rounds during the sensing phase, to ensure coverage so as to maximize the
lifetime of WSN. The decision process is carried out by a leader node, which
solves an integer program to produce the best representative sets to be used
-during the rounds of the sensing phase. Compared with some existing protocols,
+during the rounds of the sensing phase. \textcolor{red}{The integer program is solved by either GLPK solver or Genetic Algorithm (GA)}. Compared with some existing protocols,
simulation results based on multiple criteria (energy consumption, coverage
ratio, and so on) show that the proposed protocol can prolong efficiently the
network lifetime and improve the coverage performance.
low processing power from the sensor nodes, which usually have limited
processing capabilities. The main drawback of this kind of approach is its
higher cost in communications, since the node that will make the decision needs
-information from all the sensor nodes. Moreover, centralized approaches usually
+information from all the sensor nodes. \textcolor{red} {Exact or heuristics approaches are designed to provide cover sets. (Moreover, centralized approaches usually
suffer from the scalability problem, making them less competitive as the network
-size increases.
+size increases.) Contrary to exact methods, heuristic methods can handle very large and centralized problems. They are proposed to reduce computational overhead such as energy consumption, delay and generally increase in
+the network lifetime. }
The first algorithms proposed in the literature consider that the cover sets are
disjoint: a sensor node appears in exactly one of the generated cover
possibility of dividing the sensing phase into multiple rounds and we also add
an improved model of energy consumption to assess the efficiency of our
approach. In fact, in this paper we make a multiround optimization, while it was
-a single round optimization in our previous work.
+a single round optimization in our previous work. \textcolor{red}{In addition, a metaheuristic based GA is proposed to solve our multiround optimization}.
\iffalse
As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion,
where each is divided into 4 phases: Information~Exchange, Leader~Election,
Decision, and Sensing. Each sensing phase may be itself divided into $T$ rounds
-and for each round a set of sensors (a cover set) is responsible for the sensing
+\textcolor{green} {of equal duration} and for each round a set of sensors (a cover set) is responsible for the sensing
task. In this way a multiround optimization process is performed during each
period after Information~Exchange and Leader~Election phases, in order to
produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
decision, the node will not participate to this phase, and, on the other hand,
if the node failure occurs after the decision, the sensing task of the network
will be temporarily affected: only during the period of sensing until a new
-period starts.
+period starts. \textcolor{green}{The duration of the period and the duration of the rounds are predefined parameters. Round duration should be long enough to hide the system control overhead and short enough to minimize the negative effects in case of node failure.}
+
%%RC so if there are at least one failure per period, the coverage is bad...
%%MS if we want to be reliable against many node failures we need to have an
%% overcoverage...
\subsection{Decision phase}
-Each WSNL will solve an integer program to select which cover sets will be
+Each WSNL will \textcolor{red}{ execute an optimization algorithm (see section \ref{oa})} to select which cover sets will be
activated in the following sensing phase to cover the subregion to which it
-belongs. The integer program will produce $T$ cover sets, one for each round.
-The WSNL will send an Active-Sleep packet to each sensor in the subregion based
-on the algorithm's results, indicating if the sensor should be active or not in
-each round of the sensing phase. The integer program is based on the model
+belongs. The \textcolor{red}{optimization algorithm} will produce $T$ cover sets, one for each round. The WSNL will send an Active-Sleep packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
+each round of the sensing phase.
+
+%solve an integer program
+
+\subsection{Sensing phase}
+
+The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
+receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
+sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
+will be executed by each node at the beginning of a period, explains how the
+Active-Sleep packet is obtained.
+
+% 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.
+
+\begin{algorithm}[h!]
