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44 \journal{Ad Hoc Networks}
50 %% Title, authors and addresses
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70 \title{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
72 %% use optional labels to link authors explicitly to addresses:
73 %% \author[label1,label2]{}
76 %\author{Ali Kadhum Idrees, Karine Deschinkel, \\
77 %Michel Salomon, and Rapha\"el Couturier}
79 %\thanks{are members in the AND team - DISC department - FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France.
80 % e-mail: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}% <-this % stops a space
81 %\thanks{}% <-this % stops a space
83 %\address{FEMTO-ST Institute, University of Franche-Comt\'e, Belfort, France. \\
84 %e-mail: ali.idness@edu.univ-fcomte.fr, \\
85 %$\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.}
88 \author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$, \\
89 Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$ \\
90 $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
91 University Bourgogne Franche-Comt\'e, Belfort, France}} \\
92 $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
97 %One of the fundamental challenges in Wireless Sensor Networks (WSNs)
98 %is the coverage preservation and the extension of the network lifetime
99 %continuously and effectively when monitoring a certain area (or
100 %region) of interest.
101 Coverage and lifetime are two paramount problems in Wireless Sensor Networks
102 (WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage
103 Optimization protocol (MuDiLCO) is proposed to maintain the coverage and to
104 improve the lifetime in wireless sensor networks. The area of interest is first
105 divided into subregions and then the MuDiLCO protocol is distributed on the
106 sensor nodes in each subregion. The proposed MuDiLCO protocol works in periods
107 during which sets of sensor nodes are scheduled to remain active for a number of
108 rounds during the sensing phase, to ensure coverage so as to maximize the
109 lifetime of WSN. The decision process is carried out by a leader node, which
110 solves an integer program to produce the best representative sets to be used
111 during the rounds of the sensing phase. Compared with some existing protocols,
112 simulation results based on multiple criteria (energy consumption, coverage
113 ratio, and so on) show that the proposed protocol can prolong efficiently the
114 network lifetime and improve the coverage performance.
119 Wireless Sensor Networks, Area Coverage, Network Lifetime,
120 Optimization, Scheduling, Distributed Computation.
126 \section{Introduction}
128 \indent The fast developments of low-cost sensor devices and wireless
129 communications have allowed the emergence of WSNs. A WSN includes a large number
130 of small, limited-power sensors that can sense, process, and transmit data over
131 a wireless communication. They communicate with each other by using multi-hop
132 wireless communications and cooperate together to monitor the area of interest,
133 so that each measured data can be reported to a monitoring center called sink
134 for further analysis~\cite{Sudip03}. There are several fields of application
135 covering a wide spectrum for a WSN, including health, home, environmental,
136 military, and industrial applications~\cite{Akyildiz02}.
138 On the one hand sensor nodes run on batteries with limited capacities, and it is
139 often costly or simply impossible to replace and/or recharge batteries,
140 especially in remote and hostile environments. Obviously, to achieve a long life
141 of the network it is important to conserve battery power. Therefore, lifetime
142 optimization is one of the most critical issues in wireless sensor networks. On
143 the other hand we must guarantee coverage over the area of interest. To fulfill
144 these two objectives, the main idea is to take advantage of overlapping sensing
145 regions to turn-off redundant sensor nodes and thus save energy. In this paper,
146 we concentrate on the area coverage problem, with the objective of maximizing
147 the network lifetime by using an optimized multiround scheduling.
149 % One of the major scientific research challenges in WSNs, which are addressed by a large number of literature during the last few years is to design energy efficient approaches for coverage and connectivity in WSNs~\cite{conti2014mobile}. The coverage problem is one of the
150 %fundamental challenges in WSNs~\cite{Nayak04} that consists in monitoring efficiently and continuously
151 %the area of interest. The limited energy of sensors represents the main challenge in the WSNs
152 %design~\cite{Sudip03}, where it is difficult to replace and/or recharge their batteries because the the area of interest nature (such as hostile environments) and the cost. So, it is necessary that a WSN
153 %deployed with high density because spatial redundancy can then be exploited to increase the lifetime of the network. However, turn on all the sensor nodes, which monitor the same region at the same time
154 %leads to decrease the lifetime of the network. To extend the lifetime of the network, the main idea is to take advantage of the overlapping sensing regions of some sensor nodes to save energy by turning off
155 %some of them during the sensing phase~\cite{Misra05}. WSNs require energy-efficient solutions to improve the network lifetime that is constrained by the limited power of each sensor node ~\cite{Akyildiz02}.
157 %In this paper, we concentrate on the area coverage problem, with the objective
158 %of maximizing the network lifetime by using an optimized multirounds scheduling.
159 %The area of interest is divided into subregions.
161 % Each period includes four phases starts with a discovery phase to exchange information among the sensors of the subregion, in order to choose in a suitable manner a sensor node as leader to carry out a coverage strategy. This coverage strategy involves the solving of an integer program by the leader, to optimize the coverage and the lifetime in the subregion by producing a sets of sensor nodes in order to take the mission of coverage preservation during several rounds in the sensing phase. In fact, the nodes in a subregion can be seen as a cluster where each node sends sensing data to the cluster head or the sink node. Furthermore, the activities in a subregion/cluster can continue even if another cluster stops due to too many node failures.
163 The remainder of the paper is organized as follows. The next section
165 reviews the related works in the field. Section~\ref{pd} is devoted to the
166 description of MuDiLCO protocol. Section~\ref{exp} shows the simulation results
167 obtained using the discrete event simulator OMNeT++ \cite{varga}. They fully
168 demonstrate the usefulness of the proposed approach. Finally, we give
169 concluding remarks and some suggestions for future works in
170 Section~\ref{sec:conclusion}.
173 %%RC : Related works good for a phd thesis but too long for a paper. Ali you need to learn to .... summarize :-)
174 \section{Related works} % Trop proche de l'etat de l'art de l'article de Zorbas ?
177 \indent This section is dedicated to the various approaches proposed in the
178 literature for the coverage lifetime maximization problem, where the objective
179 is to optimally schedule sensors' activities in order to extend network lifetime
180 in WSNs. Cardei and Wu \cite{cardei2006energy} provide a taxonomy for coverage
181 algorithms in WSNs according to several design choices:
183 \item Sensors scheduling algorithm implementation, i.e. centralized or
184 distributed/localized algorithms.
185 \item The objective of sensor coverage, i.e. to maximize the network lifetime or
186 to minimize the number of sensors during a sensing round.
187 \item The homogeneous or heterogeneous nature of the nodes, in terms of sensing
188 or communication capabilities.
189 \item The node deployment method, which may be random or deterministic.
190 \item Additional requirements for energy-efficient and connected coverage.
193 The choice of non-disjoint or disjoint cover sets (sensors participate or not in
194 many cover sets) can be added to the above list.
195 % The independency in the cover set (i.e. whether the cover sets are disjoint or non-disjoint) \cite{zorbas2010solving} is another design choice that can be added to the above list.
197 \subsection{Centralized approaches}
199 The major approach is to divide/organize the sensors into a suitable number of
200 cover sets where each set completely covers an interest region and to activate
201 these cover sets successively. The centralized algorithms always provide nearly
202 or close to optimal solution since the algorithm has global view of the whole
203 network. Note that centralized algorithms have the advantage of requiring very
204 low processing power from the sensor nodes, which usually have limited
205 processing capabilities. The main drawback of this kind of approach is its
206 higher cost in communications, since the node that will make the decision needs
207 information from all the sensor nodes. Moreover, centralized approaches usually
208 suffer from the scalability problem, making them less competitive as the network
211 The first algorithms proposed in the literature consider that the cover sets are
212 disjoint: a sensor node appears in exactly one of the generated cover
213 sets~\cite{abrams2004set,cardei2005improving,Slijepcevic01powerefficient}. In
214 the case of non-disjoint algorithms \cite{pujari2011high}, sensors may
215 participate in more than one cover set. In some cases, this may prolong the
216 lifetime of the network in comparison to the disjoint cover set algorithms, but
217 designing algorithms for non-disjoint cover sets generally induces a higher
218 order of complexity. Moreover, in case of a sensor's failure, non-disjoint
219 scheduling policies are less resilient and reliable because a sensor may be
220 involved in more than one cover sets.
