Chapter 5 modified by Ali

[ThesisAli.git] / CHAPITRE_03.tex

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@@ -20,7 +20,8 @@ For this reason, several problems are modeled by an optimization problem for ins
 %Therefore, in order to get the optimal solutions for these mathematical optimization problems, the optimization solver is the best candidate tool to solve them. The optimization solver takes mathematical optimization problem descriptions in a certain file format and calculates their optimal solution. 
 Optimization solvers dedicated to specific resolution methods (meta-heuristics, linear programming, etc) are required.
 %Many important real-world problems have formulated as integer programming problems. 
 %Therefore, in order to get the optimal solutions for these mathematical optimization problems, the optimization solver is the best candidate tool to solve them. The optimization solver takes mathematical optimization problem descriptions in a certain file format and calculates their optimal solution. 
 Optimization solvers dedicated to specific resolution methods (meta-heuristics, linear programming, etc) are required.
 %Many important real-world problems have formulated as integer programming problems. 

-In this dissertation, we use linear programming because we used integer programs to optimize the coverage and the lifetime in WSNs.
+%In this dissertation, we use linear programming because we used integer programs to optimize the coverage and the lifetime in WSNs.
+In this dissertation, we optimize the coverage and the lifetime in WSNs and the problem is formulated through linear programming. These kind of models allow to obtain optimal solutions satisfying an objective (for instance, maximize coverage)  under constraints (for instance, available remaining energy). 

 
 The remainder of this chapter is organized as follows. The next section is devoted to the evaluation tools for evaluating and validating the  performance of proposed algorithms and protocols. Section \ref{ch3:3} gives the most popular free and commercial linear optimization solvers to solve the linear programming problems. Finally, we give concluding remarks in section \ref{ch3:4}.
  
 
 The remainder of this chapter is organized as follows. The next section is devoted to the evaluation tools for evaluating and validating the  performance of proposed algorithms and protocols. Section \ref{ch3:3} gives the most popular free and commercial linear optimization solvers to solve the linear programming problems. Finally, we give concluding remarks in section \ref{ch3:4}.