+ % \KwIn{all the parameters related to information exchange}
+% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+ \BlankLine
+ %\emph{Initialize the sensor node and determine it's position and subregion} \;
+
+ \If{ $RE_j \geq E_{R}$ }{
+ \emph{$s_j.status$ = COMMUNICATION}\;
+ \emph{Send $INFO()$ packet to other nodes in the subregion}\;
+ \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
+ %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
+ %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
+
+ %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
+ \emph{LeaderID = Leader election}\;
+ \If{$ s_j.ID = LeaderID $}{
+ \emph{$s_j.status$ = COMPUTATION}\;
+ \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
+ Execute \textcolor{red}{Optimization Algorithm}($T,J$)}\;
+ \emph{$s_j.status$ = COMMUNICATION}\;
+ \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
+ with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
+ \emph{Update $RE_j $}\;
+ }
+ \Else{
+ \emph{$s_j.status$ = LISTENING}\;
+ \emph{Wait $ActiveSleep()$ packet from the Leader}\;
+ % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+ \emph{Update $RE_j $}\;
+ }
+ % }
+ }
+ \Else { Exclude $s_j$ from entering in the current sensing phase}
+
+ % \emph{return X} \;
+\caption{MuDiLCO($s_j$)}
+\label{alg:MuDiLCO}
+
+\end{algorithm}
+
+
+
+
+
+
+\section{\textcolor{red}{ Optimization Algorithm for Multiround Lifetime Coverage Optimization}}
+\label{oa}
+As shown in Algorithm~\ref{alg:MuDiLCO}, the leader will execute an optimization algorithm based on an integer program. The integer program is based on the model
proposed by \cite{pedraza2006} with some modifications, where the objective is
to find a maximum number of disjoint cover sets. To fulfill this goal, the
authors proposed an integer program which forces undercoverage and overcoverage
large compared to $W_{\theta}$.
%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.
-\subsection{Sensing phase}
-
-The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
-receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
-sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
-will be executed by each node at the beginning of a period, explains how the
-Active-Sleep packet is obtained.
-
-% 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.
+\textcolor{red}{This integer program can be solved using two approaches:}
-\begin{algorithm}[h!]
- % \KwIn{all the parameters related to information exchange}
-% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
- \BlankLine
- %\emph{Initialize the sensor node and determine it's position and subregion} \;
-
- \If{ $RE_j \geq E_{R}$ }{
- \emph{$s_j.status$ = COMMUNICATION}\;
- \emph{Send $INFO()$ packet to other nodes in the subregion}\;
- \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
- %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
- %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
-
- %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
- \emph{LeaderID = Leader election}\;
- \If{$ s_j.ID = LeaderID $}{
- \emph{$s_j.status$ = COMPUTATION}\;
- \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
- Execute Integer Program Algorithm($T,J$)}\;
- \emph{$s_j.status$ = COMMUNICATION}\;
- \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
- with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
- \emph{Update $RE_j $}\;
- }
- \Else{
- \emph{$s_j.status$ = LISTENING}\;
- \emph{Wait $ActiveSleep()$ packet from the Leader}\;
- % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
- \emph{Update $RE_j $}\;
- }
- % }
- }
- \Else { Exclude $s_j$ from entering in the current sensing phase}
-
- % \emph{return X} \;
-\caption{MuDiLCO($s_j$)}
-\label{alg:MuDiLCO}
+\subsection{\textcolor{red}{Optimization solver for Multiround Lifetime Coverage Optimization}}
+\label{glpk}
+\textcolor{red}{The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer 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. We named the protocol which is based on GLPK solver in the decision phase as MuDiLCO.}
-\end{algorithm}
-%\textcolor{red}{\textbf{\textsc{Answer:} ali }}
-\section{Genetic Algorithm (GA) for Multiround Lifetime Coverage Optimization}
+\subsection{\textcolor{red}{Genetic Algorithm for Multiround Lifetime Coverage Optimization}}
\label{GA}
-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.
+\textcolor{red}{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. In comparison with GLPK optimization solver, GA provides a near optimal solution with acceptable execution time, as well as it requires a less amount of memory especially for large size problems. GLPK provides optimal solution, but it requires higher execution time and amount of memory for large problem.}
-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:
+\textcolor{red}{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{oa}. 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:}
-\begin{algorithm}[h!]
+\begin{algorithm}[h!]
