A Robust Optimization Approach for Regenerator Placement in Fault-Tolerant Networks Under Discrete Cost Uncertainty

TL;DR

The paper investigates robust regenerator placement in fault-tolerant networks under discrete cost uncertainty and single-edge failure, formalizing the RFTRLP that ensures two edge-disjoint, $d_{max}$-bounded paths between all node pairs even after failures. It develops a theoretical backbone connecting RFTRLP to robust weighted vertex cover via a transformation to a graph $M$, and presents two exact integer-programming formulations (flow-based and cut-based) alongside a scalable iterative method (IT-FB) for large instances. A preprocessing step with Full Recovery of Equality (FRE) improves the tractability of transformations and model construction. Empirical results show IP-FB generally outperforms IP-CB and a baseline, while IT-FB enables solving large networks with competitive optimality and strong LP-relaxation tightness (~90% of the IP optimum), demonstrating practical applicability for resilient optical and corporate networks.

Abstract

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.

Figures (8)

• Figure 1: Example of an eight-node network with $d_{\max}=200$. The optimal solutions of the RLP are either nodes $\{2,3,4\}$ or nodes $\{6,7,8\}$. Considering $\{2,3,4\}$ as the solution, nodes 1 and 5 can communicate via the path $1\leftrightarrow2\leftrightarrow3\leftrightarrow4\leftrightarrow5$. Using this placement, a valid communication path can be established for all non-adjacent node pairs in the network.
• Figure 2: Illustration of the inequivalence between the FTRLP and FTMCDSP solutions on graphs $G$ and $M$: (a) original graph $G$, (b) corresponding graph $M$, and (c) graph $M_{G\setminus(1,2)}$ after removing edge $(1,2)$.
• Figure 3: Problem equivalency on $M$
• Figure 4: Ineqivalency of solution to MP and RFTRLP
• Figure 5: Performance profile of process time for IPs (a), and ratio of SHP and IP times of IP-LA compared to our IP models (b) in Exp-1 for Gen-1.

Theorems & Definitions (22)

• Definition 1
• Definition 2: RLP on M
• Definition 3: Dominating Set Problem
• Definition 4: Equivalent RLP on $M$
• Theorem 1
• proof
• Definition 5
• Theorem 2
• Theorem 3
• proof