Establishing complete and reliable coverage for a long time-span is a crucial issue in densely surveillance wireless sensor networks (WSNs). Many scheduling algorithms have been proposed to model the problem as a maximum disjoint set covers (DSC) problem. The goal of DSC based algorithms is to schedule sensors into several disjoint subsets. One subset is assigned to be active, whereas, all remaining subsets are set to sleep. An extension to the maximum disjoint set covers problem has also been addressed in literature to allow for more advance sensors to adjust their sensing range. The problem, then, is extended to finding maximum number of overlapped set covers. Unlike all related works which concern with the disc sensing model, the contribution of this paper is to reformulate the maximum overlapped set covers problem to handle the probabilistic sensing model. The problem is addressed as a multi-objective optimization (MOO) problem and the well-known decomposition based multi-objective evolutionary algorithm (MOEA/D) is adopted to solve the stated problem. A Multi-layer MOEA/D is suggested, wherein each layer yields a distinct set cover. Performance evaluations in terms of total number of set covers, total residual energy, and coverage reliability are reported through extensive simulations. The main aspect of the results reveals that the network's lifetime (i.e. total number of set covers) can be extended by increasing number of sensors. On the other hand, the coverage reliability can be increased by increasing sensing ranges but at the expense of decreasing the network's lifetime.