Partial coverage optimization under network connectivity constraints in heterogeneous sensor networks

The maximum network lifetime problem (MLP) in heterogeneous wireless sensor networks under connectivity and coverage constraints is addressed in this paper. Two main variants of the studied problem are considered. The first variant is a-coverage where a portion ((1 - alpha) percent) of the targets are allowed to be left uncovered. The second one is called beta-coverage or beta-constraint where each target has a minimum coverage rate beta during the network's lifetime service. When the two variants are considered at the same time, the problem is called alpha beta-Connected Maximum Lifetime Problem (alpha beta-CMLP) where we consider both global (whole targets) resp. local (individual target) monitoring level thresholds to improve the coverage quality of the deployed WSN. Unlike earlier works devoted to only a coverage, we deal with both local (alpha) and global (beta) coverage leveling thresholds under network connectivity constraint. One approach to optimize the network's lifetime is to divide the sensor nodes into Non-Disjoint subsets of sensors, or cover sets, and to schedule these covers with variable activation time periods, so that the global time lifespan of the network is optimized. To this end, we provide both exact and heuristic approaches in this study. First, a novel mathematical Mixed Integer Linear Programming (MILP) is presented to solve the alpha beta-coverage with network connectivity requirement to optimality. Unfortunately, due to the NP-Completeness of the addressed problem, the MILP's resolution becomes impracticable for large optimization problems. To remedy this and to cope with large instances, we propose a new exact approach based on column generation able to achieve optimal solutions in reasonable time. In addition, since the CG's subproblem resolution is also an NP-Hard problem, a new dedicated Heuristic (DH) is designed to solve the CG's subproblem in polynomial time complexity. Moreover, we propose an exact ILP formulation for the CG's subproblem if the DH heuristic fails to compute an attractive solution in each iteration of the CG computation process. Finally, several experiments are performed to evaluate the performances of our proposals.