Robust-and-Cheap Framework for Network Resilience: A Novel Mixed-Integer Formulation and Solution Method

TL;DR

This paper introduces a novel mixed-integer programming framework to evaluate and enhance network resilience against attacks, offering an exact, efficient solution method applicable to various network types including power systems.

Contribution

It develops a two-stage MIP model for network resilience, including a solution approach with relaxation, problem structure exploitation, and lifted cover inequalities, advancing exact methods in the field.

Findings

The framework effectively identifies worst-case attacks and optimizes link additions.

Numerical experiments show high computational efficiency and applicability.

Results extend successfully from random networks to power system networks.

Abstract

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.