The design of networks which are robust to multiple failures is gaining increasing attention in areas such as telecommunications. In this paper, we consider the problem of upgrading an existent network in order to enhance its robustness to events involving multiple node failures. This problem is modeled as a bi-objective mixed linear integer formulation considering both the minimization of the cost of the added edges and the maximization of the robustness of the resulting upgraded network. As the robustness metric of the network, we consider the value of the Critical Node Detection (CND) problem variant which provides the minimum pairwise connectivity between all node pairs when a set of c critical nodes are removed from the network. We present a general iterative framework to obtain the complete Pareto frontier that alternates between the minimum cost edge selection problem and the CND problem. Two different approaches based on a cover model are introduced for the edge selection problem. Computational results conducted on different network topologies show that the proposed methodology based on the cover model is effective in computing Pareto solutions for graphs with up to 100 nodes, which includes four commonly used telecommunication networks.

对多重故障具有鲁棒性的网络设计在电信等领域越来越受到关注。在本文中，我们考虑升级现有网络以增强其对涉及多个节点故障的事件的鲁棒性的问题。这个问题被建模为双目标混合线性整数公式，同时考虑到最小化添加边的成本和最大化升级后网络的鲁棒性。作为网络的鲁棒性度量，我们考虑关键节点检测 (CND) 问题变体的值，当一组c从网络中删除关键节点。我们提出了一个通用的迭代框架，以获得在最小成本边选择问题和 CND 问题之间交替的完整帕累托边界。针对边缘选择问题引入了两种基于覆盖模型的不同方法。在不同网络拓扑结构上进行的计算结果表明，所提出的基于覆盖模型的方法可有效计算具有多达 100 个节点的图的帕累托解，其中包括四个常用的电信网络。