This paper addresses the problem of wireless sensor network (WSN) lifetime maximization, under limited available energy constraint. The investigations have shown that the valid amount of energy was not used by the existing disjoint set covers (DSC) based scheduling method for WSNs' lifetime maximization, because of the DSC constraints. Instead, we suggest in this paper to schedule non-disjoint sets covers (NDSC) for maximizing WSNs' lifetime. Thus, we have formulated this problem, using the integer linear programming (ILP) mathematical model, then we developed an approach based on genetic algorithm GA to find the maximal lifespan. As main contributions, we investigated and designed a new method using the NDSC instead of the DSC. This approach removes the latter's constraint and gives the opportunity to a sensor to participate in more than one cover, and thereby improves significantly the WSNs' lifetime. We proposed an exact method and a genetic algorithms (GA) for the NDSC efficient scheduling for the WSN lifetime maximization. The exact method lies on the integer linear programming (ILP). For the GA based heuristics, we used a specific arrangement of chromosomes combining several crossover and mutation strategies for encoding the solutions. We provided experimental results for different instances involving sensors with non-identical amount of initial energy and power consumption. In addition, we provided comparative analysis results between the solutions obtained by our both methods and the existing methods based on DSC. The comparisons of the run times and the solutions' quality revealed the dominance of the solutions yielded by our methods based on the NDSC compared to those based on the DSC.