+
\small
- \SetKwInput{Input}{Input}
- \SetKwInput{Output}{Output}
- \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}$}
- \Output{$\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}
+ \SetKwInput{Input}{\textcolor{red}{Input}}
+ \SetKwInput{Output}{\textcolor{red}{Output}}
+ \Input{ \textcolor{red}{$ 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}$}}
+ \Output{\textcolor{red}{$\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}}
\BlankLine
%\emph{Initialize the sensor node and determine it's position and subregion} \;
- \ForEach {Individual $ind$ $\in$ $S_{pop}$} {
- \emph{Generate Randomly Chromosome $\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}\;
+ \ForEach {\textcolor{red}{Individual $ind$ $\in$ $S_{pop}$}} {
+ \emph{\textcolor{red}{Generate Randomly Chromosome $\left\{\left(X_{1,1},\dots, X_{t,j}, \dots, X_{T,J}\right)\right\}_{t \in T, j \in J}$}}\;
- \emph{Update O-U-Coverage $\left\{(P, J, \alpha_{j,p}^{ind}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})\right\}_{p \in P}$}\;
+ \emph{\textcolor{red}{Update O-U-Coverage $\left\{(P, J, \alpha_{j,p}^{ind}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})\right\}_{p \in P}$}}\;
- \emph{Evaluate Individual $(P, J, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})$}\;
+ \emph{\textcolor{red}{Evaluate Individual $(P, J, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind})$}}\;
}
- \While{ Stopping criteria is not satisfied }{
+ \While{\textcolor{red}{ Stopping criteria is not satisfied} }{
- \emph{Selection $(ind_1, ind_2)$}\;
- \emph{Crossover $(P_c, X_{t,j}^{ind_1}, X_{t,j}^{ind_2}, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}\;
- \emph{Mutation $(P_m, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}\;
+ \emph{\textcolor{red}{Selection $(ind_1, ind_2)$}}\;
+ \emph{\textcolor{red}{Crossover $(P_c, X_{t,j}^{ind_1}, X_{t,j}^{ind_2}, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}}\;
+ \emph{\textcolor{red}{Mutation $(P_m, Child_{t,j}^{ind_1}, Child_{t,j}^{ind_2})$}}\;
- \emph{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}\;
- \emph{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}\;
+ \emph{\textcolor{red}{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}}\;
+ \emph{\textcolor{red}{Update O-U-Coverage $(P, J, \alpha_{j,p}^{ind}, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}}\;
-\emph{Evaluate New Individual$(P, J, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}\;
- \emph{Replacement $(P, J, T, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind} )$ }\;
+\emph{\textcolor{red}{Evaluate New Individual$(P, J, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1})$}}\;
+ \emph{\textcolor{red}{Replacement $(P, J, T, Child_{t,j}^{ind_1}, Ch.\Theta_{t,p}^{ind_1}, Ch.U_{t,p}^{ind_1}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind} )$ }}\;
- \emph{Evaluate New Individual$(P, J, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}\;
+ \emph{\textcolor{red}{Evaluate New Individual$(P, J, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2})$}}\;
- \emph{Replacement $(P, J, T, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind} )$ }\;
+ \emph{\textcolor{red}{Replacement $(P, J, T, Child_{t,j}^{ind_2}, Ch.\Theta_{t,p}^{ind_2}, Ch.U_{t,p}^{ind_2}, X_{t,j}^{ind}, \Theta_{t,p}^{ind}, U_{t,p}^{ind} )$ }}\;
}
- \emph{$\left\{\left(X_{1,1},\dots,X_{t,j},\dots,X_{T,J}\right)\right\}$ =
- Select Best Solution ($S_{pop}$)}\;
- \emph{return X} \;
-\caption{GA-MuDiLCO($s_j$)}
+ \emph{\textcolor{red}{$\left\{\left(X_{1,1},\dots,X_{t,j},\dots,X_{T,J}\right)\right\}$ =
+ Select Best Solution ($S_{pop}$)}}\;
+ \emph{\textcolor{red}{return X}} \;
+\caption{\textcolor{red}{GA($T, J$)}}
\label{alg:GA}
\end{algorithm}
\begin{enumerate} [I)]
-\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.
+
+\item \textcolor{red}{\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 sensing phase, the chromosome is defined as a schedule for alive sensors and each chromosome contains $T$ rounds. The proposed GA uses binary representation, where 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.}
%[scale=0.3]
\begin{figure}[h!]
\centering
- \includegraphics [scale=0.35] {rep.eps}
+ \includegraphics [scale=0.35] {rep.pdf}
\caption{Candidate Solution representation by the proposed GA. }
\label{chromo}
\end{figure}
-\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.
+\item \textcolor{red}{\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 the current round. Otherwise, the value is set to 0. The energy constraint is applied for each sensor during all rounds. }
-\item \textbf{Update O-U-Coverage:}
-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.
