Modeling, Scheduling and Optimization of Wireless Sensor Networks lifetime. (Modélisation, ordonnancement et optimisation de la durée de vie des réseaux de capteurs sans fil)

Wireless sensor networks (WSNs), as a collection of sensing nodes with limited processing, limited energy reserve and radio communication capabilities, are widely implemented in many areas of applications such as industry, environment, healthcare, etc. Regarding this large range of applications, many research issues are introduced including the applications, performance, reliability, lifetime, etc. The WSNs lifetime considered in this work is the period of time through which theWSN is perfectly completing its function. This lifetime is affected by many factors including the amount of energy available, failure probability and components degradation. The amount of energy available become the most important factor in case of non renewable components applications. Different algorithms, strategies and optimization techniques were developed and implemented for this purpose based on the possibility of activating a subset of sensors that satisfied the monitoring constraint, while keeping the others in sleep mode to be implemented later. This is an NP complete maximization problem that can be solved using disjoint set covers (DSCs). But the solution obtained using DSCs does not extend always significantly the WSNs lifetime. So, the present work aims to search for a better solution using non-disjoint set covers (NDSCs). This approach gives the opportunity for a sensor to be implemented in one or more subset covers. For that purpose, we studied a binary representation based model to maximize the number of NDSCs. Also, we developed a genetic algorithm based heuristic based on this model to find out the maximum number of NDSCs in a reasonable time. Thus, for a set of m sensors used to monitor a set of n targets or a field, this heuristic allows to construct a maximum number q of NDSCs. Additional effort is required to find the best scheduling for implementing the NDSCs so as to maximize the lifetime of the sensors involved in the WSNs, considering their limited available energy. This problem is formulated using integer linear programming (ILP) mathematical model. The objective function of this problem is the sum of all monitoring seasons on which all q NDSCs scheduled, and the constraint is the energy consumption in all sensors included in all NDSCs. Solving this problem using ILP in a period of time depends on the complexity of the model and the instances used. To find the solution in reasonable time, we have developed a NDSCs based genetic algorithm (NDSC-GA). The candidate solutions are represented in chromosomes composed of a number of genes equal to the number q of NDSCs, and each gene is the number of monitoring seasons on which a NDSC is scheduled. We have then developed a GA that combines the four crossover operators and four mutation operators. The GA based methods are coded in C programming language to obtain a satisfying solution and the Cplex software was used to obtain the corresponding exact solution. Comparing the optimal solution obtained using the ILP on small instances, to the solutions obtained using our GA based method explained that our methods can find a solution near the optimal in reasonable time. Then, comparing the solution obtained using our NDSCs GA based methods, to the DSCs GA based method in the literature, we showed that the NDSCs GA can prolong the WSNs lifetime better than DSCs GA for the same instances. Our approach combines together the scheduling principles and the optimization techniques to maximizing the WSNs lifetime