221 %For instance, the proposed work in ~\cite{cardei2005energy, berman04}
223 In~\cite{yang2014maximum}, the authors have considered a linear programming
224 approach to select the minimum number of working sensor nodes, in order to
225 preserve a maximum coverage and to extend lifetime of the network. Cheng et
226 al.~\cite{cheng2014energy} have defined a heuristic algorithm called Cover Sets
227 Balance (CSB), which chooses a set of active nodes using the tuple (data
228 coverage range, residual energy). Then, they have introduced a new Correlated
229 Node Set Computing (CNSC) algorithm to find the correlated node set for a given
230 node. After that, they proposed a High Residual Energy First (HREF) node
231 selection algorithm to minimize the number of active nodes so as to prolong the
232 network lifetime. Various centralized methods based on column generation
233 approaches have also been
234 proposed~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
236 \subsection{Distributed approaches}
237 %{\bf Distributed approaches}
238 In distributed and localized coverage algorithms, the required computation to
239 schedule the activity of sensor nodes will be done by the cooperation among
240 neighboring nodes. These algorithms may require more computation power for the
241 processing by the cooperating sensor nodes, but they are more scalable for large
242 WSNs. Localized and distributed algorithms generally result in non-disjoint set
245 Many distributed algorithms have been developed to perform the scheduling so as
246 to preserve coverage, see for example
247 \cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02, yardibi2010distributed,
248 prasad2007distributed,Misra}. Distributed algorithms typically operate in
249 rounds for a predetermined duration. At the beginning of each round, a sensor
250 exchanges information with its neighbors and makes a decision to either remain
251 turned on or to go to sleep for the round. This decision is basically made on
252 simple greedy criteria like the largest uncovered area
253 \cite{Berman05efficientenergy} or maximum uncovered targets
254 \cite{lu2003coverage}. The Distributed Adaptive Sleep Scheduling Algorithm
255 (DASSA) \cite{yardibi2010distributed} does not require location information of
256 sensors while maintaining connectivity and satisfying a user defined coverage
257 target. In DASSA, nodes use the residual energy levels and feedback from the
258 sink for scheduling the activity of their neighbors. This feedback mechanism
259 reduces the randomness in scheduling that would otherwise occur due to the
260 absence of location information. In \cite{ChinhVu}, the author have designed a
261 novel distributed heuristic, called Distributed Energy-efficient Scheduling for
262 k-coverage (DESK), which ensures that the energy consumption among the sensors
263 is balanced and the lifetime maximized while the coverage requirement is
264 maintained. This heuristic works in rounds, requires only one-hop neighbor
265 information, and each sensor decides its status (active or sleep) based on the
266 perimeter coverage model from~\cite{Huang:2003:CPW:941350.941367}.
268 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
269 %heterogeneous energy wireless sensor networks.
270 %In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions.
272 The works presented in \cite{Bang, Zhixin, Zhang} focus on coverage-aware,
273 distributed energy-efficient, and distributed clustering methods respectively,
274 which aim at extending the network lifetime, while the coverage is ensured.
275 More recently, Shibo et al. \cite{Shibo} have expressed the coverage problem as
276 a minimum weight submodular set cover problem and proposed a Distributed
277 Truncated Greedy Algorithm (DTGA) to solve it. They take advantage from both
278 temporal and spatial correlations between data sensed by different sensors, and
279 leverage prediction, to improve the lifetime. In \cite{xu2001geography}, Xu et
280 al. have described an algorithm, called Geographical Adaptive Fidelity (GAF),
281 which uses geographic location information to divide the area of interest into
282 fixed square grids. Within each grid, it keeps only one node staying awake to
283 take the responsibility of sensing and communication.
285 Some other approaches (outside the scope of our work) do not consider a
286 synchronized and predetermined time-slot where the sensors are active or not.
287 Indeed, each sensor maintains its own timer and its wake-up time is randomized
288 \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
290 The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization
291 protocol) presented in this paper is an extension of the approach introduced
292 in~\cite{idrees2014coverage}. In~\cite{idrees2014coverage}, the protocol is
293 deployed over only two subregions. Simulation results have shown that it was
294 more interesting to divide the area into several subregions, given the
295 computation complexity. Compared to our previous paper, in this one we study the
296 possibility of dividing the sensing phase into multiple rounds and we also add
297 an improved model of energy consumption to assess the efficiency of our
298 approach. In fact, in this paper we make a multiround optimization, while it was
299 a single round optimization in our previous work.
303 \subsection{Centralized Approaches}
304 %{\bf Centralized approaches}
305 The major approach is to divide/organize the sensors into a suitable number of
306 set covers where each set completely covers an interest region and to activate
307 these set covers successively. The centralized algorithms always provide nearly
308 or close to optimal solution since the algorithm has global view of the whole
309 network. Note that centralized algorithms have the advantage of requiring very
310 low processing power from the sensor nodes, which usually have limited
311 processing capabilities. The main drawback of this kind of approach is its
312 higher cost in communications, since the node that will take the decision needs
313 information from all the sensor nodes. Moreover, centralized approaches usually
314 suffer from the scalability problem, making them less competitive as the network
317 The first algorithms proposed in the literature consider that the cover sets are
318 disjoint: a sensor node appears in exactly one of the generated cover sets. For
319 instance, Slijepcevic and Potkonjak \cite{Slijepcevic01powerefficient} have
320 proposed an algorithm, which allocates sensor nodes in mutually independent sets
321 to monitor an area divided into several fields. Their algorithm builds a cover
322 set by including in priority the sensor nodes which cover critical fields, that
323 is to say fields that are covered by the smallest number of sensors. The time
324 complexity of their heuristic is $O(n^2)$ where $n$ is the number of sensors.
325 Abrams et al.~\cite{abrams2004set} have designed three approximation algorithms
326 for a variation of the set k-cover problem, where the objective is to partition
327 the sensors into covers such that the number of covers that include an area,
328 summed over all areas, is maximized. Their work builds upon previous work
329 in~\cite{Slijepcevic01powerefficient} and the generated cover sets do not
330 provide complete coverage of the monitoring zone.
332 In \cite{cardei2005improving}, the authors have proposed a method to efficiently
333 compute the maximum number of disjoint set covers such that each set can monitor
334 all targets. They first transform the problem into a maximum flow problem, which
335 is formulated as a mixed integer programming (MIP). Then their heuristic uses
336 the output of the MIP to compute disjoint set covers. Results show that this
337 heuristic provides a number of set covers slightly larger compared to
338 \cite{Slijepcevic01powerefficient}, but with a larger execution time due to the
339 complexity of the mixed integer programming resolution.
341 Zorbas et al. \cite{zorbas2010solving} presented a centralized greedy algorithm
342 for the efficient production of both node disjoint and non-disjoint cover sets.
343 Compared to algorithm's results of Slijepcevic and Potkonjak
344 \cite{Slijepcevic01powerefficient}, their heuristic produces more disjoint cover
345 sets with a slight growth rate in execution time. When producing non-disjoint
346 cover sets, both Static-CCF and Dynamic-CCF algorithms, where CCF means that
347 they use a cost function called Critical Control Factor, provide cover sets
348 offering longer network lifetime than those produced by \cite{cardei2005energy}.
349 Also, they require a smaller number of participating nodes in order to achieve
352 In the case of non-disjoint algorithms \cite{pujari2011high}, sensors may
353 participate in more than one cover set. In some cases, this may prolong the
354 lifetime of the network in comparison to the disjoint cover set algorithms, but
355 designing algorithms for non-disjoint cover sets generally induces a higher
356 order of complexity. Moreover, in case of a sensor's failure, non-disjoint
357 scheduling policies are less resilient and less reliable because a sensor may be
358 involved in more than one cover sets. For instance, Cardei et
359 al.~\cite{cardei2005energy} present a linear programming (LP) solution and a
360 greedy approach to extend the sensor network lifetime by organizing the sensors
361 into a maximal number of non-disjoint cover sets. Simulation results show that
362 by allowing sensors to participate in multiple sets, the network lifetime
363 increases compared with related work~\cite{cardei2005improving}.
