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One of the most critical issues in wireless sensor network is represented by the limited availability of energy on sensor nodes. In this paper, we propose the power efficient organization of k-separate cover sets as a backbone to maximum network lifetime. All the sensors are divided into K-separate sets on the basis of multi-objective genetic algorithm, guaranteeing each cover set is pareto optimal. By alternating subsets of sensor nodes and using only one at each round, redundancy elimination can contribute to reduce energy consumption. The algorithm is evaluated via a simulation study. Clearly, by solving the optimization model, a network designer can gain useful insights into the possible gains in term of network lifetime.