A directional sensor network consists of numerous small sensor nodes that have limited battery power and operate within a restricted sensing range angle. Coverage and connectivity, as two important issues,are widely studied in directional sensor networks. Different from conventional directional sensor nodes in previous studies, those in the present study could adjust their sensing ranges within a range of several values. This paper addresses the Connected adjusted-ranges directional cover(CARDC) problem. The purpose is to organize the directional sensor nodes into a group of connected covers, and assign activities to them, thereby maximizing the network lifetime. We propose a hybrid approach that combines column generation with a genetic algorithm to solve the CARDC problem. The genetic algorithm is utilized to settle the auxiliary problem of column generation, which has the ability to efficiently provide attractive columns for the master problem. Compared with pure integer linear programming formulations, the proposed genetic algorithm significantly improves the speed of column generation method, especially in large-scale networks. The effect variety of number of directions, number of power levels,and communication range on the network lifetime are also investigated.
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