Combining simulated annealing with Lagrangian relaxation and weighted Dantzig-Wolfe decomposition for integrated design decisions in wireless sensor networks

A Wireless Sensor Network (WSN) is the outcome of the collaborative effort of multi-functional, low-power, low-cost, tiny electronic devices called sensors. Their ability to work autonomously provides a distributed environment capable to monitor even remote or inaccessible areas, which explains the wide application range of WSNs. There are four main issues in the design of a WSN: determining sensor locations (deployment), scheduling sensors, finding sink locations, and obtaining sensor-to-sink data routes. Sensors have very limited energy resources and their efficient management becomes critical for elongating network lifetime. As a result, most of the works on optimal WSN design are concerned with efficient energy usage. Unfortunately, only a few of them use an integrated approach and try to address these four issues simultaneously. In this work we also follow this line of research and develop first a monolithic mixed-integer linear programming model that maximizes network lifetime by optimally determining sensor and sink locations, sensor-to-sink data flows, active and stand-by periods of the sensors subject to data flow conservation, energy consumption and budget usage constraints. Then we propose a nested solution method consisting of two procedures: simulated annealing that performs search for the best sink locations in the outer level and Lagrangian relaxation based heuristic employed with weighted Dantzig-Wolfe decomposition for the multiplier update in the inner level, which determines sensor locations, activity schedules of the sensors and data flows routes. We demonstrate the efficiency and accuracy of the new approach on randomly generated instances by extensive numerical experiments.