Optimal sub-tree scheduling for wireless sensor networks with partial coverage

Abstract In this paper, we consider the problem of scheduling optimal sub-trees at different time intervals for wireless sensor network (WSN) communications with partial coverage. More precisely, we minimize the total power consumption of the network while taking into account time dimension and multichannel diversity where different disjoint subsets of nodes are required to be active and connected under a tree topology configuration. Optimization problems of these types may arise when designing new wireless communication protocols in order to increase network lifetime. We propose mixed integer quadratic and linear programming (resp. MIQP and MILP) models to compute optimal solutions for the problem. Subsequently, we propose Kruskal-based variable neighborhood search (VNS) and simulated annealing (SA) meta-heuristic procedures. In particular, we introduce a new embedded guided local search strategy in our VNS algorithm to further strengthen the solutions obtained. Our numerical results indicate that some of the proposed models allow to obtain optimal solutions with CPLEX in significantly less CPU time. Similarly, VNS and SA algorithms proved to be highly efficient when compared to the optimal solutions and allow to obtain near optimal solutions for large instances. In particular, VNS and guided VNS strategies allow to obtain solutions in less CPU time whilst SA methods can reach better solutions at higher CPU times. Finally, optimizing over time dimension allows one to obtain important reductions in power savings which has never been reported before in the literature.

[1]  Jennifer C. Hou,et al.  Maintaining Sensing Coverage and Connectivity in Large Sensor Networks , 2005, Ad Hoc Sens. Wirel. Networks.

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  Deying Li,et al.  Wireless Sensor Networks with Energy Efficient Organization , 2002, J. Interconnect. Networks.

[4]  Guoliang Xing,et al.  Integrated coverage and connectivity configuration in wireless sensor networks , 2003, SenSys '03.

[5]  Abdel Lisser,et al.  Stochastic maximum weight forest problem , 2015, Networks.

[6]  Xiaoling Zhang,et al.  Reliable transmission scheduling for multi-channel wireless sensor networks with low-cost channel estimation , 2013, IET Commun..

[7]  Pierre Hansen,et al.  Variable Neighborhood Search , 2018, Handbook of Heuristics.

[8]  Eyuphan Bulut,et al.  Sleep scheduling with expected common coverage in wireless sensor networks , 2011, Wirel. Networks.

[9]  Maurice Eggen,et al.  A transition to advanced mathematics , 1983 .

[10]  Abdel Lisser,et al.  Resource allocation in uplink wireless multi-cell OFDMA networks , 2016, Comput. Stand. Interfaces.

[11]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[12]  Songwu Lu,et al.  GRAdient Broadcast: A Robust Data Delivery Protocol for Large Scale Sensor Networks , 2005, Wirel. Networks.

[13]  Robert Tappan Morris,et al.  Span: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks , 2002, Wirel. Networks.

[14]  Ezhan Karasan,et al.  A distributed activity scheduling algorithm for wireless sensor networks with partial coverage , 2010, Wirel. Networks.

[15]  Christos Koulamas,et al.  A survey of simulated annealing applications to operations research problems , 1994 .

[16]  Sanghwa Chung,et al.  Adaptive channel quality estimation method for enhanced time slotted channel hopping on wireless sensor networks , 2017, 2017 Ninth International Conference on Ubiquitous and Future Networks (ICUFN).

[17]  Rodrigo C. de Lamare,et al.  Low-Complexity Set-Membership Channel Estimation for Cooperative Wireless Sensor Networks , 2011, IEEE Transactions on Vehicular Technology.

[18]  Miodrag Potkonjak,et al.  Power efficient organization of wireless sensor networks , 2001, ICC 2001. IEEE International Conference on Communications. Conference Record (Cat. No.01CH37240).

[19]  Pablo Adasme,et al.  Visible light communication networks under ring and tree topology constraints , 2017, Comput. Stand. Interfaces.

[20]  Abdel Lisser,et al.  Uplink scheduling for joint wireless orthogonal frequency and time division multiple access networks , 2016, J. Sched..

[21]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[22]  Edward P. K. Tsang,et al.  Guided local search and its application to the traveling salesman problem , 1999, Eur. J. Oper. Res..

[23]  B. Suman,et al.  A survey of simulated annealing as a tool for single and multiobjective optimization , 2006, J. Oper. Res. Soc..

[24]  Eyuphan Bulut,et al.  DSSP: A Dynamic Sleep Scheduling Protocol for Prolonging the Lifetime of Wireless Sensor Networks , 2007, 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW'07).

[25]  Samir R. Das,et al.  Connected sensor cover: self-organization of sensor networks for efficient query execution , 2006, TNET.

[26]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[27]  Di Tian,et al.  A coverage-preserving node scheduling scheme for large wireless sensor networks , 2002, WSNA '02.

[28]  Yang Xiao,et al.  A Survey of Energy-Efficient Scheduling Mechanisms in Sensor Networks , 2006, Mob. Networks Appl..

[29]  Pierre Hansen,et al.  The p-median problem: A survey of metaheuristic approaches , 2005, Eur. J. Oper. Res..

[30]  Deborah Estrin,et al.  Geography-informed energy conservation for Ad Hoc routing , 2001, MobiCom '01.

[31]  Pablo Adasme,et al.  p-Median based formulations with backbone facility locations , 2018, Appl. Soft Comput..

[32]  Abdel Lisser,et al.  Minimum cost dominating tree sensor networks under probabilistic constraints , 2017, Comput. Networks.

[33]  Pierre Hansen,et al.  Variable Neighborhood Decomposition Search , 1998, J. Heuristics.

[34]  Songwu Lu,et al.  PEAS: a robust energy conserving protocol for long-lived sensor networks , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[35]  Pierre Hansen,et al.  Variable neighborhood search: Principles and applications , 1998, Eur. J. Oper. Res..

[36]  Abdel Lisser,et al.  Improved solution strategies for dominating trees , 2018, Expert Syst. Appl..

[37]  Jie Wu,et al.  Energy-efficient coverage problems in wireless ad-hoc sensor networks , 2006, Comput. Commun..