Update by Ali

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@@ -1059,7 +1059,7 @@ $S_{pop}$ & 50
 \textcolor{red}{Our first protocol based GLPK optimization solver is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
 and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
 rounds in one sensing period). The second protocol based GA is declined into  four versions: GA-MuDiLCO-1,  GA-MuDiLCO-3, GA-MuDiLCO-5,
 \textcolor{red}{Our first protocol based GLPK optimization solver is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
 and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
 rounds in one sensing period). The second protocol based GA is declined into  four versions: GA-MuDiLCO-1,  GA-MuDiLCO-3, GA-MuDiLCO-5,

-and  GA-MuDiLCO-7 for the same reason of the first protocol}.  In  the following, we will make comparisons with
+and  GA-MuDiLCO-7 for the same reason of the first protocol. After extensive experiments, we chose the dedicated values for the parameters $P_c$, $P_m$, and $S_{pop}$ because they gave the best results}.  In  the following, we will make comparisons with

 two other methods. The first method, called DESK and proposed by \cite{ChinhVu},
 is  a   full  distributed  coverage   algorithm.   The  second   method,  called
 GAF~\cite{xu2001geography}, consists in dividing  the region into fixed squares.
 two other methods. The first method, called DESK and proposed by \cite{ChinhVu},
 is  a   full  distributed  coverage   algorithm.   The  second   method,  called
 GAF~\cite{xu2001geography}, consists in dividing  the region into fixed squares.


@@ -1273,19 +1273,20 @@ rounds, and thus should extend the network lifetime.
 \label{fig3}
 \end{figure} 
 
 \label{fig3}
 \end{figure} 
 

+\textcolor{red}{ We
+can see that for the first thirty nine rounds GA-MuDiLCO provides a little bit better coverage ratio  than MuDiLCO. Both DESK and GAF provide a coverage
+which is a little bit better than the one of MuDiLCO and GA-MuDiLCO for the first thirty rounds because they activate a larger number of nodes during sensing phase. After that GA-MuDiLCO provides a coverage ratio near to the  MuDiLCO and better than DESK and GAF. GA-MuDiLCO gives approximate solution with activation a larger number of nodes than MuDiLCO during sensing phase while it activates a less number of nodes in comparison with both DESK and GAF. The results of GA-MuDiLCO seems to be comparable and can maintain the lifetime coverage as long as possible.}
+
+
+

 \subsubsection{Active sensors ratio} 
 
 It is crucial to have as few active nodes as possible in each round, in order to
 \subsubsection{Active sensors ratio} 
 
 It is crucial to have as few active nodes as possible in each round, in order to

-minimize    the    communication    overhead    and   maximize    the    network
-lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed
+minimize the communication overhead and maximize    the network lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed

 nodes all along the network lifetime. It appears that up to round thirteen, DESK
 and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas
 nodes all along the network lifetime. It appears that up to round thirteen, DESK
 and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas

-MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
-thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
-with  the  dual  observation  of  higher  level  of  coverage  made  previously.
-Obviously, in  that case DESK  and GAF have  less active nodes, since  they have
-activated many nodes  at the beginning. Anyway, MuDiLCO  activates the available
-nodes in a more efficient manner.
+MuDiLCO clearly outperforms them  with only 24.8\%  of active nodes. \textcolor{red}{GA-MuDiLCO activates a number of sensor nodes larger than MuDiLCO but lower than both DESK and GAF. GA-MuDiLCO-1, GA-MuDiLCO-3, and GA-MuDiLCO-5 continue in providing a larger number of active sensors until the forty-sixth round after that it provides less number of active nodes due to the died nodes. GA-MuDiLCO-7 provides a larger number of sensor nodes and maintains a better coverage ratio compared to MuDiLCO-7 until the fifty-seventh round.  After the thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes compared with DESK  and GAF, which agrees with  the  dual  observation  of  higher  level  of  coverage  made  previously}.
+Obviously, in that case DESK  and GAF have less active nodes, since  they have activated many nodes  at the beginning. Anyway, MuDiLCO  activates the available nodes in a more efficient manner. \textcolor{red}{GA-MuDiLCO activates near optimal number of sensor nodes also in efficient manner compared with both DESK  and GAF}.

 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering


@@ -1294,6 +1295,9 @@ nodes in a more efficient manner.
 \label{fig4}
 \end{figure} 
 
 \label{fig4}
 \end{figure} 
 

+%\textcolor{red}{GA-MuDiLCO activates a sensor nodes larger than MuDiLCO but lower than both DESK and GAF }
+
+

 \subsubsection{Stopped simulation runs}
 %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
 %runs per round for 150 deployed nodes. 
 \subsubsection{Stopped simulation runs}
 %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
 %runs per round for 150 deployed nodes. 


@@ -1301,11 +1305,9 @@ nodes in a more efficient manner.
 Figure~\ref{fig6} reports the cumulative  percentage of stopped simulations runs
 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
 more energy by  turning on a large number of redundant  nodes during the sensing
 Figure~\ref{fig6} reports the cumulative  percentage of stopped simulations runs
 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
 more energy by  turning on a large number of redundant  nodes during the sensing

-phase. GAF  stops secondly for the  same reason than  DESK.  MuDiLCO overcomes
-DESK and GAF because the  optimization process distributed on several subregions
-leads  to coverage  preservation and  so extends  the network  lifetime.  Let us
-emphasize that the  simulation continues as long as a network  in a subregion is
-still connected.
+phase. GAF  stops secondly for the  same reason than  DESK. \textcolor{red}{GA-MuDiLCO  stops thirdly for the  same reason than  DESK and GAF.} \textcolor{red}{MuDiLCO and GA-MuDiLCO overcome}
+DESK and GAF because \textcolor{red}{they activate less number of sensor nodes, as well as }the optimization process distributed on several subregions leads to coverage  preservation and  so extends  the network  lifetime.  
+Let us emphasize that the  simulation continues as long as a network  in a subregion is still connected. 

 
 %%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
 %%% The optimization effectively continues as long as a network in a subregion is still connected. A VOIR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%