In this paper we face the problem of maximizing the amount of time over which a set of target points, located in a given geographic region, can be monitored by means of a wireless sensor network. The problem is well known in the literature as Maximum Network Lifetime Problem (MLP). In the last few years the problem and a number of variants have been tackled with success by means of different resolution approaches, including exact approaches based on column generation techniques. In this work we propose an exact approach which combines a column generation approach with a genetic algorithm aimed at solving efficiently its separation problem. The genetic algorithm is specifically aimed at the Maximum Network α-Lifetime Problem (α-MLP), a variant of MLP in which a given fraction of targets is allowed to be left uncovered at all times; however, since α-MLP is a generalization of MLP, it can be used to solve the classical problem as well. The computational results, obtained on the benchmark instances, show that our approach overcomes the algorithms, available in the literature, to solve both MLP and α-MLP.