Multi-objective optimization for sensor placement: An integrated combinatorial approach with reduced order model and Gaussian process

We develop a novel sensor placement method that maximizes monitoring performance while minimizing deployment cost. Our method integrates a reduced order model and multi-objective combinatorial optimization. We first decompose the spatio-temporal state field to be monitored by proper orthogonal decomposition (POD), and we use the Gaussian Process to model the uncertainty in each POD mode. Next, we develop a lazy greedy (LG)-∊-constraint optimization to derive the Pareto-optimal sensor configurations. We further design a branch and bound algorithm to calculate the global optimum and validate the correctness of select configurations on the LG-derived Pareto frontier. We evaluate and benchmark our algorithm in computational experiments based on the temperature dataset of the Berkeley Intel Lab. The computational results demonstrate that our algorithm places sensors at locations of large magnitude in the POD modes, and that our method achieves better state estimation accuracy and smaller reconstruction errors compared with alternative methods.