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.

中文翻译：

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定向传感器网络寿命最大化的拉格朗日松弛方法

我们考虑定向传感器网络寿命最大化问题（DSLMP）。给定一组方向传感器和目标位置，问题在于在给定时间范围的每个时间单位上为所有传感器分配动作半径、孔径角和方向。目标是在传感器可用能量的某些限制下，在覆盖所有目标时最大化时间单位的数量。我们提出了一个混合整数非线性规划公式，并通过拉格朗日分解和次梯度优化来解决它。该算法配备了修复启发式算法，旨在为 DSLMP 找到高质量的可行解。还报告了将所提出的方法应用于许多问题实例的结果。