We study the design of resilient and reliable communication networks in which a signal can be transferred only up to a limited distance before its quality falls below an acceptable threshold. When excessive signal degradation occurs, regeneration is required through regenerators installed at selected network nodes. In this work, both network links and nodes are subject to uncertainty. The installation costs of regenerators are modeled using a budgeted uncertainty set. In addition, link lengths follow a dynamic budgeted uncertainty set introduced in this paper, where deviations may vary over time. Robust optimization seeks solutions whose performance is guaranteed under all scenarios represented by the underlying uncertainty set. Accordingly, the objective is to identify a minimum-cost subset of nodes for regenerator deployment that ensures full network connectivity, even under the worst possible realizations of uncertainty. To solve the problem, we first formulate it within a robust optimization framework, and then develop scalable solution methods based on column-and-constraint generation, Benders decomposition, and iterative robust optimization. In addition, we formulate a learning-based hide-and-seek game to further analyze the problem structure. The proposed approaches are evaluated against classical static budgeted robust models and deterministic worst-case formulations. Both theoretical analysis and computational results demonstrate the effectiveness and advantages of our methodology.

翻译：本文研究弹性可靠通信网络的设计问题，其中信号在传输距离超过一定限度后，其质量将低于可接受阈值。当信号衰减过度时，需要通过部署在选定网络节点的再生器进行信号再生。本工作中，网络链路与节点均存在不确定性。再生器的安装成本通过预算不确定性集合进行建模。此外，链路长度遵循本文提出的动态预算不确定性集合，其偏差可能随时间变化。鲁棒优化旨在寻求在基础不确定性集合所代表的所有场景下均能保证性能的解决方案。因此，本研究的目标是确定一个成本最小的节点子集用于部署再生器，以确保即使在最不利的不确定性实现下，网络仍能保持完全连通性。为解决该问题，我们首先在鲁棒优化框架内建立数学模型，随后开发基于列与约束生成、Benders分解及迭代鲁棒优化的可扩展求解方法。此外，我们构建了一个基于学习的捉迷藏博弈模型以进一步分析问题结构。所提出的方法通过与经典静态预算鲁棒模型及确定性最坏情况模型进行比较评估。理论分析与计算结果均验证了本方法的有效性和优越性。