterparts, the number of simulation cycles performed in a certain amount of time tends to be higher for ICRP. More cycles being executed

2815

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

100

Messages received rate (%)

98

96

94

92

90

88

86

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

100

200

300

400

500

600

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

450

Message delivery latency (seconds)

400

350

ILS/K=1 GRASP−ILS−VND/K=2 GRASP−ILS−VND/K=3 GRASP−ILS−VND/K=4 CIA_ICRP/K=1 CIA_ICRP/K=2 CIA_ICRP/K=3 CIA_ICRP/K=4

300

250

200

150

100

50

100

200

300

400

500

600

Number of sensors 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 control algorithm to be executed more often, being thus more efficient. Another aspect that should be raised is that, after 5 simulation hours, the coverage rates for both SHS and ICRP drop from almost 100% to nearly 90% and then, a little bit later, increase again. These drops in coverage rates occur when the first set of sensor nodes die. Therefore, coverage rates remain a bit lower until all sinks return to the base, DCP is run again and new density control policies are implemented. Since ICRP routes are shorter, the network remains shorter periods of time under lower cover-

age rates. This is confirmed by the figure, since all curves drop more or less at the same time, but ICRP with K = 4 recovers coverage much faster than other methods. Similar fast falls followed by fast recovers of coverage rates occur again, after around 11 h of simulation. Note that in Fig. 6, the coverage rates for the CSP model is zero, after 5 h of simulation. In practice, after 5 h, all sensor nodes were already dead, i.e., all sensor nodes had depleted their batteries entirely. Significantly higher coverage rates were attained by ICRP due to the implementation of the density control algorithm. For the CSP case, the increase on the number of mobile sinks imply higher cov-

2816

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

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

0.9 0.8

Coverage

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

5

10

15

20

25

Time (h) Fig. 6. Network coverage, n = 400.

of time. In other works, the time required for the total energy to drop below 50% of the initial energy is used. In this study, the first two of these metrics are evaluated. As it will be shown, they have to be considered together, in order to fully appreciate the benefits and drawbacks of a particular protocol. In Fig. 7, we present how the network lifetime varies as a function of n and in Fig. 8, we show the percentage of the total initial energy that remains available during the simulation. Fig. 8 was generated for n = 400. As it can be appreciated from Fig. 7, the network lifetime remains almost unchanged when the number of nodes rises up to 400. After that point, for ICRP and SHS, a sharp increase in network lifetime is observed. Consider-

erage rates. Contrarily to what one may expect, for the ICRP case, the use of more mobile sinks does not systematically improve the coverage rates, for longer periods of simulation. Explanations for that will be given in the next section, together with the analysis of network lifetime. 4.1.3. Network lifetime In the literature, different metrics are used to measure how efficient the network is in terms of energy consumption. According to some authors [38], the best metric to measure the energy efficiency is application dependent. Some evaluation metrics usually considered in the literature are: the network lifetime (the elapsed time until the first node dies) and the overall energy spent during a defined period 340

320

300

Time (m)

280

260

240

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

220

200

180

100

200

300

Number of sensors Fig. 7. Network lifetime.

400

500

600

2817

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

100

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

90

Network Residual Energy (%)

80 70 60 50 40 30 20 10 0

0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h) Fig. 8. Network Residual Energy, n = 400.

