Integer Programming Formulations for Minimum Spanning Tree Interdiction

We consider a two-player interdiction problem staged over a graph where the attacker’s objective is to minimize the cost of removing edges from the graph so that the defender’s objective, that is, the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level r. Standard approaches for graph interdiction frame this type of problems as bilevel formulations, which are commonly solved by replacing the inner problem by its dual to produce a single-level reformulation. In this paper, we study an alternative integer program derived directly from the attacker’s solution space and show that this formulation yields a stronger linear relaxation than the bilevel counterpart. Furthermore, we analyze the convex hull of the feasible solutions of the problem and identify several families of facet-defining inequalities that can be used to strengthen this integer program. We then proceed by introducing a different formulation defined by a set of so-called supervalid inequalities that may exclude feasible solutions, albeit solutions whose objective value is not better than that of an edge cut of minimum cost. We discuss several computational aspects required for an efficient implementation of the proposed approaches. Finally, we perform an extensive set of computational experiments to test the quality of these formulations, analyzing and comparing the benefits of each model, as well as identifying further enhancements. Summary of Contribution: Network interdiction has received significant attention over the last couple of decades, with a notable peak of interest in recent years. This paper provides an interesting balance between the theoretical and computational aspects of solving a challenging network interdiction problem via integer programming. We present several technical developments, including a detailed study of the problem's solution space, multiple formulations, and a polyhedral analysis of the convex hull of feasible solutions. We then analyze the results of an extensive set of computational experiments that were used to validate the effectiveness of the different methods we developed in this paper.

The Shortest Path Interdiction Problem with Randomized Interdiction Strategies: Complexity and Algorithms

New algorithms and models enable randomized network interdiction strategies

Bi-Layer Shortest-Path Network Interdiction Game for Internet of Things

Network security is a crucial challenge facing Internet-of-Things (IoT) systems worldwide, which leads to serious safety alarms and great economic loss. This paper studies the problem of malicious interdicting network exploitation of IoT systems that are modeled as a bi-layer logical–physical network. In this problem, a virtual attack takes place at the logical layer (the layer of Things), while the physical layer (the layer of Internet) provides concrete support for the attack. In the interdiction problem, the attacker attempts to access a target node on the logical layer with minimal communication cost, but the defender can strategically interdict some key edges on the physical layer given a certain budget of interdiction resources. This setting generalizes the classic single-layer shortest-path network interdiction problem, but brings in nonlinear objective functions, which are notoriously challenging to optimize. We reformulate the model and apply Benders decomposition process to solve this problem. A layer-mapping module is introduced to improve the decomposition algorithm and a random-search process is proposed to accelerate the convergence. Extensive numerical experiments demonstrate the computational efficiency of our methods.

NIHBA: a network interdiction approach for metabolic engineering design

Motivation Flux balance analysis (FBA) based bilevel optimization has been a great success in redesigning metabolic networks for biochemical overproduction. To date, many computational approaches have been developed to solve the resulting bilevel optimization problems. However, most of them are of limited use due to biased optimality principle, poor scalability with the size of metabolic networks, potential numeric issues or low quantity of design solutions in a single run. Results Here, we have employed a network interdiction model free of growth optimality assumptions, a special case of bilevel optimization, for computational strain design and have developed a hybrid Benders algorithm (HBA) that deals with complicating binary variables in the model, thereby achieving high efficiency without numeric issues in search of best design strategies. More importantly, HBA can list solutions that meet users’ production requirements during the search, making it possible to obtain numerous design strategies at a small runtime overhead (typically ∼1 h, e.g. studied in this article). Availability and implementation Source code implemented in the MATALAB Cobratoolbox is freely available at https://github.com/chang88ye/NIHBA. Contact [email protected] or [email protected] Supplementary information Supplementary data are available at Bioinformatics online.