364 In~\cite{berman04}, the authors have formulated the lifetime problem and
365 suggested another (LP) technique to solve this problem. A centralized solution
366 based on the Garg-K\"{o}nemann algorithm~\cite{garg98}, provably near the
367 optimal solution, is also proposed.
369 In~\cite{yang2014maximum}, the authors have proposed a linear programming
370 approach for selecting the minimum number of working sensor nodes, in order to
371 as to preserve a maximum coverage and extend lifetime of the network. Cheng et
372 al.~\cite{cheng2014energy} have defined a heuristic algorithm called Cover Sets
373 Balance (CSB), which choose a set of active nodes using the tuple (data coverage
374 range, residual energy). Then, they have introduced a new Correlated Node Set
375 Computing (CNSC) algorithm to find the correlated node set for a given node.
376 After that, they proposed a High Residual Energy First (HREF) node selection
377 algorithm to minimize the number of active nodes so as to prolong the network
378 lifetime. Various centralized methods based on column generation approaches have
379 also been proposed~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
381 \subsection{Distributed approaches}
382 %{\bf Distributed approaches}
383 In distributed and localized coverage algorithms, the required computation to
384 schedule the activity of sensor nodes will be done by the cooperation among
385 neighboring nodes. These algorithms may require more computation power for the
386 processing by the cooperating sensor nodes, but they are more scalable for large
387 WSNs. Localized and distributed algorithms generally result in non-disjoint set
390 Many distributed algorithms have been developed to perform the scheduling so as
391 to preserve coverage, see for example
392 \cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02,yardibi2010distributed}.
393 Distributed algorithms typically operate in rounds for a predetermined
394 duration. At the beginning of each round, a sensor exchanges information with
395 its neighbors and makes a decision to either remain turned on or to go to sleep
396 for the round. This decision is basically made on simple greedy criteria like
397 the largest uncovered area \cite{Berman05efficientenergy} or maximum uncovered
398 targets \cite{lu2003coverage}. In \cite{Tian02}, the scheduling scheme is
399 divided into rounds, where each round has a self-scheduling phase followed by a
400 sensing phase. Each sensor broadcasts a message containing the node~ID and the
401 node location to its neighbors at the beginning of each round. A sensor
402 determines its status by a rule named off-duty eligible rule, which tells him to
403 turn off if its sensing area is covered by its neighbors. A back-off scheme is
404 introduced to let each sensor delay the decision process with a random period of
405 time, in order to avoid simultaneous conflicting decisions between nodes and
406 lack of coverage on any area. In \cite{prasad2007distributed} a model for
407 capturing the dependencies between different cover sets is defined and it
408 proposes localized heuristic based on this dependency. The algorithm consists of
409 two phases, an initial setup phase during which each sensor computes and
410 prioritizes the covers and a sensing phase during which each sensor first
411 decides its on/off status, and then remains on or off for the rest of the
414 The authors in \cite{yardibi2010distributed} have developed a Distributed
415 Adaptive Sleep Scheduling Algorithm (DASSA) for WSNs with partial coverage.
416 DASSA does not require location information of sensors while maintaining
417 connectivity and satisfying a user defined coverage target. In DASSA, nodes use
418 the residual energy levels and feedback from the sink for scheduling the
419 activity of their neighbors. This feedback mechanism reduces the randomness in
420 scheduling that would otherwise occur due to the absence of location
421 information. In \cite{ChinhVu}, the author have proposed a novel distributed
422 heuristic, called Distributed Energy-efficient Scheduling for k-coverage (DESK),
423 which ensures that the energy consumption among the sensors is balanced and the
424 lifetime maximized while the coverage requirement is maintained. This heuristic
425 works in rounds, requires only one-hop neighbor information, and each sensor
426 decides its status (active or sleep) based on the perimeter coverage model
427 proposed in \cite{Huang:2003:CPW:941350.941367}.
429 %Our Work, which is presented in~\cite{idrees2014coverage} proposed a coverage optimization protocol to improve the lifetime in
430 %heterogeneous energy wireless sensor networks.
431 %In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We consider only distributing the coverage protocol over two subregions.
433 The works presented in \cite{Bang, Zhixin, Zhang} focus on coverage-aware,
434 distributed energy-efficient, and distributed clustering methods respectively,
435 which aim to extend the network lifetime, while the coverage is ensured. S.
436 Misra et al. \cite{Misra} have proposed a localized algorithm for coverage in
437 sensor networks. The algorithm conserve the energy while ensuring the network
438 coverage by activating the subset of sensors with the minimum overlap area. The
439 proposed method preserves the network connectivity by formation of the network
440 backbone. More recently, Shibo et al. \cite{Shibo} have expressed the coverage
441 problem as a minimum weight submodular set cover problem and proposed a
442 Distributed Truncated Greedy Algorithm (DTGA) to solve it. They take advantage
443 from both temporal and spatial correlations between data sensed by different
444 sensors, and leverage prediction, to improve the lifetime. In
445 \cite{xu2001geography}, Xu et al. have proposed an algorithm, called
446 Geographical Adaptive Fidelity (GAF), which uses geographic location information
447 to divide the area of interest into fixed square grids. Within each grid, it
448 keeps only one node staying awake to take the responsibility of sensing and
451 Some other approaches (outside the scope of our work) do not consider a
452 synchronized and predetermined period of time where the sensors are active or
453 not. Indeed, each sensor maintains its own timer and its wake-up time is
454 randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
456 The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization
457 protocol) presented in this paper is an extension of the approach introduced
458 in~\cite{idrees2014coverage}. In~\cite{idrees2014coverage}, the protocol is
459 deployed over only two subregions. Simulation results have shown that it was
460 more interesting to divide the area into several subregions, given the
461 computation complexity. Compared to our previous paper, in this one we study the
462 possibility of dividing the sensing phase into multiple rounds and we also add
463 an improved model of energy consumption to assess the efficiency of our
470 %The main contributions of our MuDiLCO Protocol can be summarized as follows:
471 %(1) The high coverage ratio, (2) The reduced number of active nodes, (3) The distributed optimization over the subregions in the area of interest, (4) The distributed dynamic leader election at each round based on some priority factors that led to energy consumption balancing among the nodes in the same subregion, (5) The primary point coverage model to represent each sensor node in the network, (6) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes for a multirounds to take the mission of the coverage in each subregion, (7) The very low energy consumption, (8) The higher network lifetime.
472 %\section{Preliminaries}
477 %\subsection{Network Lifetime}
478 %Various definitions exist for the lifetime of a sensor
479 %network~\cite{die09}. The main definitions proposed in the literature are
480 %related to the remaining energy of the nodes or to the coverage percentage.
481 %The lifetime of the network is mainly defined as the amount
482 %of time during which the network can satisfy its coverage objective (the
483 %amount of time that the network can cover a given percentage of its
484 %area or targets of interest). In this work, we assume that the network
485 %is alive until all nodes have been drained of their energy or the
486 %sensor network becomes disconnected, and we measure the coverage ratio
487 %during the WSN lifetime. Network connectivity is important because an
488 %active sensor node without connectivity towards a base station cannot
489 %transmit information on an event in the area that it monitors.
491 \section{MuDiLCO protocol description}
494 %Our work will concentrate on the area coverage by design
495 %and implementation of a strategy, which efficiently selects the active
496 %nodes that must maintain both sensing coverage and network
497 %connectivity and at the same time improve the lifetime of the wireless
498 %sensor network. But, requiring that all physical points of the
499 %considered region are covered may be too strict, especially where the
500 %sensor network is not dense. Our approach represents an area covered
501 %by a sensor as a set of primary points and tries to maximize the total
502 %number of primary points that are covered in each round, while
503 %minimizing overcoverage (points covered by multiple active sensors
506 %In this section, we introduce a Multiround Distributed Lifetime Coverage Optimization protocol, which is called MuDiLCO. It is distributed on each subregion in the area of interest. It is based on two efficient techniques: network
507 %leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.