ing the sensing area represented by our instances, networks with 400 or less nodes are indeed sparse. Therefore, it is very likely that a certain discretized part of the sensing area is covered by only one sensor node. However, for larger values of n, every discretized part is typically covered by more than one sensor node. Consequently, the density control implemented here is more likely to increase the network lifetime. Since for CSP density control algorithms are not implemented, the network lifetime remains almost constant for the entire range of network size considered here. Because of that, the network lifetime observed for CSP is always much lower than for SHS and for ICRP. Note that ICRP provides higher lifetime than SHS, for all values of n. Therefore, one could possibly argue that, based on network lifetime alone, ICRP also allowed gains in energy consumption when compared to SHS. To address this issue properly, two other parameters need to be considered: the fraction of the total initial energy that remains available during the simulation time (see Fig. 8) and the percentage of dead sensors as a function of time (see Fig. 9). Figs. 8 and 9 indicate that ICRP energy consumption is indeed higher when compared to SHS. The number of dead sensors is also higher when ICRP is used. Higher energy consumption rates occur since shorter ICRP routes imply that sensor nodes communicate more often with the sinks. Since for the application considered here, information is sensed at low rates (32 bits at 1/ 20 Hz), just a tiny fraction of the sensor memory is actually used at each transmission. Therefore, the energy spent per transmission at the MAC layer is pretty much the same for SHS and ICRP, irrespective of the volume of data being transmitted. Since more transmissions take place when ICRP is used, more energy is spent. This also explains why coverage levels decrease when more sinks are used in ICRP. Clearly, these experiments indicate how little value the network lifetime alone has to capture the overall behavior of WSN in terms of energy efficiency.

We must point out that, however, the advantage of SHS over ICRP in terms of smaller energy expenditures should vanish in other applications, where messages are generated at much higher rates and, consequently, node memory becomes a concern. For the particular application treated in this study, thanks to the density control algorithms, higher energy expenditure levels of ICPR did not imply worse coverage rates, as it could be expected. Nevertheless, ICRP could be easily adapted in order to achieve a better balance between energy consumption and delay rates. That could be accomplished by imposing that all mobile sinks should wait a minimum amount of time at the central station, before the beginning of a new simulation cycle. We must stress that, when message delivery latency is analyzed together with energy related parameters, the trade off between energy consumption, message latency and network lifetime becomes very clear. For networks with n = 400, the average latency for ICRP with K = 4 is around 30% of the corresponding SHS figures, whilst only 50% of the remaining SHS energy was available for ICRP at the end of the simulation time. Considering that our primary goal was to reduce SHS message delivery latency in networks with mobile sinks without incurring in excessive coverage losses, we claim that ICRP allowed us to achieve the goals we aimed for. Compared to CSP, on the other hand, ICRP performed worse when more mobile sinks (K = 4) were used. However, ICRP is capable to allow the network to operate for much longer periods of time; this one being, certainly, one of the primary goals of any network designer. One may argue that the advantages of ICRP over CSP for QoS parameters other than message delivery latency are due mostly to the implementation of density control algorithms. Although ICRP benefits a lot from it, in our view, advantages of ICRP over CSP cannot be resumed to that. To substantiate this claim, we should point out

2818

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

100 ICRP/K=1 ICRP/K=2 ICRP/K=3 ICRP/K=4 SHS CSP/K=1 CSP/K=2 CSP/K=4

Dead Sensors (%)

80

60

40

20

0

2

4

6

8

10

12

14

16

18

20

22

24

Time (h) Fig. 9. Percentage of dead sensors, n = 400.

that ICRP is better suited for WSN in which sensor nodes are not deployed uniformly over the area being sensed. Since the resolution of the clustering and routing problems is conducted as a result of an optimization process, ICRP is likely to behave better than CSP for networks where the density of sensor nodes varies too much. Being adaptive, ICRP is also likely to behave better when the configuration of the network changes, for example, when some sensor nodes die and the network becomes sparser. In CSP, clustering is done by dividing the area to be sensed into rectangles having, ideally, the same area. Routing, on the other hand, is always done in the same way since mobile sinks always perform a predictable snake-like movement. Thus, QoS parameters like network coverage and rate of messages received may deteriorate even further when the whole area to be sensed is difficult to be split into rectangles where a snake-like movement can be easily implemented and when the density of sensor nodes vary significantly. 5. Concluding remarks and future research In this paper, we presented optimization algorithms and a simulation framework for Wireless Sensor Networks with multiple mobile sinks. Since sink speed is much slower than communication between sensor nodes, higher message delivery latency is expected for this type of network topology. Traditional approaches to deal with this undesired feature are the use of clustering (to group sets of sensor nodes) and routing algorithms. In doing so, one allows the sink to visit just a small subset of the sensor nodes and, therefore, to reduce the time needed to collect all sensed information. As an alternative to other approaches in the literature, we proposed an integrated method that simultaneously provides the sets of sensor nodes that should be visited by each sink as well as their routes. This was accom-