+\item \textcolor{red}{\textbf{Update O-U-Coverage:}
+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.}
\begin{algorithm}[h!]
- \SetKwInput{Input}{Input}
- \SetKwInput{Output}{Output}
- \Input{ parameters $P, J, ind, \alpha_{j,p}^{ind}, X_{t,j}^{ind}$}
- \Output{$U^{ind} = \left\lbrace U_{1,1}^{ind}, \dots, U_{t,p}^{ind}, \dots, U_{T,P}^{ind} \right\rbrace$ and $\Theta^{ind} = \left\lbrace \Theta_{1,1}^{ind}, \dots, \Theta_{t,p}^{ind}, \dots, \Theta_{T,P}^{ind} \right\rbrace$}
+ \SetKwInput{Input}{\textcolor{red}{Input}}
+ \SetKwInput{Output}{\textcolor{red}{Output}}
+ \Input{ \textcolor{red}{parameters $P, J, ind, \alpha_{j,p}^{ind}, X_{t,j}^{ind}$}}
+ \Output{\textcolor{red}{$U^{ind} = \left\lbrace U_{1,1}^{ind}, \dots, U_{t,p}^{ind}, \dots, U_{T,P}^{ind} \right\rbrace$ and $\Theta^{ind} = \left\lbrace \Theta_{1,1}^{ind}, \dots, \Theta_{t,p}^{ind}, \dots, \Theta_{T,P}^{ind} \right\rbrace$}}
\BlankLine
- \For{$t\leftarrow 1$ \KwTo $T$}{
- \For{$p\leftarrow 1$ \KwTo $P$}{
+ \For{\textcolor{red}{$t\leftarrow 1$ \KwTo $T$}}{
+ \For{\textcolor{red}{$p\leftarrow 1$ \KwTo $P$}}{
% \For{$i\leftarrow 0$ \KwTo $I_j$}{
- \emph{$SUM\leftarrow 0$}\;
- \For{$j\leftarrow 1$ \KwTo $J$}{
- \emph{$SUM \leftarrow SUM + (\alpha_{j,p}^{ind} \times X_{t,j}^{ind})$ }\;
+ \emph{\textcolor{red}{$SUM\leftarrow 0$}}\;
+ \For{\textcolor{red}{$j\leftarrow 1$ \KwTo $J$}}{
+ \emph{\textcolor{red}{$SUM \leftarrow SUM + (\alpha_{j,p}^{ind} \times X_{t,j}^{ind})$ }}\;
}
- \If { SUM = 0} {
- \emph{$U_{t,p}^{ind} \leftarrow 0$}\;
- \emph{$\Theta_{t,p}^{ind} \leftarrow 1$}\;
+ \If { \textcolor{red}{SUM = 0}} {
+ \emph{\textcolor{red}{$U_{t,p}^{ind} \leftarrow 0$}}\;
+ \emph{\textcolor{red}{$\Theta_{t,p}^{ind} \leftarrow 1$}}\;
}
\Else{
- \emph{$U_{t,p}^{ind} \leftarrow SUM -1$}\;
- \emph{$\Theta_{t,p}^{ind} \leftarrow 0$}\;
+ \emph{\textcolor{red}{$U_{t,p}^{ind} \leftarrow SUM -1$}}\;
+ \emph{\textcolor{red}{$\Theta_{t,p}^{ind} \leftarrow 0$}}\;
}
}
}
-\emph{return $U^{ind}, \Theta^{ind}$ } \;
+\emph{\textcolor{red}{return $U^{ind}, \Theta^{ind}$ }} \;
\caption{O-U-Coverage}
\label{OU}
-\item \textbf{Evaluate Population:}
-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.
+\item \textcolor{red}{\textbf{Evaluate Population:}
+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 gets 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. }
\begin{equation}
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}
\end{equation}
-\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
-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.
+\item \textcolor{red}{\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 the population and the better of the two
+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.}
-\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.
+\item \textcolor{red}{\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.}
\begin{figure}[h!]
\centering
- \includegraphics [scale = 0.3] {crossover.eps}
+ \includegraphics [scale = 0.3] {crossover.pdf}
\caption{Two-point crossover. }
\label{cross}
\end{figure}
-\item \textbf{Mutation:}
-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.
