# Credible Interdiction for Transmission Systems

## TL;DR

This paper introduces new formulations and algorithms for $N$-$k$ interdiction in transmission networks, modeling localized attacks constrained by geography or topology, and provides case studies comparing these to traditional methods.

## Contribution

It develops spatial and topological resource-constrained $N$-$k$ interdiction models and a novel solution algorithm, advancing the modeling of localized network attacks.

## Key findings

- Spatial and topological attack models better represent real-world localized threats.
- The proposed algorithms effectively solve complex interdiction problems.
- Case studies demonstrate differences from traditional $N$-$k$ models.

## Abstract

This paper presents novel formulations and algorithms for $N$-$k$ interdiction problem in transmission networks. In particular, it formulates spatial and topological resource constraints on attackers for $N$-$k$ interdiction problems and illustrates the formulation with two new classes of $N$-$k$ attacks: (i) Spatial $N$-$k$ attacks where the attack is constrained by geographic distance of a bus chosen by an attacker and (ii) Topological $N$-$k$ attacks where the attack is constrained to connected components. These two specific types of $N$-$k$ attacks compute interdiction plans designed to better model localized attacks, such as those induced by natural disasters or physical attacks. We then formulate these two resource-constrained interdiction problems as bilevel, max-min optimization problems and present a novel constraint generation algorithm to solve these formulations. Detailed case studies analyzing the behavior of spatially and topologically resource-constrained problems and comparing them to the traditional $N$-$k$ interdiction problem are also presented.