Sensor placement optimization methods have been studied extensively. They can be applied to a wide range of applications, including surveillance of known environments, optimal locations for 5G towers, and placement of missile defense systems. However, few works explore the robustness and efficiency of the resulting sensor network concerning sensor failure or adversarial attacks. This paper addresses this issue by optimizing for the least number of sensors to achieve multiple coverage of non-simply connected domains by a prescribed number of sensors. We introduce a new objective function for the greedy (next-best-view) algorithm to design efficient and robust sensor networks and derive theoretical bounds on the network's optimality. We further introduce a Deep Learning model to accelerate the algorithm for near real-time computations. The Deep Learning model requires the generation of training examples. Correspondingly, we show that understanding the geometric properties of the training data set provides important insights into the performance and training process of deep learning techniques. Finally, we demonstrate that a simple parallel version of the greedy approach using a simpler objective can be highly competitive.

传感器布置优化方法研究广泛，但很少有研究考虑到传感器网络在传感器故障或对抗性攻击方面的鲁棒性和效率。本文通过优化寻找最少数量的传感器来实现预定数量传感器对非连通域进行多次覆盖，从而解决了这个问题。我们提出了一种新的目标函数用于贪婪算法设计高效而鲁棒的传感器网络，并推导出了网络的可优化性的理论界限。我们进一步引入了一个深度学习模型加速算法以进行近实时计算。该深度学习模型需要生成训练样本，相关地，我们展示了了解训练数据集的几何属性对深度学习技术的性能和训练过程提供了重要见解。最后，我们展示了使用较简单目标的简单并行贪婪方法可以具有很高的竞争力。

优化多覆盖感知网络设计