  Resilience and robustness are important properties in the reliability and
attack-tolerance analysis of networks. In recent decades, various qualitative
and heuristic-based quantitative approaches have made significant contributions
in addressing network resilience and robustness. However, the lack of exact
methods such as mixed-integer programming (MIP) models is sensible in the
literature. In this paper, we contribute to the literature on the network
resilience and robustness for targeted and random attacks and propose a MIP
model considering graph-theoretical aspects of networks. The proposed MIP model
consists of two stages where in the first stage the worst-case attack is
identified. Then, the second-stage problem maximizes the network resilience
under the worst-case attack by adding links considering a link addition
financial budget. In addition, we propose a solution method that (i) provides a
tight relaxation for the MIP formulation by relaxing some of the integrality
restrictions, (ii) exploits the structure of the problem and reduces the
second-stage problem to a less complex but equivalent problem, and (iii)
identifies underlying knapsack constraints and generates lifted cover
inequalities (LCI) for such constraints. We conclude numerical experiments for
randomly-generated networks and then extend our results to power system
networks. Numerical experiments demonstrate the applicability and computational
efficiency of the proposed robust-and-cheap framework for network resilience.