508 %The main features of our MuDiLCO protocol:
509 %i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into periods, which consists in round(s), iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi) it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative non-disjoint sets of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our Protocol.
511 \subsection{Assumptions}
513 We consider a randomly and uniformly deployed network consisting of static
514 wireless sensors. The sensors are deployed in high density to ensure initially
515 a high coverage ratio of the interested area. We assume that all nodes are
516 homogeneous in terms of communication and processing capabilities, and
517 heterogeneous from the point of view of energy provision. Each sensor is
518 supposed to get information on its location either through hardware such as
519 embedded GPS or through location discovery algorithms.
521 To model a sensor node's coverage area, we consider the boolean disk coverage
522 model which is the most widely used sensor coverage model in the
523 literature. Thus, each sensor has a constant sensing range $R_s$ and all space
524 points within the disk centered at the sensor with the radius of the sensing
525 range is said to be covered by this sensor. We also assume that the
526 communication range satisfies $R_c \geq 2R_s$. In fact, Zhang and
527 Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous
528 hypothesis, a complete coverage of a convex area implies connectivity among the
531 Instead of working with a continuous coverage area, we make it discrete by
532 considering for each sensor a set of points called primary points. Consequently,
533 we assume that the sensing disk defined by a sensor is covered if all of its
534 primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here.
536 %By knowing the position (point center: ($p_x,p_y$)) of a wireless
537 %sensor node and its $R_s$, we calculate the primary points directly
538 %based on the proposed model. We use these primary points (that can be
539 %increased or decreased if necessary) as references to ensure that the
540 %monitored region of interest is covered by the selected set of
541 %sensors, instead of using all the points in the area.
543 %The MuDiLCO protocol works in periods and executed at each sensor node in the network, each sensor node can still sense data while being in
544 %LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
545 %sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The MuDiLCO protocol algorithm works as follow:
546 %Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list $L$.
547 %The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader after the decision to apply multi-round activity scheduling during the sensing phase. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will produce the cover sets of sensor nodes to take the mission of coverage during the sensing phase for $T$ rounds. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's schedule for $T$ rounds during the period of sensing, either Active or sleep until the starting of next period. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep based on it's schedule for $T$ rounds during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, which are includes $T$ rounds, all the sensor nodes in the same subregion will start new period by executing the MuDiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
549 \subsection{Background idea}
550 %%RC : we need to clarify the difference between round and period. Currently it seems to be the same (for me at least).
551 The area of interest can be divided using the divide-and-conquer strategy into
552 smaller areas, called subregions, and then our MuDiLCO protocol will be
553 implemented in each subregion in a distributed way.
555 As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion,
556 where each is divided into 4 phases: Information~Exchange, Leader~Election,
557 Decision, and Sensing. Each sensing phase may be itself divided into $T$ rounds
558 and for each round a set of sensors (a cover set) is responsible for the sensing
559 task. In this way a multiround optimization process is performed during each
560 period after Information~Exchange and Leader~Election phases, in order to
561 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
563 \centering \includegraphics[width=100mm]{Modelgeneral.pdf} % 70mm
564 \caption{The MuDiLCO protocol scheme executed on each node}
568 %Each period is divided into 4 phases: Information Exchange,
569 %Leader Election, Decision, and Sensing. Each sensing phase may be itself divided into $T$ rounds.
570 % set cover responsible for the sensing task.
571 %For each round a set of sensors (said a cover set) is responsible for the sensing task.
573 This protocol minimizes the impact of unexpected node failure (not due to batteries
574 running out of energy), because it works in periods.
575 %This protocol is reliable against an unexpected node failure, because it works in periods.
576 %%RC : why? I am not convinced
577 On the one hand, if a node failure is detected before making the
578 decision, the node will not participate to this phase, and, on the other hand,
579 if the node failure occurs after the decision, the sensing task of the network
580 will be temporarily affected: only during the period of sensing until a new
582 %%RC so if there are at least one failure per period, the coverage is bad...
583 %%MS if we want to be reliable against many node failures we need to have an
586 The energy consumption and some other constraints can easily be taken into
587 account, since the sensors can update and then exchange their information
588 (including their residual energy) at the beginning of each period. However, the
589 pre-sensing phases (Information Exchange, Leader Election, and Decision) are
590 energy consuming for some nodes, even when they do not join the network to
593 %%%%%%%%%%%%%%%%%parler optimisation%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
595 We define two types of packets that will be used by the proposed protocol:
596 \begin{enumerate}[(a)]
597 \item INFO packet: such a packet will be sent by each sensor node to all the
598 nodes inside a subregion for information exchange.
599 \item Active-Sleep packet: sent by the leader to all the nodes inside a
600 subregion to inform them to remain Active or to go Sleep during the sensing
604 There are five status for each sensor node in the network:
605 \begin{enumerate}[(a)]
606 \item LISTENING: sensor node is waiting for a decision (to be active or not);
607 \item COMPUTATION: sensor node has been elected as leader and applies the
608 optimization process;
609 \item ACTIVE: sensor node is taking part in the monitoring of the area;
610 \item SLEEP: sensor node is turned off to save energy;
611 \item COMMUNICATION: sensor node is transmitting or receiving packet.
614 Below, we describe each phase in more details.
616 \subsection{Information Exchange Phase}
618 Each sensor node $j$ sends its position, remaining energy $RE_j$, and the number
619 of neighbors $NBR_j$ to all wireless sensor nodes in its subregion by using an
620 INFO packet (containing information on position coordinates, current remaining
621 energy, sensor node ID, number of its one-hop live neighbors) and then waits for
622 packets sent by other nodes. After that, each node will have information about
623 all the sensor nodes in the subregion. In our model, the remaining energy
624 corresponds to the time that a sensor can live in the active mode.
626 %\subsection{\textbf Working Phase:}
628 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
630 \subsection{Leader Election phase}
632 This step consists in choosing the Wireless Sensor Node Leader (WSNL), which
633 will be responsible for executing the coverage algorithm. Each subregion in the
634 area of interest will select its own WSNL independently for each period. All
635 the sensor nodes cooperate to elect a WSNL. The nodes in the same subregion
636 will select the leader based on the received information from all other nodes
637 in the same subregion. The selection criteria are, in order of importance:
638 larger number of neighbors, larger remaining energy, and then in case of
639 equality, larger index. Observations on previous simulations suggest to use the
640 number of one-hop neighbors as the primary criterion to reduce energy
641 consumption due to the communications.
643 %the more priority selection factor is the number of $1-hop$ neighbors, $NBR j$, which can minimize the energy consumption during the communication Significantly.
644 %The pseudo-code for leader election phase is provided in Algorithm~1.
646 %Where $E_{th}$ is the minimum energy needed to stay active during the sensing phase. As shown in Algorithm~1, the more priority selection factor is the number of $1-hop$ neighbours, $NBR j$, which can minimize the energy consumption during the communication Significantly.
648 \subsection{Decision phase}
650 Each WSNL will solve an integer program to select which cover sets will be
651 activated in the following sensing phase to cover the subregion to which it
652 belongs. The integer program will produce $T$ cover sets, one for each round.
653 The WSNL will send an Active-Sleep packet to each sensor in the subregion based
654 on the algorithm's results, indicating if the sensor should be active or not in
655 each round of the sensing phase. The integer program is based on the model
656 proposed by \cite{pedraza2006} with some modifications, where the objective is
657 to find a maximum number of disjoint cover sets. To fulfill this goal, the
658 authors proposed an integer program which forces undercoverage and overcoverage
659 of targets to become minimal at the same time. They use binary variables
660 $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model, we
661 consider binary variables $X_{t,j}$ to determine the possibility of activating
662 sensor $j$ during round $t$ of a given sensing phase. We also consider primary
663 points as targets. The set of primary points is denoted by $P$ and the set of
664 sensors by $J$. Only sensors able to be alive during at least one round are
665 involved in the integer program.
