In wireless sensor networks applications involving a huge number of sensors, some of the sensor devices may result to be redundant. As a consequence, the simultaneous usage of all the sensors may lead to a faster depletion of the available energy and to a shorter network lifetime. In this context, one of the well-known and most important problems is Maximum Network Lifetime Problem (MLP). MLP consists in finding non-necessarily disjoint subsets of sensors (covers), which are autonomously able to surveil specific locations (targets) in an area of interest, and activating each cover, one at a time, in order to guarantee the network activity as long as possible. MLP is a challenging optimization problem and several approaches have been proposed to address it in the last years. A recently proposed variant of the MLP is the Maximum Lifetime Problem with Time Slots (MLPTS), where the sensors belonging to a cover must be operational for a fixed amount of time, called operating time slot, whenever the cover is activated. In this paper, we generalize MLPTS by taking into account the possibility, for each subset of active sensors, to neglect the coverage of a small percentage of the whole set of targets. We define such new problem as \(\alpha _c\)-MLPTS, where \(\alpha _c\) defines the percentage of targets that each cover has to monitor. For this new scenario we propose three approaches: a classical Greedy algorithm, a Carousel Greedy algorithm and a modified version of the genetic algorithm already proposed for MLPTS. The comparison of the three heuristic approaches is carried out through extensive computational experiments. The computational results show that the Carousel Greedy represents the best trade-off between the proposed approaches and confirm that the network lifetime can be considerably improved by omitting the coverage of a percentage of the targets.

在涉及大量传感器的无线传感器网络应用中，一些传感器设备可能导致冗余。因此，同时使用所有传感器可能会导致可用能量更快耗尽并缩短网络寿命。在这种情况下，众所周知且最重要的问题之一是最大网络生命周期问题 (MLP)。MLP 包括寻找不必要不相交的传感器子集（覆盖物），这些子集能够自主地监视特定位置（目标) 在感兴趣的区域中，并一次激活每个封面，以保证尽可能长时间的网络活动。MLP 是一个具有挑战性的优化问题，在过去几年中已经提出了几种方法来解决它。最近提出的 MLP 变体是带时隙的最大寿命问题 (MLPTS)，其中，只要盖子被激活，属于盖子的传感器必须在固定的时间内运行，称为运行时隙。在本文中，我们通过考虑每个有源传感器子集的可能性来概括 MLPTS，以忽略整个目标集的一小部分覆盖范围。我们将这样的新问题定义为\(\alpha _c\) -MLPTS，其中\(\alpha _c\)定义每个封面必须监视的目标百分比。对于这个新场景，我们提出了三种方法：经典的贪婪算法、轮播贪婪算法和已经为 MLPTS 提出的遗传算法的修改版本。三种启发式方法的比较是通过广泛的计算实验进行的。计算结果表明，Carousel Greedy 代表了所提出方法之间的最佳权衡，并确认可以通过省略一定百分比的目标覆盖率来显着提高网络寿命。