+\item \textcolor{red}{\textbf{Mutation:}
+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 operator in the proposed GA-MuDiLCO works as follow: If mutation probability $P_m$ is 100$\%$, then the mutation operation takes place on 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.}
-\item \textbf{Update O-U-Coverage for children:}
-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.
+\item \textcolor{red}{\textbf{Update O-U-Coverage for children:}
+Before evaluating each new individual, Algorithm \ref{OU} is called for each new individual to compute the new undercoverage $Ch.U$ and overcoverage $Ch.\Theta$ parameters. }
-\item \textbf{Evaluate New Individuals:}
-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.
+\item \textcolor{red}{\textbf{Evaluate New Individuals:}
+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.}
-\item \textbf{Replacement:}
-After evaluatation of new children, Triple Tournament Replacement (TTR) will be applied for each new individual. In TTR strategy, three individuals are selected
-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.
+\item \textcolor{red}{\textbf{Replacement:}
+After evaluation of new children, Triple Tournament Replacement (TTR) will be applied for each new individual. In TTR strategy, three individuals are selected
+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. }
-\item \textbf{Stopping criteria:}
-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.
+\item \textcolor{red}{\textbf{Stopping criteria:}
+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. The best solution will be selected as a schedule of sensors for $T$ rounds during the sensing phase in the current period.}
$W_{\theta}$ & 1 \\
% [1ex] adds vertical space
%\hline
-$W_{U}$ & $|P|^2$
+$W_{U}$ & $|P|^2$ \\
+$P_c$ & 0.95 \\
+$P_m$ & 0.6 \\
+$S_{pop}$ & 50
%inserts single line
\end{tabular}
\label{table3}
% is used to refer this table in the text
\end{table}
-Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, 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). In the following, we will make comparisons with
+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. 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.
\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. MuDiLCO and GA-MuDiLCO clearly outperform DESK and GAF for
+a number of periods between 31 and 103. This is because they optimize the coverage and the lifetime in a wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase.}
+
+
+
\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
-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
\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.
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 results show that MuDiLCO is the most competitive from the energy
consumption point of view. The other approaches have a high energy consumption
-due to activating a larger number of redundant nodes as well as the energy
-consumed during the different status of the sensor node. Among the different
-versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
-versions. This is easy to understand since the bigger the number of rounds and
-the number of sensors involved in the integer program are, the larger the time
-computation to solve the optimization problem is. To improve the performances of
-MuDiLCO-7, we should increase the number of subregions in order to have less
-sensors to consider in the integer program.
-
+due to activating a larger number of redundant nodes as well as the energy consumed during the different status of the sensor node. Among the different versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
+versions. This is easy to understand since the bigger the number of rounds and the number of sensors involved in the integer program are, the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we should increase the number of subregions in order to have less sensors to consider in the integer program.
+\textcolor{red}{As shown in Figure~\ref{fig7}, GA-MuDiLCO consumes less energy than both DESK and GAF, but a little bit higher than MuDiLCO because it provides a near optimal solution by activating a larger number of nodes during the sensing phase. GA-MuDiLCO consumes less energy in comparison with MuDiLCO-7 version, especially for the dense networks. However, MuDiLCO protocol and GA-MuDiLCO protocol are the most competitive from the energy
+consumption point of view. The other approaches have a high energy consumption
+due to activating a larger number of redundant nodes.}
%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.
difficulty of the optimization problem to be solved by the integer program.
This point was already noticed in subsection \ref{subsec:EC} devoted to the
energy consumption, since network lifetime and energy consumption are directly
-linked.
-
+linked. \textcolor{red}{As can be seen in these figures, the lifetime increases with the size of the network, and it is clearly largest for the MuDiLCO
+and the GA-MuDiLCO protocols. GA-MuDiLCO prolongs the network lifetime obviously in comparison with both DESK and GAF, as well as the MuDiLCO-7 version for $lifetime_{95}$. However, comparison shows that MuDiLCO protocol and GA-MuDiLCO protocol, which use distributed optimization over the subregions are the best ones because they are robust to network disconnection during the network lifetime as well as they consume less energy in comparison with other approaches.}
\begin{figure}[t!]
\centering
\begin{tabular}{cl}