667 %parler de la limite en energie Et pour un round
669 For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
670 whether the point $p$ is covered, that is:
672 \alpha_{j,p} = \left \{
674 1 & \mbox{if the primary point $p$ is covered} \\
675 & \mbox{by sensor node $j$}, \\
676 0 & \mbox{otherwise.}\\
680 The number of active sensors that cover the primary point $p$ during
681 round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
685 1& \mbox{if sensor $j$ is active during round $t$,} \\
686 0 & \mbox{otherwise.}\\
690 We define the Overcoverage variable $\Theta_{t,p}$ as:
692 \Theta_{t,p} = \left \{
694 0 & \mbox{if the primary point $p$}\\
695 & \mbox{is not covered during round $t$,}\\
696 \left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
700 More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
701 minus one that cover the primary point $p$ during round $t$. The
702 Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
707 1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
708 0 & \mbox{otherwise.}\\
713 Our coverage optimization problem can then be formulated as follows:
715 \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
720 \sum_{j=1}^{|J|} \alpha_{j,p} * X_{t,j} = \Theta_{t,p} - U_{t,p} + 1 \label{eq16} \hspace{6 mm} \forall p \in P, t = 1,\dots,T
724 \sum_{t=1}^{T} X_{t,j} \leq \floor*{RE_{j}/E_{R}} \hspace{6 mm} \forall j \in J, t = 1,\dots,T
729 X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
733 U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
737 \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
741 %(W_{\theta}+W_{\psi} = P) \label{eq19}
744 %%RC why W_{\theta} is not defined (only one sentence)? How to define in practice Wtheta and Wu?
747 \item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
748 during round $t$ (1 if yes and 0 if not);
749 \item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus one that
750 are covering the primary point $p$ during round $t$;
751 \item $U_{t,p}$ - {\it undercoverage}: indicates whether or not the primary
752 point $p$ is being covered during round $t$ (1 if not covered and 0 if
756 The first group of constraints indicates that some primary point $p$ should be
757 covered by at least one sensor and, if it is not always the case, overcoverage
758 and undercoverage variables help balancing the restriction equations by taking
759 positive values. The constraint given by equation~(\ref{eq144}) guarantees that
760 the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be
761 alive during the selected rounds knowing that $E_{R}$ is the amount of energy
762 required to be alive during one round.
764 There are two main objectives. First, we limit the overcoverage of primary
765 points in order to activate a minimum number of sensors. Second we prevent the
766 absence of monitoring on some parts of the subregion by minimizing the
767 undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as
768 to guarantee that the maximum number of points are covered during each round.
769 %% MS W_theta is smaller than W_u => problem with the following sentence
770 In our simulations priority is given to the coverage by choosing $W_{U}$ very
771 large compared to $W_{\theta}$.
772 %The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
774 \subsection{Sensing phase}
776 The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
777 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
778 sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
779 will be executed by each node at the beginning of a period, explains how the
780 Active-Sleep packet is obtained.
782 % In each round during the sensing phase, there is a cover set of sensor nodes, in which the active sensors will execute their sensing task to preserve maximal coverage and lifetime in the subregion and this will continue until finishing the round $T$ and starting new period.
784 \begin{algorithm}[h!]
785 % \KwIn{all the parameters related to information exchange}
786 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
788 %\emph{Initialize the sensor node and determine it's position and subregion} \;
790 \If{ $RE_j \geq E_{R}$ }{
791 \emph{$s_j.status$ = COMMUNICATION}\;
792 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
793 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
794 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
795 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
797 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
798 \emph{LeaderID = Leader election}\;
799 \If{$ s_j.ID = LeaderID $}{
800 \emph{$s_j.status$ = COMPUTATION}\;
801 \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
802 Execute Integer Program Algorithm($T,J$)}\;
803 \emph{$s_j.status$ = COMMUNICATION}\;
804 \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
805 with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
806 \emph{Update $RE_j $}\;
809 \emph{$s_j.status$ = LISTENING}\;
810 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
811 % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
812 \emph{Update $RE_j $}\;
816 \Else { Exclude $s_j$ from entering in the current sensing phase}
819 \caption{MuDiLCO($s_j$)}
824 %\textcolor{red}{\textbf{\textsc{Answer:} ali }}
827 \section{Genetic Algorithm (GA) for Multiround Lifetime Coverage Optimization}
829 Metaheuristics are a generic search strategies for exploring search spaces for solving the complex problems. These strategies have to dynamically balance between the exploitation of the accumulated search experience and the exploration of the search space. On one hand, this balance can find regions in the search space with high-quality solutions. On the other hand, it prevents waste too much time in regions of the search space which are either already explored or don’t provide high-quality solutions. Therefore, metaheuristic provides an enough good solution to an optimization problem, especially with incomplete information or limited computation capacity \cite{bianchi2009survey}. Genetic Algorithm (GA) is one of the population-based metaheuristic methods that simulates the process of natural selection \cite{hassanien2015applications}. GA starts with a population of random candidate solutions (called individuals or phenotypes) . GA uses genetic operators inspired by natural evolution, such as selection, mutation, evaluation, crossover, and replacement so as to improve the initial population of candidate solutions. This process repeated until a stopping criterion is satisfied.
831 In this section, we present a metaheuristic based GA to solve our multiround lifetime coverage optimization problem. The proposed GA provides a near optimal sechedule for multiround sensing per period. The proposed GA is based on the mathematical model which is presented in Section \ref{pd}. Algorithm \ref{alg:GA} shows the proposed GA to solve the coverage lifetime optimization problem. We named the new protocol which is based on GA in the decision phase as GA-MuDiLCO. The proposed GA can be explained in more details as follow:
833 \begin{algorithm}[h!]
835 \SetKwInput{Input}{Input}
836 \SetKwInput{Output}{Output}
837 \Input{ $ P, J, T, S_{pop}, \alpha_{j,p}^{ind}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind}, Child_{t,j}^{ind}, Ch.\Theta_{t,p}^{ind}, Ch.U_{t,p}^{ind_1}$}
838 \Output{$\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}
841 %\emph{Initialize the sensor node and determine it's position and subregion} \;
842 \ForEach {Individual $ind$ $\in$ $S_{pop}$} {
843 \emph{Generate Randomly Chromosome $\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}\;
845 \emph{Update O-U-Coverage $\left\{(P, J, \alpha_{j,p}^{ind}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})\right\}_{p \in P}$}\;
848 \emph{Evaluate Individual $(P, J, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})$}\;
851 \While{ Stopping criteria is not satisfied }{
853 \emph{Selection $(ind_1, ind_2)$}\;
854 \emph{Crossover $(P_c, X_{t,j}^{ind_1}, X_{t,j}^{ind_2}, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}\;
855 \emph{Mutation $(P_m, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}\;
858 \emph{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}\;
859 \emph{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}\;
861 \emph{Evaluate New Individual$(P, J, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}\;
862 \emph{Replacement $(P, J, T, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind} )$ }\;
864 \emph{Evaluate New Individual$(P, J, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}\;
866 \emph{Replacement $(P, J, T, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind} )$ }\;
870 \emph{$\left\{\left(X_{1,1},\dots,X_{t,j},\dots,X_{T,J}\right)\right\}$ =
871 Select Best Solution ($S_{pop}$)}\;
873 \caption{GA-MuDiLCO($s_j$)}
879 \begin{enumerate} [I)]
880 \item \textbf{Representation:} Since the proposed GA's goal is to find the optimal schedule of the sensor nodes which take the responsibility of monitoring the subregion for $T$ rounds in the next phase, the chromosome is defined as a schedule for alive sensors and each chromosome contains $T$ rounds. Each round in the schedule includes J genes, the total alive sensors in the subregion. Therefore, the gene of such a chromosome is a schedule of a sensor. In other words, The genes corresponding to active nodes have the value of one, the others are zero. Figure \ref{chromo} shows solution representation in the proposed GA.
