Robust Optimization Models for Energy-Limited Wireless Sensor Networks under Distance Uncertainty

The actual performance of a wireless sensor network (WSN) can be severely influenced by uncertainty present in the environment where it is deployed. For example, the distance between nodes, the quality of the communication channel, and the energy consumed in transmission are all problem parameters that may be subject to uncertainty in real domains and can affect performance. In this paper we consider optimization models of WSN subject to distance uncertainty for three classic problems in energy limited WSNs: minimizing the energy consumed, maximizing the data extracted, and maximizing the network lifetime. We use robust optimization to take into account the uncertainty present. In a robust optimization model the uncertainty is represented by considering that the uncertain parameters belong to a bounded, convex uncertainty set U. A robust solution is the one with best worst case objective over this set U. We show that solving for the robust solution in these problems is just as difficult as solving for the problem without uncertainty. Our computational experiments show that, as the uncertainty increases, a robust solution provides a significant improvement in worst case performance at the expense of a small loss in optimality when compared to the optimal solution of a fixed scenario.