A matheuristic approach for maximum lifetime coverage in wireless sensor networks under connectivity constraints F. Casta˜ no a,b,1 , A. Rossi a , M. Sevaux a and N. Velasco b a b
Universit´e de Bretagne-Sud – Lab-STICC – Lorient, France
Universidad de los Andes – Dept. Industrial Engineering – Bogot´ a, Colombia
Keywords: Wireless Sensor Networks, Column Generation, VNS
Power limitation is a major concern regarding the implementation of wireless sensor networks [1]. Sometimes, precise placement of the sensors is not feasible, so it is not possible to devote any effort into designing an energyefficient network before its deployment. To overcome this issue, more sensors than actually needed are deployed in such a way that the targets are redundantly monitored. Then, targets may be covered by different subsets of sensors enabling to extend the network lifetime. Furthermore, direct or indirect sensor connectivity to the base station is required in some applications, where the base station is a special node for gathering information and sending data [2]. Consequently, only connected subsets of sensors are valid. In order to maximize the network lifetime whilst guaranteeing connectivity and coverage constraints, a matheuristic approach is proposed. The method uses a column generation approach [3] to solve the problem by dividing it into two subproblems. First, a master problem is used to define an energy optimal 1
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schedule for a set of sensor subsets. A second subproblem is used to identify the valid sensor subsets that are profitable, i.e., are likely to contribute in increasing the overall network lifetime based on the reduced cost in the master problem. A network flow model is used to identify such attractive connected sensor subsets, where a solution is represented by a binary vector indicating the connected sensor subset associated with the maximum reduced cost that covers the whole set of targets. The main drawback of the decomposition approach lies on the fact that the computation of attractive subsets is slow, which limits the use of exact approaches to small instances. To overcome this issue and find attractive subsets of sensors, a Variable Neighborhood Search (VNS) [4] approach is proposed. Each subset is coded as a binary vector and different types of neighborhoods are defined. The Hamming distance [5] to the current solution will limit the size of the neighborhood (the first neighborhood will have a Hamming distance 1 to the current solution, the second neighborhood will have a Hamming distance of 2, etc). A depth-first search strategy is used to verify connectivity and coverage at the same time. Results show that the use of VNS to compute the subsets improves the efficiency of the decomposition based approach compared with exact methods and allows to obtain near optimal solutions in a lower computational time.
References [1] W. Dargie and C. Poellabauer “Fundamental of Wireless Sensor Networks: Theory and Practice”. Wiley Series on Wireless Communication and Mobile Computing, 2010. [2] M. Lu, J. Wu, M. Cardei, M. Li Energy-efficient connected coverage of discrete targets in wireless sensor networks, International Journal of Ad Hoc and Ubiquitous Computing 4, (3) , 137 - 147, 2009 [3] G. Dantzig and P. Wolf. Decomposition Principle for Linear Programs. Operations Research, 8 (1), 101–111, 1960. [4] N. Mladenovi´c and P. Hansen. Variable neighborhood decomposition search. Computers and Operations Research, 24 (1997), 1097–1100, 1997. [5] R. Hamming “Error Detecting and Error Detection Codes”. The Bell System Technical Journal, 24, (2) , 1950.
