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[JournalMultiPeriods.git] / article.tex

diff --git a/article.tex b/article.tex
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--- a/article.tex
+++ b/article.tex
@@ -108,7 +108,7 @@ during which sets of sensor nodes are scheduled to remain active for a number of
 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
 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.
 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.


@@ -204,9 +204,10 @@ network. Note that  centralized algorithms have the advantage  of requiring very
 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
 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
 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
 
 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


@@ -296,7 +297,7 @@ computation complexity. Compared to our previous paper, in this one we study the
 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
 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
    
 
 \iffalse
    


@@ -555,7 +556,7 @@ implemented in each subregion in a distributed way.
 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
 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.
 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.


@@ -578,7 +579,8 @@ running out of energy), because it works in periods.
 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
 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...  
 %%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...  


@@ -837,12 +839,11 @@ large compared to $W_{\theta}$.
 \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.}
 
 
 \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.}
 
 

-%\textcolor{red}{\textbf{\textsc{Answer:}   ali   }}

 
 
 
 

-\subsection{\textcolor{red}{Genetic Algorithm (GA) for Multiround Lifetime Coverage Optimization}}
+\subsection{\textcolor{red}{Genetic Algorithm for Multiround Lifetime Coverage Optimization}}

 \label{GA}
 \label{GA}

-\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. Compared to GLPK optimization solver, GA provides a near optimal solution with acceptible execution time, while GLPK provides optimal solution but it requires high execution time for large problem.}
+\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.}

 
 \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:}
 
 
 \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:}
 


@@ -895,7 +896,7 @@ large compared to $W_{\theta}$.
 
 \begin{enumerate} [I)]
 
 
 \begin{enumerate} [I)]
 

-\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 next 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.}
+\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
 %[scale=0.3]
 \begin{figure}[h!]
 \centering


@@ -906,7 +907,7 @@ large compared to $W_{\theta}$.
 
 
 
 
 
 

-\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 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 \textcolor{red}{\textbf{Update O-U-Coverage:} 
 
 
 \item \textcolor{red}{\textbf{Update O-U-Coverage:} 


@@ -951,14 +952,14 @@ After creating the initial population, The overcoverage $\Theta_{t,p}$ and under
 
 
 \item \textcolor{red}{\textbf{Evaluate Population:}
 
 
 \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 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. }
+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}
 
 
 
 \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 \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 population and the better of the two
+\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.}
 
 
 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.}
 
 


@@ -975,22 +976,22 @@ individuals is selected. If they have similar fitness values, one of them will b
 
 
 \item \textcolor{red}{\textbf{Mutation:}
 
 
 \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 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.}
+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 \textcolor{red}{\textbf{Update O-U-Coverage for children:}
 
 
 \item \textcolor{red}{\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. }
+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 \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 \textcolor{red}{\textbf{Replacement:}
  
 \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 \textcolor{red}{\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
+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 \textcolor{red}{\textbf{Stopping criteria:}
 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{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.}
+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.}