Maher Rebai

Sensor deployment optimization methods to achieve both coverage and connectivity in wireless sensor networks

In this study, we aim to cover a sensing area by deploying a minimum number of wireless sensors while maintaining the connectivity between the deployed sensors. The problem may be reduced to a two-dimensional critical coverage problem which is an NP-Complete problem. We develop an integer linear programming model to solve the problem optimally. We also propose a local search (LS) algorithm and a genetic algorithm (GA) as approximate methods. We verify by computational experiments that the integer linear model, using Cplex, is able to provide an optimal solution of all our small and medium size problems. We also show that the proposed methods outperform some regular sensor deployment patterns.

Earliness---tardiness minimization on a single machine to schedule preventive maintenance tasks: metaheuristic and exact methods

In this paper, we consider the problem of scheduling a set of M preventive maintenance tasks to be performed on M machines. The machines are assigned to execute production tasks. We aim to minimize the total preventive maintenance cost such that the maintenance tasks have to continuously be run during the schedule horizon. Such a constraint holds when the maintenance resources are not sufficient. We solve the problem by two exact methods and meta-heuristic algorithms. As exact procedures we used linear programming and branch and bound methods. As meta-heuristics, we propose a local search approach as well as a genetic algorithm. Computational experiments are performed on randomly generated instances to show that the proposed methods produce appropriate solutions for the problem. The computational results show that the deviation of the meta-heuristics solutions to the optimal one is very small, which confirms the effectiveness of meta-heuristics as new approaches for solving hard scheduling problems.

Linear models for the total coverage problem in wireless sensor networks

In this paper, we consider the total grid coverage problem in wireless sensor networks. Our proposal aims to determine the optimal number of sensors and their positions in a sensing area represented by a grid. The deployed sensors should achieve the total grid point coverage. The problem is proved NP-complete in [15]. We propose two mathematical linear models to solve optimally two problem cases. In the first case, the connectivity between deployed sensors is not required. However, in the second case, the sensors should communicate with each other. Computational experiments are generated on different grid sizes and multiple sensor ranges. The results show that the proposed linear models can produce appropriate solutions for the two problem cases.

A Branch and Bound Algorithm for the Critical Grid Coverage Problem in Wireless Sensor Networks

We aim to cover a grid fully by deploying the necessary wireless sensors while maintaining connectivity between the deployed sensors and a base station (the sink). The problem is NP-Complete as it can be reduced to a 2-dimensional critical coverage problem, which is an NP-Complete problem. We develop a branch and bound (B&B) algorithm to solve the problem optimally. We verify by computational experiments that the proposed B&B algorithm is more efficient, in terms of computation time, than the integer linear programming model developed by Rebai et al. (2013), for the same problem.

A bi-objective model for wireless sensor deployment considering coverage and tracking applications

In recent years, wireless sensor networks WSNs have become very attractive for surveillance applications and particularly for target tracking. When a target has to be located by a WSN, accuracy is an important constraint. Most of the studies made in the WSNs problems deal with either coverage or tracking focus objectives. In this paper, we study a bi-objective sensor placement problem taking into account both coverage and accuracy. The objectives are the minimisation of the number of deployed sensors and the minimisation of the imprecision, under the coverage constraints. The non sorting genetic algorithm NSGA-II and multi objective evolutionary algorithm based on decomposition MOEA/D have been implemented to solve the problem. The performances of these algorithms are checked with integer programming results for small size instances, and they are compared on large size instances by multi-objective metrics. Results have shown that both implemented algorithms provide optimal solutions for almost small size instances. NSGA-II results are better than MOEA/D on the small size instance set, while MOEA/D outperforms NSGA-II on the large size instance set.

Exact methods for sensor deployment problem with connectivity constraint in wireless sensor networks

In wireless sensor networks, coverage and connectivity are two essential issues. They indicate how all the points of an area of interest are covered and how the sensor devices of the wireless sensor network are connected in an efficient way. In this study, the problem of minimising total grid coverage cost with connectivity constraint is considered. The connectivity constraint means that each deployed sensor has to find a path, composed of connected sensors, until to reach the base station the sink. The problem may be reduced to a 2-dimensional critical grid coverage problem which is an NP-Complete problem. We propose mixed integer linear programming models to solve the problem optimally. We verify by computational experiments that the developed approaches can provide the optimal solution of grid sizes of 15 × 15 width × length in a reasonable time. We also show that one of the proposed methods is more efficient than some methods developed for similar problems.

Exact Biobjective Optimization Methods for Camera Coverage Problem in Three-Dimensional Areas

This paper deals with the problem of deploying necessary camera sensors ensuring the maximum sum of weighted target points in 3-D areas while minimizing the total sensor network camera cost. The problem is NP-complete as it can be considered as a total grid coverage problem, which is an NP-complete problem when the sensing field is a 2-D area. We solve the problem optimally by three exact biobjective methods: 1) weighted sum scalarization approach; 2) a two-phase method; and 3) an ε-constraint method. The simulation results show that each adopted resolution approach dominates the other approaches in at least one criterium when the problem size increases and the resolution process is stopped after a predefined computation time limit.

A Specific Heuristic Dedicated to a Coverage/Tracking Bi-objective Problem for Wireless Sensor Deployment

In recent years, wireless sensor networks (WSN) have become very attractive for surveillance applications and particularly for target tracking. When a target has to be located by a WSN, accuracy is an important constraint. Most of the studies made in the WSNs problems deal with either coverage or tracking focus objectives. In this paper, we propose a modification of a previously studied bi-objective sensor placement problem taking into account both coverage and accuracy. The objectives are the minimization of the number of deployed sensors and the minimization of the tracking constraints violations, under the coverage constraints. The non sorting genetic algorithm and multi objective particle swarm optimization have been implemented to solve the problem. A specific heuristic (H3P) based on the mathematical decomposition of the problem has also been proposed. The performances of these algorithms are checked with integer programming results for small size instances, and they are compared on large size instances by multi-objective metrics. Results have shown that implemented metaheuristics provide less optimal solutions than the H3P for the small size instances. The comparison between the algorithms on large size instances set show that the H3P dominates the other implemented methods.

Scheduling jobs and maintenance activities on parallel machines

In this article, we deal with the problem of scheduling N production jobs on M parallel machines. Each machine should be maintained once during the planning horizon. We consider the case where the maintenance of the machines should start at time zero and the resources that ensure the maintenance are not sufficient. For such a reason, the maintenance tasks must be continuously run during the planning horizon. We aim to find a schedule composed of the production jobs and the maintenance tasks for which the total sum of the jobs’ weighted completion times and the preventive maintenance cost are minimized. We optimally solve the problem by an integer linear programming method. We also propose a heuristic method computed in two phases. Computational experiments are performed on randomly generated instances and the results show that the proposed methods produce satisfactory solutions for the problem.

Evolutionary Algorithm for Scheduling Production Jobs and Preventive Maintenance Activities

We propose in this article an evolutionary algorithm for the problem of scheduling N production jobs on M parallel machines. Each machine should be blocked once during the planning horizon for reasons of preventive maintenance. In our study, the maintenance tasks should continuously be performed because the maintenance resources are not sufficient. We aim to find a schedule composed of the production jobs and the maintenance tasks with a minimal preventive maintenance cost and total sum of production job’s weighted completion times.