We focus on robust, survivable communication networks, where network links and nodes are affected by an uncertainty set. In this sense, any network links might fail. Besides, a signal can only travel a maximum distance before its quality falls below a certain threshold, necessitating its regeneration by regenerators installed at network nodes. In addition, the price of installing and maintaining regenerators belongs to a discrete uncertainty set. Robust optimization seeks a solution with guaranteed performance against all scenarios modeled in an uncertainty set. Thus, the problem is to find a subset of nodes with minimum cost for the placement of the regenerator, ensuring that all nodes can communicate even if a subset of network links fails. To solve the problem optimally, we propose two solution approaches, including one flow-based and one cut-based integer programming formulation, as well as their iterative exact method. Our theoretical and experimental results show the effectiveness of our methods.

翻译：本文研究鲁棒、可生存的通信网络，其中网络链路和节点受到不确定性集合的影响。在此背景下，任何网络链路均可能发生故障。此外，信号在传输质量低于特定阈值前仅能传播最大距离，因此需要在网络节点安装的再生器对其进行再生处理。同时，再生器的安装与维护成本属于离散不确定性集合。鲁棒优化旨在寻求一种能在不确定性集合建模的所有场景下保证性能的解决方案。因此，该问题的核心在于寻找成本最小的节点子集以部署再生器，确保即使部分网络链路发生故障，所有节点仍能保持通信。为精确求解此问题，我们提出了两种解决方案，包括基于流的整数规划模型和基于割的整数规划模型，并设计了相应的迭代精确算法。理论与实验结果表明了所提方法的有效性。