884 \includegraphics [scale=0.35] {rep.pdf}
885 \caption{Candidate Solution representation by the proposed GA. }
891 \item \textbf{Initialize Population:} The initial population is randomly generated and each chromosome in the GA population represents a possible sensors schedule solution to cover the entire subregion for $T$ rounds during current period. Each sensor in the chromosome is given a random value (0 or 1) for all rounds. If the random value is 1, the remaining energy of this sensor should be adequate to activate this sensor during current round. Otherwise, the value is set to 0. The energy constraint is applied for each sensor during all rounds.
894 \item \textbf{Update O-U-Coverage:}
895 After creating the initial population, The overcoverage $\Theta_{t,p}$ and undercoverage $U_{t,p}$ for each candidate solution are computed (see Algorithm \ref{OU}) so as to use them in the next step.
897 \begin{algorithm}[h!]
899 \SetKwInput{Input}{Input}
900 \SetKwInput{Output}{Output}
901 \Input{ parameters $P, J, ind, \alpha_{j,p}^{ind}, X_{t,j}^{ind}$}
902 \Output{$U^{ind} = \left\lbrace U_{1,1}^{ind}, \dots, U_{t,p}^{ind}, \dots, U_{T,P}^{ind} \right\rbrace$ and $\Theta^{ind} = \left\lbrace \Theta_{1,1}^{ind}, \dots, \Theta_{t,p}^{ind}, \dots, \Theta_{T,P}^{ind} \right\rbrace$}
906 \For{$t\leftarrow 1$ \KwTo $T$}{
907 \For{$p\leftarrow 1$ \KwTo $P$}{
909 % \For{$i\leftarrow 0$ \KwTo $I_j$}{
910 \emph{$SUM\leftarrow 0$}\;
911 \For{$j\leftarrow 1$ \KwTo $J$}{
912 \emph{$SUM \leftarrow SUM + (\alpha_{j,p}^{ind} \times X_{t,j}^{ind})$ }\;
916 \emph{$U_{t,p}^{ind} \leftarrow 0$}\;
917 \emph{$\Theta_{t,p}^{ind} \leftarrow 1$}\;
920 \emph{$U_{t,p}^{ind} \leftarrow SUM -1$}\;
921 \emph{$\Theta_{t,p}^{ind} \leftarrow 0$}\;
927 \emph{return $U^{ind}, \Theta^{ind}$ } \;
928 \caption{O-U-Coverage}
935 \item \textbf{Evaluate Population:}
936 After creating the initial population, each individual is evaluated and assigned a fitness value according to the fitness function is illustrated in Eq. \eqref{eqf}. In the proposed GA, the optimal (or near optimal) candidate solution, is the one with the minimum value for the fitness function. The lower the fitness values been assigned to an individual, the better opportunity it get survived. In our works, the function rewards the decrease in the sensor nodes which cover the same primary point and penalizes the decrease to zero in the sensor nodes which cover the primary point.
939 F^{ind} \leftarrow \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eqf}
943 \item \textbf{Selection:} In order to generate a new generation, a portion of the existing population is elected based on a fitness function that ranks the fitness of each candidate solution and preferentially select the best solutions. Two parents should be selected to the mating pool. In the proposed GA-MuDiLCO algorithm, the first parent is selected by using binary tournament selection to select one of the parents \cite{goldberg1991comparative}. In this method, two individuals are chosen at random from population and the better of the two
944 individuals is selected. If they have similar fitness values, one of them will be selected randomly. The best individual in the population is selected as a second parent.
948 \item \textbf{Crossover:} Crossover is a genetic operator used to take more than one parent solutions and produce a child solution from them. If crossover probability $P_c$ is 100$\%$, then the crossover operation takes place between two individuals. If it is 0$\%$, the two selected individuals in the mating pool will be the new chromosomes without crossover. In the proposed GA, a two-point crossover is used. Figure \ref{cross} gives an example for a two-point crossover for 8 sensors in the subregion and the schedule for 3 rounds.
953 \includegraphics [scale = 0.3] {crossover.pdf}
954 \caption{Two-point crossover. }
959 \item \textbf{Mutation:}
960 Mutation is a divergence operation which introduces random modifications. The purpose of the mutation is to maintain diversity within the population and prevent premature convergence. Mutation is used to add new genetic information (divergence) in order to achieve a global search over the solution search space and avoid to fall in local optima. The mutation oprator in the proposed GA-MuDiLCO works as follow: If mutation probability $P_m$ is 100$\%$, then the mutation operation takes place on the the new individual. The round number is selected randomly within (1..T) in the schedule solution. After that one sensor within this round is selected randomly within (1..J). If the sensor is scheduled as active "1", it should be rescheduled to sleep "0". If the sensor is scheduled as sleep, it rescheduled to active only if it has adequate remaining energy.
963 \item \textbf{Update O-U-Coverage for children:}
964 Before evalute each new individual, Algorithm \ref{OU} is called for each new individual to compute the new undercoverage $Ch.U$ and overcoverage $Ch.\Theta$ parameters.
966 \item \textbf{Evaluate New Individuals:}
967 Each new individual is evaluated using Eq. \ref{eqf} but with using the new undercoverage $Ch.U$ and overcoverage $Ch.\Theta$ parameters of the new children.
969 \item \textbf{Replacement:}
970 After evaluatation of new children, Triple Tournament Replacement (TTR) will be applied for each new individual. In TTR strategy, three individuals are selected
971 randomly from the population. Find the worst from them and then check its fitness with the new individual fitness. If the fitness of the new individual is better than the fitness of the worst individual, replace the new individual with the worst individual. Otherwise, the replacement is not done.
974 \item \textbf{Stopping criteria:}
975 The proposed GA-MuDiLCO stops when the stopping criteria is met. It stops after running for an amount of time in seconds equal to \textbf{Time limit}. The \textbf{Time limit} is the execution time obtained by the optimization solver GLPK for solving the same size of problem divided by two. The best solution will be selected as a schedule of sensors for $T$ rounds during the sensing phase in the current period.
983 \section{Experimental study}
985 \subsection{Simulation setup}
987 We conducted a series of simulations to evaluate the efficiency and the
988 relevance of our approach, using the discrete event simulator OMNeT++
989 \cite{varga}. The simulation parameters are summarized in
990 Table~\ref{table3}. Each experiment for a network is run over 25~different
991 random topologies and the results presented hereafter are the average of these
993 %Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions.
994 We performed simulations for five different densities varying from 50 to
995 250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
996 precisely, the deployment is controlled at a coarse scale in order to ensure
997 that the deployed nodes can cover the sensing field with the given sensing
1000 %%RC these parameters are realistic?
1001 %% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
1004 \caption{Relevant parameters for network initializing.}
1007 % used for centering table
1008 \begin{tabular}{c|c}
1009 % centered columns (4 columns)
1011 %inserts double horizontal lines
1012 Parameter & Value \\ [0.5ex]
1014 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
1018 % inserts single horizontal line
1019 Sensing field size & $(50 \times 25)~m^2 $ \\
1020 % inserting body of the table
1022 Network size & 50, 100, 150, 200 and 250~nodes \\
1024 Initial energy & 500-700~joules \\
1026 Sensing time for one round & 60 Minutes \\
1027 $E_{R}$ & 36 Joules\\
1031 % [1ex] adds vertical space
1034 %inserts single line
1037 % is used to refer this table in the text
1040 Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5,
1041 and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of
1042 rounds in one sensing period). In the following, we will make comparisons with
1043 two other methods. The first method, called DESK and proposed by \cite{ChinhVu},
1044 is a full distributed coverage algorithm. The second method, called
1045 GAF~\cite{xu2001geography}, consists in dividing the region into fixed squares.
1046 During the decision phase, in each square, one sensor is then chosen to remain
1047 active during the sensing phase time.