plished by modeling the clustering and routing problems jointly, as a variant of the Vehicle Routing Problem, where the fleet size is fixed, not all clients need to be visited and the goal is to minimize the length of the longest vehicle route. Several metaheuristic based heuristics were implemented to tackle this VRP variant. After the routes are found, we implemented a density control algorithm, in order to reduce unnecessary energy consumption in the network. Thanks to the good results achieved by the optimization algorithms introduced here, a simulation framework that predicts the network dynamics over the time was also implemented and tested computationally. The optimization and simulation results indicate that the proposed optimization procedures allowed significant reductions in message delivery latency, for example, with the Single Hop Strategy in [40] (the method from which ICRP derived). Albeit being less efficient than the strategies in [40] in terms of overall energy expenditures, thanks to a more frequent implementation of density control policies, ICRP also provided higher network coverage and lifetime. Compared to the Centralized Spatial Partitioning in [17], ICRP provided smaller message delivery latency when few mobile sinks were considered. When more mobile sinks were considered, the approach in [17] provided better rates. However, for all other QoS parameters, ICRP performed better than the Centralized Spatial Partitioning. In the future, we plan to investigate the impact of allowing multi-hop communication between sensor nodes and the mobile sinks on the message delivery latency. Acknowledgements The authors thank four anonymous referees for their careful reading, for providing additional relevant references and suggestions that improved this paper.

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

References [1] A.A. Somasundara, A. Ramamoorthy, M.B. Srivastava, Mobile element scheduling with dynamic deadlines, IEEE Transactions on Mobile Computing 6 (4) (2007) 395–410. [2] B.A. Julstrom, Coding TSP tours as permutations via an insertion heuristic, in: SAC ’99: Proceedings of the 1999 ACM Symposium on Applied Computing, San Antonio, Texas, United States, ACM Press, 1999, pp. 297–301. [3] C.A. Valle, A.S. Cunha, W.M. Aioffi, G.R. Mateus, Algorithms for improving the quality of service in wireless sensor networks with multiple mobile sinks, in: MSWIM: Proceedings of the 11th International Symposium on Modeling Analysis and Simulation of Wireless and Mobile Systems, Vancouver, BC, Canada, ACM Press, 2008, pp. 239–243. [4] C.A. Valle, C. Bechelane, W.M. Aioffi, G.R. Mateus, Improving the message delivery delay in wireless sensor networks with mobile sink, in: ACM/IEEE MSWiM 2007 Poster, 2007. [5] C.A. Valle, L.C. Martinez, A.S. da Cunha, G.R. Mateus, Heuristic and exact algorithms for a min–max selective vehicle routing problem, Computers and Operations Research 38 (7) (2011) 1054–1065. [6] E.M. Saad, M.H. Awadalla, R.R. Darwish, A data gathering algorithm for a mobile sink in large-scale sensor networks, in: Proceedings of the 4th International Conference on Wireless