X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/ec3eb1e7f256da3a709bb498434bd5c8f6b87c38..473fcf6b4a8be17eb285310e31be480bffcb7138:/article.tex diff --git a/article.tex b/article.tex index e32ed72..ca8c2c3 100644 --- a/article.tex +++ b/article.tex @@ -106,9 +106,14 @@ divided into subregions and then the MuDiLCO protocol is distributed on the sensor nodes in each subregion. The proposed MuDiLCO protocol works in periods 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 -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, +lifetime of WSN. \textcolor{green}{The decision process is carried out by a leader node, which +solves an optimization problem to produce the best representative sets to be used +during the rounds of the sensing phase. The optimization problem formulated as an integer program is solved either to optimality through a branch-and-Bound method or to near-optimality using a genetic algorithm-based heuristic. } +%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. +%\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. @@ -183,7 +188,7 @@ algorithms in WSNs according to several design choices: \item Sensors scheduling algorithm implementation, i.e. centralized or distributed/localized algorithms. \item The objective of sensor coverage, i.e. to maximize the network lifetime or - to minimize the number of sensors during a sensing round. + to minimize the number of active sensors during a sensing round. \item The homogeneous or heterogeneous nature of the nodes, in terms of sensing or communication capabilities. \item The node deployment method, which may be random or deterministic. @@ -204,9 +209,12 @@ 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 -information from all the sensor nodes. Moreover, centralized approaches usually -suffer from the scalability problem, making them less competitive as the network -size increases. +information from all the sensor nodes. \textcolor{green} {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.) +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 @@ -231,7 +239,8 @@ node. After that, they proposed a High Residual Energy First (HREF) node selection algorithm to minimize the number of active nodes so as to prolong the network lifetime. Various centralized methods based on column generation approaches have also been -proposed~\cite{castano2013column,rossi2012exact,deschinkel2012column}. +proposed~\cite{gentili2013,castano2013column,rossi2012exact,deschinkel2012column}. +\textcolor{green}{In~\cite{gentili2013}, authors highlight the trade-off between the network lifetime and the coverage percentage. They show that network lifetime can be hugely improved by decreasing the coverage ratio. } \subsection{Distributed approaches} %{\bf Distributed approaches} @@ -296,7 +305,8 @@ 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 -a single round optimization in our previous work. \textcolor{red}{In addition, a metaheuristic based GA is proposed to solve our multiround optimization}. +a single round optimization in our previous work. \textcolor{green}{The idea is to take advantage of the pre-sensing phase + to plan the sensor's activity for several rounds instead of one, thus saving energy. In addition, as the optimization problem has become more complex, a GA-based heuristic is proposed to solve it}. \iffalse @@ -528,10 +538,64 @@ Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the active nodes. -Instead of working with a continuous coverage area, we make it discrete by -considering for each sensor a set of points called primary points. Consequently, -we assume that the sensing disk defined by a sensor is covered if all of its -primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here. +%Instead of working with a continuous coverage area, we make it discrete by considering for each sensor a set of points called primary points. Consequently, we assume that the sensing disk defined by a sensor is covered if all of its primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here. + + +\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By knowing the position (point center: ($p_x,p_y$)) of a wireless sensor node and it's sensing range $R_s$, we calculate the primary points directly based on the proposed model. We use these primary points (that can be increased or decreased if necessary) as references to ensure that the monitored region of interest is covered by the selected set of sensors, instead of using all the points in the area. +We can calculate the positions of the selected primary +points in the circle disk of the sensing range of a wireless sensor +node (see Figure~\ref{fig1}) as follows:\\ +Assuming that the point center of a wireless sensor node is located at $(p_x,p_y)$, we can define up to 25 primary points $X_1$ to $X_{25}$.\\ +%$(p_x,p_y)$ = point center of wireless sensor node\\ +$X_1=(p_x,p_y)$ \\ +$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\ +$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\ +$X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\ +$X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\ +$X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\ +$X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\ +$X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\ +$X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\ +$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\ +$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\ +$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\ +$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\ +$X_{14}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\ +$X_{15}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\ +$X_{16}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\ +$X_{17}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\ +$X_{18}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (0) $\\ +$X_{19}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (0) $\\ +$X_{20}=( p_x + R_s * (0), p_y + R_s * (\frac{1}{2})) $\\ +$X_{21}=( p_x + R_s * (0), p_y + R_s * (-\frac{1}{2})) $\\ +$X_{22}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\ +$X_{23}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\ +$X_{24}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $\\ +$X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $. + + + +\begin{figure} %[h!] +\centering + \begin{multicols}{2} +\centering +\includegraphics[scale=0.28]{fig21.pdf}\\~ (a) +\includegraphics[scale=0.28]{principles13.pdf}\\~(c) +\hfill \hfill +\includegraphics[scale=0.28]{fig25.pdf}\\~(e) +\includegraphics[scale=0.28]{fig22.pdf}\\~(b) +\hfill \hfill +\includegraphics[scale=0.28]{fig24.pdf}\\~(d) +\includegraphics[scale=0.28]{fig26.pdf}\\~(f) +\end{multicols} +\caption{Wireless Sensor Node represented by (a) 5, (b) 9, (c) 13, (d) 17, (e) 21 and (f) 25 primary points respectively} +\label{fig1} +\end{figure} + + + + + %By knowing the position (point center: ($p_x,p_y$)) of a wireless %sensor node and its $R_s$, we calculate the primary points directly @@ -555,7 +619,7 @@ 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 -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. @@ -578,7 +642,8 @@ 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 -period starts. +period starts. \textcolor{green}{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... @@ -989,7 +1054,7 @@ randomly from the population. Find the worst from them and then check its fitnes \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.}