Data-gathering Wireless Sensor Networks (WSNs) are operated unattended over long time horizons to collect data in several applications. Typically, sensors have limited energy (e.g., an on-board battery) and are subject to the elements in the terrain. In network operations, which largely involve periodically changing network flow decisions to prolong the network lifetime, are managed remotely, and the collected data are retrieved by a user via internet. An integrated topology control and routing problem in cluster-based WSNs are analyzed to improve the network lifetime. To prolong network lifetime via efficient use of the limited energy at the sensors , a hierarchical network structure with multiple sinks at which the data collected by the sensors are gathered through the cluster heads are adopted . A Mixed Integer Linear Programming (MILP) model to optimally determine the sink and CH locations as well as the data flow in the network is considered. This model effectively utilizes both the position and the energy-level aspects of the sensors while selecting the CHs and avoids the highest-energy sensors. For the solution of the MILP model, an effective Benders Decomposition (BD) approach that incorporates an upper bound heuristic algorithm is used.