and Mobile Communications, ICWMC ’08, 2008, pp. 207–213. [7] G.A. Croes, A method for solving traveling-salesman problems, Operations Research 6 (6) (1958) 791–812. [8] G. Xing, T. Wang, W. Jia, M. Li, Rendezvous design algorithms for wireless sensor networks with a mobile base station, in: Proceedings of the 9th ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc ’08, 2008, pp. 231–240. [9] G.B. Dantzig, D.R. Fulkerson, S.M. Johnson, Solution of a large scale traveling salesman problem, Operations Research 2 (1954) 393–410. [10] G.B. Dantzig, R.H. Hamser, The truck dispatching problem, Management Science 6 (1959) 80–91. [11] H.C.B. de Oliveira, G.C. Vasconcelos, G.B. Alvarenga, R.V. Mesquita, M.M. Souza. A robust method for the VRPTW with multi-start simulated annealing and statistical analysis, in: SCIS ’07: IEEE Symposium on Computational Intelligence in Scheduling, 2007, pp. 198–205. [12] H. Glaab, A new variant of a vehicle routing problem: lower and upper bounds, European Journal of Operational Research 139 (2002) 557–577. [13] H.H. Hoos, T. Stützle, Stochastic Local Search – Foundations and Applications, Elsevier, 2004. [14] H. Nakayama, N. Ansari, A. Jamalipour, N. Kato, Fault-resilient sensing in wireless sensor networks, Computer Communications 30 (2007) 2375–2384. [15] H.S. Kim, T.F. Abdelzaher, W.H. Kwon, Minimum-energy asynchronous dissemination to mobile sinks in wireless sensor networks, in: SenSys ’03: Proceedings of the 1st International Conference on Embedded Networked Sensor Systems, New York, NY, USA, ACM, 2003, pp. 193–204. [16] I. Chatzigiannakis, A. Kinalis, S. Nikoletseas, Efficient data propagation strategies in wireless sensor networks using a single mobile sink, Computer Communications 31 (2008) 896–914. [17] I. Chatzigiannakis, A. Kinalis, S. Nikoletseas, J. Rolim, Fast and energy efficient sensor data collection by multiple mobile sinks, in: MobiWac 07: Proceedings of the 5th ACM International Workshop on Mobility Management and Wireless Access, ACM, 2007, pp. 25–32. [18] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, E. Cayirci, Wireless sensor networks: a survey, Computer Networks 38 (2002) 393– 422. [19] J. Albath, M. Thakur, S. Madria, Energy constrained dominating set for clustering in wireless sensor networks, in: Proceedings of the 24th IEEE International Conference on Advanced Information Networking and Applications, 2010, pp. 812–819. [20] J.L. Bentley, Experiments on traveling salesman heuristics, in: SODA ’90: Proceedings of the First Annual ACM–SIAM Symposium on Discrete Algorithms, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics, 1990, pp. 91–99. [21] J. Luo, J. Hubaux, Joint mobility and routing for lifetime elongation in wireless sensor networks, in: The 24th IEEE INFOCOM, 2005. [22] J.N. Al-Karaki, A.E. Kamal, Routing techniques in wireless sensor networks: a survey, IEEE Wireless Communications 11 (6) (2004) 6– 28. [23] J. Polastre, J. Hill, D. Culler, Versatile low power media access for wireless sensor networks, in: SenSys ’04: Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, New York, NY, USA, ACM Press, 2004, pp. 95–107.

