{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/robust-and-cheap-framework-for-network","title":"Robust-and-Cheap Framework for Network Resilience: A Novel Mixed-Integer Formulation and Solution Method","arxiv_id":"2110.09694","date":"2021-10-19","proceeding":null,"authors":["Milad Dehghani Filabadi"],"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.","url_abs":"https://arxiv.org/abs/2110.09694v4","url_pdf":"https://arxiv.org/pdf/2110.09694v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"robust-and-cheap-framework-for-network","repo_url":"https://github.com/miladdf94/network-resilience","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}