1049 Some preliminary experiments were performed to study the choice of the number of
1050 subregions which subdivides the sensing field, considering different network
1051 sizes. They show that as the number of subregions increases, so does the network
1052 lifetime. Moreover, it makes the MuDiLCO protocol more robust against random
1053 network disconnection due to node failures. However, too many subdivisions
1054 reduce the advantage of the optimization. In fact, there is a balance between
1055 the benefit from the optimization and the execution time needed to solve
1056 it. Therefore, we have set the number of subregions to 16 rather than 32.
1058 \subsection{Energy model}
1060 We use an energy consumption model proposed by~\cite{ChinhVu} and based on
1061 \cite{raghunathan2002energy} with slight modifications. The energy consumption
1062 for sending/receiving the packets is added, whereas the part related to the
1063 sensing range is removed because we consider a fixed sensing range.
1065 % We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node.
1066 %The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU.
1069 For our energy consumption model, we refer to the sensor node Medusa~II which
1070 uses an Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The
1071 typical architecture of a sensor is composed of four subsystems: the MCU
1072 subsystem which is capable of computation, communication subsystem (radio) which
1073 is responsible for transmitting/receiving messages, the sensing subsystem that
1074 collects data, and the power supply which powers the complete sensor node
1075 \cite{raghunathan2002energy}. Each of the first three subsystems can be turned
1076 on or off depending on the current status of the sensor. Energy consumption
1077 (expressed in milliWatt per second) for the different status of the sensor is
1078 summarized in Table~\ref{table4}.
1081 \caption{The Energy Consumption Model}
1084 % used for centering table
1085 \begin{tabular}{|c|c|c|c|c|}
1086 % centered columns (4 columns)
1088 %inserts double horizontal lines
1089 Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
1091 % inserts single horizontal line
1092 LISTENING & on & on & on & 20.05 \\
1093 % inserting body of the table
1095 ACTIVE & on & off & on & 9.72 \\
1097 SLEEP & off & off & off & 0.02 \\
1099 COMPUTATION & on & on & on & 26.83 \\
1101 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
1106 % is used to refer this table in the text
1109 For the sake of simplicity we ignore the energy needed to turn on the radio, to
1110 start up the sensor node, to move from one status to another, etc.
1111 %We also do not consider the need of collecting sensing data. PAS COMPRIS
1112 Thus, when a sensor becomes active (i.e., it has already chosen its status), it can
1113 turn its radio off to save battery. MuDiLCO uses two types of packets for
1114 communication. The size of the INFO packet and Active-Sleep packet are 112~bits
1115 and 24~bits respectively. The value of energy spent to send a 1-bit-content
1116 message is obtained by using the equation in ~\cite{raghunathan2002energy} to
1117 calculate the energy cost for transmitting messages and we propose the same
1118 value for receiving the packets. The energy needed to send or receive a 1-bit
1119 packet is equal to 0.2575~mW.
1121 The initial energy of each node is randomly set in the interval $[500;700]$. A
1122 sensor node will not participate in the next round if its remaining energy is
1123 less than $E_{R}=36~\mbox{Joules}$, the minimum energy needed for the node to
1124 stay alive during one round. This value has been computed by multiplying the
1125 energy consumed in active state (9.72 mW) by the time in second for one round
1126 (3600 seconds). According to the interval of initial energy, a sensor may be
1127 alive during at most 20 rounds.
1129 \subsection{Metrics}
1131 To evaluate our approach we consider the following performance metrics:
1133 \begin{enumerate}[i]
1135 \item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
1136 of a sensor field is covered. In our case, the sensing field is represented as
1137 a connected grid of points and we use each grid point as a sample point to
1138 compute the coverage. The coverage ratio can be calculated by:
1141 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
1143 where $n^t$ is the number of covered grid points by the active sensors of all
1144 subregions during round $t$ in the current sensing phase and $N$ is the total number
1145 of grid points in the sensing field of the network. In our simulations $N = 51
1146 \times 26 = 1326$ grid points.
1147 %The accuracy of this method depends on the distance between grids. In our
1148 %simulations, the sensing field has been divided into 50 by 25 grid points, which means
1149 %there are $51 \times 26~ = ~ 1326$ points in total.
1150 % Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
1152 \item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
1153 few active nodes as possible in each round, in order to minimize the
1154 communication overhead and maximize the network lifetime. The Active Sensors
1155 Ratio is defined as follows:
1157 \scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
1158 \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
1160 where $A_r^t$ is the number of active sensors in the subregion $r$ during round
1161 $t$ in the current sensing phase, $|J|$ is the total number of sensors in the
1162 network, and $R$ is the total number of subregions in the network.
1164 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until
1165 the coverage ratio drops below a predefined threshold. We denote by
1166 $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during
1167 which the network can satisfy an area coverage greater than $95\%$
1168 (respectively $50\%$). We assume that the network is alive until all nodes have
1169 been drained of their energy or the sensor network becomes
1170 disconnected. Network connectivity is important because an active sensor node
1171 without connectivity towards a base station cannot transmit information on an
1172 event in the area that it monitors.
1174 \item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
1175 seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
1176 $Lifetime_{50}$ divided by the number of rounds. EC can be computed as
1179 % New version with global loops on period
1182 \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T_m},
1186 % Old version with loop on round outside the loop on period
1189 % \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
1195 %\mbox{EC} = \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
1198 % Old version -> where $M_L$ and $T_L$ are respectively the number of periods and rounds during
1199 %$Lifetime_{95}$ or $Lifetime_{50}$.
1201 where $M$ is the number of periods and $T_m$ the number of rounds in a
1202 period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
1203 consumed by the sensors (EC) comes through taking into consideration four main
1204 energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
1205 represents the energy consumption spent by all the nodes for wireless
1206 communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
1207 factor, corresponds to the energy consumed by the sensors in LISTENING status
1208 before receiving the decision to go active or sleep in period $m$.
1209 $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
1210 nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
1211 indicate the energy consumed by the whole network in round $t$.
1213 %\item {Network Lifetime:} we have defined the network lifetime as the time until all
1214 %nodes have been drained of their energy or each sensor network monitoring an area has become disconnected.
1216 \item {{\bf Execution Time}:} a sensor node has limited energy resources and
1217 computing power, therefore it is important that the proposed algorithm has the
1218 shortest possible execution time. The energy of a sensor node must be mainly
1219 used for the sensing phase, not for the pre-sensing ones.
1221 \item {{\bf Stopped simulation runs}:} a simulation ends when the sensor network
1222 becomes disconnected (some nodes are dead and are not able to send information
1223 to the base station). We report the number of simulations that are stopped due
1224 to network disconnections and for which round it occurs.
1228 \subsection{Results and analysis}
1230 \subsubsection{Coverage ratio}
1232 Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
1233 can notice that for the first thirty rounds both DESK and GAF provide a coverage
1234 which is a little bit better than the one of MuDiLCO.
1235 %%RC : need to uniformize MuDiLCO or MuDiLCO-T?
1236 %%MS : MuDiLCO everywhere
1237 %%RC maybe increase the size of the figure for the reviewers, no?
1238 This is due to the fact that, in comparison with MuDiLCO which uses optimization
1239 to put in SLEEP status redundant sensors, more sensor nodes remain active with
1240 DESK and GAF. As a consequence, when the number of rounds increases, a larger
1241 number of node failures can be observed in DESK and GAF, resulting in a faster
1242 decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
1243 coverage ratio greater than 50\% for far more rounds. Overall, the proposed
1244 sensor activity scheduling based on optimization in MuDiLCO maintains higher
1245 coverage ratios of the area of interest for a larger number of rounds. It also
1246 means that MuDiLCO saves more energy, with less dead nodes, at most for several
1247 rounds, and thus should extend the network lifetime.
1251 \includegraphics[scale=0.5] {R/CR.pdf}
1252 \caption{Average coverage ratio for 150 deployed nodes}
1256 \subsubsection{Active sensors ratio}
1258 It is crucial to have as few active nodes as possible in each round, in order to
1259 minimize the communication overhead and maximize the network
1260 lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
1261 nodes all along the network lifetime. It appears that up to round thirteen, DESK
1262 and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
1263 MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
1264 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
1265 with the dual observation of higher level of coverage made previously.