2819

[24] J. Rao, S. Biswas, Network-assisted sink navigation for distributed data gathering: Stability and delay-energy trade-offs, Computer Communications 33 (2) (2010) 160–175. [25] J. Wu, H. Li, Domination and its applications in ad hoc wireless networks with unidirectional links, in: Proceedings of the 2000 International Conference on Parallel Processing, Washington, DC, USA, IEEE Computer Society, 2000. [26] Java in Simulation Time – Scalable Wireless Ad Hoc Network Simulator, 2007. . [27] L.H.A. Correia, D.F. Macedo, D.A.C. Silva, A.L. dos Santos, A.A.F. Loureiro, J.M.S. Nogueira, Transmission power control in MAC protocols for wireless sensor networks, in: MSWiM ’05: Proceedings of the 8th ACM International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems, ACM Press, New York, NY, USA, 2005, pp. 282–289. [28] M. Fischetti, A. Lodi, Local branching, Mathematical Programming 98 (2003) 23–47. [29] M. Fischetti, J.J.S. Gonzalez, P. Toth, A branch-and-cut algorithm for the symmetric generalized traveling salesman problem, Operations Research 45 (3) (1997) 378–394. [30] M. Gendreau, G. Laporte, F. Semet, The covering tour problem, Operations Research 45 (4) (1997) 568–576. [31] M. Junger, G. Reinelt, G. Rinaldi, The traveling salesman problem, in: M.O. Ball (Ed.), Handbooks in OR and MS, vol. 7, Elsevier Science Publishers, 1995, pp. 225–330. [32] M. Prais, C.C. Ribeiro, Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment, INFORMS Journal on Computing 12 (2000) 164–176. [33] M.W. Padberg, G. Rinaldi, A branch-and-cut algorithm for resolution of large scale of Symmetric Traveling Salesman Problem, SIAM Review 33 (1991) 60–100. [34] N. Mladenovic´, P. Hansen, Variable neighborhood search, Computers and Operations Research 24 (1997) 1097–1100. [35] P. Mirchandani, R. Francis, Discrete location theory, John Wiley and Sons, 1990. [36] R.C. Shah, S. Roy, S. Janin, W. Brunette, Data MULEs: modeling a three-tier architecture for sparse sensor networks, in: Proceedings of the First IEEE, 2003 IEEE International Workshop on Sensor Network Protocols and Applications, 2003, pp. 30–41. [37] S. Basagni, A. Carosi, E. Melachrinoudis, C. Petrioli, Z.M. Wang, Controlled sink mobility for prolonging wireless sensor networks lifetime, Wireless Networks 14 (2008) 831–858. [38] S. Gandham, M. Dawande, R. Prakash, S. Venkatesan, Energy efficient schemes for wireless sensor networks with multiple mobile base stations, in: IEEE GLOBECOM, San Fransisco, USA, December 2003. [39] T.A. Feo, M.G.C. Resende, Greedy randomized adaptive search procedures, Journal of Global Optimization 6 (1995) 109–133. [40] W.M. Aioffi, F.P. Quintão, G.R. Mateus, Integrated methods for organization of wireless sensor networks with mobile sink, in: International Workshop on Design and Reliable Communication Networks, La Rochelle, France, October 2007. [41] W. Michiels, E. Aarts, J. Korst, Theoretical Aspects of Local Search (Monographs in Theoretical Computer Science. An EATCS Series), Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2007. [42] XBOW, MICA2 – Wireless Measurement System, April 2006. . [43] Z. Wang, S. Basagni, E. Melachrinoudis, C. Petrioli, Exploiting sink mobility for maximizing sensor networks lifetime, in: HICSS ’05, IEEE Computer Society, Washington, DC, USA, 2005, p. 287.1. Wagner Moro Aioffi received his B.Sc. and M.Sc. degrees in Computer Science from Federal University of Minas Gerais (UFMG), Brazil, in 2004 and 2006, respectively. His research interests include applied Combinatorial Optimization, on-line algorithms and simulation. Cristiano Arbex Valle is currently undertaking a PhD program in Applied Mathematics at Brunel University, London. He received his Msc., in Computer Science in 2009 from the Federal University of Minas Gerais, Belo Horizonte, Brazil. His research interests include combinatorial optimization, mathematical programming and related applications such as computer networks and financial problems.

2820

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

Geraldo Robson Mateus is Full Professor in Computer Science at Federal University of Minas Gerais, Belo Horizonte, Brazil. He received his PhD and MS in computer science from Federal University of Rio de Janeiro, Brazil, in 1980 and 1986, respectively. He spent 1991 and 1992 at the University of Ottawa, Canada, as a visiting researcher. His research interests span network optimization, combinatorial optimization, algorithms, logistic, transport and telecommunication. He is a member of INFORMS, IFORS, SBC, SIAM and SOBRAPO. He has published over 200 scientific papers, 50 journal papers and book chapters and two books, and is a leader of several

national and international projects. He has worked as a consultant for some companies such as Usiminas, CVRD, MBR, Telemig, Telemar, France Telecom, Embratel and for the Brazilian government. Alexandre Salles da Cunha has B.S. and M.Sc. degrees in Mechanical Engineering from Federal University of Minas Gerais, Belo Horizonte, Brazil (1994, 2002). He holds a PhD degree in Systems Engineering and Computing from Federal University of Rio de Janeiro (2006). During 20042005, he visited the Center for Operations Research and Econometrics at l’Universithé Catholique de Louvain (Belgium), as part of his doctorate research. He currently serves as Associate Professor at the Computer Science Department of Federal University of Minas Gerais, Brazil. His research spans Mathematical Programming, Combinatorial Optimization and their applications in Network Optimization.