Maximum Network Lifetime Problem with Time Slots and coverage constraints: heuristic approaches

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 αc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _c$$\end{document}-MLPTS, where αc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _c$$\end{document} 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.