1266 Obviously, in that case DESK and GAF have less active nodes, since they have
1267 activated many nodes at the beginning. Anyway, MuDiLCO activates the available
1268 nodes in a more efficient manner.
1272 \includegraphics[scale=0.5]{R/ASR.pdf}
1273 \caption{Active sensors ratio for 150 deployed nodes}
1277 \subsubsection{Stopped simulation runs}
1278 %The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
1279 %runs per round for 150 deployed nodes.
1281 Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs
1282 per round for 150 deployed nodes. This figure gives the breakpoint for each method. DESK stops first, after approximately 45~rounds, because it consumes the
1283 more energy by turning on a large number of redundant nodes during the sensing
1284 phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes
1285 DESK and GAF because the optimization process distributed on several subregions
1286 leads to coverage preservation and so extends the network lifetime. Let us
1287 emphasize that the simulation continues as long as a network in a subregion is
1290 %%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1294 \includegraphics[scale=0.5]{R/SR.pdf}
1295 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
1299 \subsubsection{Energy consumption} \label{subsec:EC}
1301 We measure the energy consumed by the sensors during the communication,
1302 listening, computation, active, and sleep status for different network densities
1303 and compare it with the two other methods. Figures~\ref{fig7}(a)
1304 and~\ref{fig7}(b) illustrate the energy consumption, considering different
1305 network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
1310 \parbox{9.5cm}{\includegraphics[scale=0.5]{R/EC95.pdf}} & (a) \\
1312 \parbox{9.5cm}{\includegraphics[scale=0.5]{R/EC50.pdf}} & (b)
1314 \caption{Energy consumption for (a) $Lifetime_{95}$ and
1315 (b) $Lifetime_{50}$}
1319 The results show that MuDiLCO is the most competitive from the energy
1320 consumption point of view. The other approaches have a high energy consumption
1321 due to activating a larger number of redundant nodes as well as the energy
1322 consumed during the different status of the sensor node. Among the different
1323 versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
1324 versions. This is easy to understand since the bigger the number of rounds and
1325 the number of sensors involved in the integer program are, the larger the time
1326 computation to solve the optimization problem is. To improve the performances of
1327 MuDiLCO-7, we should increase the number of subregions in order to have less
1328 sensors to consider in the integer program.
1330 %In fact, a distributed optimization decision, which produces T rounds, on the subregions is greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically.
1333 \subsubsection{Execution time}
1335 We observe the impact of the network size and of the number of rounds on the
1336 computation time. Figure~\ref{fig77} gives the average execution times in
1337 seconds (needed to solve optimization problem) for different values of $T$. The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the Mixed Integer Linear Program instance in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. The
1338 original execution time is computed on a laptop DELL with Intel Core~i3~2370~M
1339 (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second)
1340 rate equal to 35330. To be consistent with the use of a sensor node with Atmels
1341 AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the
1342 optimization resolution, this time is multiplied by 2944.2 $\left(
1343 \frac{35330}{2} \times \frac{1}{6} \right)$ and reported on Figure~\ref{fig77}
1344 for different network sizes.
1348 \includegraphics[scale=0.5]{R/T.pdf}
1349 \caption{Execution Time (in seconds)}
1353 As expected, the execution time increases with the number of rounds $T$ taken
1354 into account to schedule the sensing phase. The times obtained for $T=1,3$
1355 or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
1356 node, especially when the sensor network size increases. Again, we can notice
1357 that if we want to schedule the nodes activities for a large number of rounds,
1358 we need to choose a relevant number of subregions in order to avoid a complicated
1359 and cumbersome optimization. On the one hand, a large value for $T$ permits to
1360 reduce the energy-overhead due to the three pre-sensing phases, on the other
1361 hand a leader node may waste a considerable amount of energy to solve the
1362 optimization problem.
1364 %While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T. We think that in distributed fashion the solving of the optimization problem to produce T rounds in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
1366 \subsubsection{Network lifetime}
1368 The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
1369 network lifetime for different network sizes, respectively for $Lifetime_{95}$
1370 and $Lifetime_{50}$. Both figures show that the network lifetime increases
1371 together with the number of sensor nodes, whatever the protocol, thanks to the
1372 node density which results in more and more redundant nodes that can be
1373 deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
1374 protocol maximizes the lifetime of the network. In particular the gain in
1375 lifetime for a coverage over 95\% is greater than 38\% when switching from GAF
1376 to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case
1377 of $Lifetime_{95}$ with large wireless sensor networks results from the
1378 difficulty of the optimization problem to be solved by the integer program.
1379 This point was already noticed in subsection \ref{subsec:EC} devoted to the
1380 energy consumption, since network lifetime and energy consumption are directly
1386 \parbox{9.5cm}{\includegraphics[scale=0.5]{R/LT95.pdf}} & (a) \\
1388 \parbox{9.5cm}{\includegraphics[scale=0.5]{R/LT50.pdf}} & (b)
1390 \caption{Network lifetime for (a) $Lifetime_{95}$ and
1391 (b) $Lifetime_{50}$}
1395 % By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO protocol efficiently prolonges the network lifetime.
1397 %In Figure~\ref{fig8}, Comparison shows that our MuDiLCO protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each sensor node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
1400 %We see that our MuDiLCO-7 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumption seems to be huge because it used a larger number of rounds T during performing the optimization decision in the subregions, which is led to decrease the network lifetime. On the other side, our MuDiLCO-1, 3, and 5 protocol seems to be more efficient in comparison with other approaches because they are prolonged the lifetime of the network more than DESK and GAF.
1403 \section{Conclusion and future works}
1404 \label{sec:conclusion}
1406 We have addressed the problem of the coverage and of the lifetime optimization in
1407 wireless sensor networks. This is a key issue as sensor nodes have limited
1408 resources in terms of memory, energy, and computational power. To cope with this
1409 problem, the field of sensing is divided into smaller subregions using the
1410 concept of divide-and-conquer method, and then we propose a protocol which
1411 optimizes coverage and lifetime performances in each subregion. Our protocol,
1412 called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines
1413 two efficient techniques: network leader election and sensor activity
1415 %, where the challenges
1416 %include how to select the most efficient leader in each subregion and
1417 %the best cover sets %of active nodes that will optimize the network lifetime
1418 %while taking the responsibility of covering the corresponding
1419 %subregion using more than one cover set during the sensing phase.
1420 The activity scheduling in each subregion works in periods, where each period
1421 consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
1422 Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
1423 Phase itself divided into $T$ rounds.
1425 Simulations results show the relevance of the proposed protocol in terms of
1426 lifetime, coverage ratio, active sensors ratio, energy consumption, execution
1427 time. Indeed, when dealing with large wireless sensor networks, a distributed
1428 approach, like the one we propose, allows to reduce the difficulty of a single
1429 global optimization problem by partitioning it in many smaller problems, one per
1430 subregion, that can be solved more easily. Nevertheless, results also show that
1431 it is not possible to plan the activity of sensors over too many rounds, because
1432 the resulting optimization problem leads to too high resolution times and thus to
1433 an excessive energy consumption.
1435 %In future work, we plan to study and propose adjustable sensing range coverage optimization protocol, which computes all active sensor schedules in one time, by using
1436 %optimization methods. This protocol can prolong the network lifetime by minimizing the number of the active sensor nodes near the borders by optimizing the sensing range of sensor nodes.
1437 % use section* for acknowledgement
1439 \section*{Acknowledgment}
1440 This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
1441 As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the
1442 University of Babylon - Iraq for the financial support, Campus France (The
1443 French national agency for the promotion of higher education, international
1444 student services, and international mobility).%, and the University ofFranche-Comt\'e - France for all the support in France.
1455 %% The Appendices part is started with the command \appendix;
1456 %% appendix sections are then done as normal sections
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