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 The coverage problem in WSNs is becoming more and more important for many applications ranging from military applications such as battlefield surveillance to the civilian applications such as health-care surveillance and habitant monitoring. The main contributions in this dissertation concentrate on design a distributed optimization protocols so as to extend the lifetime of the WSNs.  We summarize the main contributions of our research as follows:
  
 \begin{enumerate} [i)]
- \item We design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization (DILCO) protocol, maintains the coverage and improves the lifetime in WSNs. DILCO protocol presented in chapter 3 is an extension of our approach introduced in \cite{ref159}. In \cite{ref159}, the protocol is deployed over only two subregions. In DILCO protocol, the area of interest is first divided into subregions using a divide-and-conquer algorithm and an activity scheduling for sensor nodes is then planned by the elected leader in each subregion. 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. DiLCO protocol considers periods, where a period starts with a discovery phase to exchange information between sensors of the same subregion, in order to choose in a suitable manner a sensor node (the leader) to carry out the coverage strategy. In each subregion, the activation of the sensors for the sensing phase of the current period is obtained by solving an integer program. The resulting activation vector is broadcast by a leader to every node of its subregion.
+ \item We design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization (DILCO) protocol, maintains the coverage and improves the lifetime in WSNs. DILCO protocol presented in chapter 4 is an extension of our approach introduced in \cite{ref159}. In \cite{ref159}, the protocol is deployed over only two subregions. In DILCO protocol, the area of interest is first divided into subregions using a divide-and-conquer algorithm and an activity scheduling for sensor nodes is then planned by the elected leader in each subregion. 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. DiLCO protocol considers periods, where a period starts with a discovery phase to exchange information between sensors of the same subregion, in order to choose in a suitable manner a sensor node (the leader) to carry out the coverage strategy. In each subregion, the activation of the sensors for the sensing phase of the current period is obtained by solving an integer program. The resulting activation vector is broadcast by a leader to every node of its subregion.
 
-\item We extend our work that explained in chapter 3 and present a generalized framework that can be applied to provide the cover sets of all rounds in each period. The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in chapter 4 is an extension of the approach introduced in chapter 3. In DiLCO protocol, the activity scheduling based optimization is planned for each subregion periodically only for one round. Whilst, we study the possibility of dividing the sensing phase into multiple rounds. In fact, we make a multiround optimization while it was a single round optimization in our previous contribution.
+\item We extend our work that explained in chapter 5 and present a generalized framework that can be applied to provide the cover sets of all rounds in each period. The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in chapter 4 is an extension of the approach introduced in chapter 3. In DiLCO protocol, the activity scheduling based optimization is planned for each subregion periodically only for one round. Whilst, we study the possibility of dividing the sensing phase into multiple rounds. In fact, we make a multiround optimization while it was a single round optimization in our previous contribution.
 
-\item We devise a framework to schedule nodes to be activated alternatively such that the network lifetime is prolonged  while ensuring that a certain level of   coverage is preserved. A key idea in our framework is  to exploit the spatial-temporal subdivision. On the one hand, the area of interest is divided into several smaller subregions and, on the other hand, the timeline is divided into periods of equal length. In each subregion, the sensor nodes will cooperatively choose a  leader which will schedule  nodes' activities, and this grouping of sensors is similar to typical cluster architecture. We  propose a new mathematical  optimization model. Instead of  trying to cover a set of specified points/targets as in most of the methods proposed in the literature, we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the actual level of coverage and the required  level. So that an optimal scheduling  will be  obtained by  minimizing a  weighted sum  of these deviations. This contribution is demonstrated in Chapter 5.
+\item We devise a framework to schedule nodes to be activated alternatively such that the network lifetime is prolonged  while ensuring that a certain level of   coverage is preserved. A key idea in our framework is  to exploit the spatial-temporal subdivision. On the one hand, the area of interest is divided into several smaller subregions and, on the other hand, the timeline is divided into periods of equal length. In each subregion, the sensor nodes will cooperatively choose a  leader which will schedule  nodes' activities, and this grouping of sensors is similar to typical cluster architecture. We  propose a new mathematical  optimization model. Instead of  trying to cover a set of specified points/targets as in most of the methods proposed in the literature, we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the actual level of coverage and the required  level. So that an optimal scheduling  will be  obtained by  minimizing a  weighted sum  of these deviations. This contribution is demonstrated in Chapter 6.
 
 \item We add an improved model of energy consumption to assess the efficiency of our protocols as well as we conducted extensive simulation experiments, using the discrete event simulator OMNeT++, to demonstrate the  efficiency of our protocols. We compared our proposed distributed optimization protocols to two approaches found in the literature: DESK~\cite{DESK} and GAF~\cite{GAF}, simulation results based on multiple criteria (energy consumption, coverage ratio, network lifetime and so on) show that the proposed protocols can prolong efficiently the network lifetime and improve the coverage performance.
 
