Robust Optimization Approach and Learning Based Hide-and-Seek Game for Resilient Network Design
Mohammad Khosravi, Setareh Maghsudi
TL;DR
This work tackles resilient network design under a signal-distance constraint $d_{max}$ by placing regenerators at selected nodes to maintain connectivity. It introduces a robust weighted RLP with static budgeted uncertainty for node costs and a dynamic budgeted model for edge lengths, solved via three scalable methods (CCG, Benders, IRO) and a learning-based hide-and-seek framework. The proposed approaches are validated through extensive experiments, showing that accounting for dynamic uncertainty yields cost savings and scalability, especially for large networks, while the HSL framework provides insight into the problem structure. Overall, the paper advances robust survivable network design and offers practical tools for cost-efficient, resilient regenerator placement in the face of time-varying and adversarial uncertainty.
Abstract
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.