Optimal placement and activity scheduling to maximize coverage lifetime in wireless sensor networks

In this paper, we consider the differentiated coverage problem for heterogeneous sensor networks over a finite planning horizon consisting of discrete time intervals. We assume that there are different types of sensors, and the characteristics of each sensor type such as unit cost, sensing range and energy consumption level is known. Furthermore, each sensor is capable to operate in either active or standby modes with different energy consumption rates. The goal is to determine optimal types and locations of the sensors as well as their activity schedules subject to coverage and budget constraints with the objective of maximizing the network lifetime. We first give a mixed-integer linear programming formulation which is computationally intractable and can only be solved optimally for small instances. Therefore, we propose a heuristic based on Lagrangian relaxation and subgradient optimization. Computational experiments performed on various test instances indicate that the new heuristic is efficient and accurate.