A Lagrangean relaxation approach to lifetime maximization of directional sensor networks

We consider the directional sensor network lifetime maximization problem (DSLMP). Given a set of directional sensor and target locations, the problem consists in assigning, at each time unit of a given time horizon, the action radius, the aperture angle, and the orientation direction to all sensors. The objective is to maximize the number of time units when all targets are covered, under certain constraints on sensor available energy. We present a mixed integer nonlinear programming formulation and tackle it by Lagrangean decomposition and subgradient optimization. The algorithm is equipped with a repairing heuristics aimed at finding good-quality feasible solutions to DSLMP. The results of the application of the proposed approach to a number of problem instances are also reported.