Synthesis, Interdiction, and Protection of Layered Networks

This research developed the foundation, theory, and framework for a set of analysis techniques to assist decision makers in analyzing questions regarding the synthesis, interdiction, and protection of infrastructure networks. This includes extension of traditional network interdiction to directly model nodal interdiction; new techniques to identify potential targets in social networks based on extensions of shortest path network interdiction; extension of traditional network interdiction to include layered network formulations; and develops models/techniques to design robust layered networks while considering trade-offs with cost. These approaches identify the maximum protection/disruption possible across layered networks with limited resources, find the most robust layered network design possible given the budget limitations while ensuring that the demands are met, include traditional social network analysis, and incorporate new techniques to model the interdiction of nodes and edges throughout the formulations. In addition, the importance and effects of multiple optimal solutions for these (and similar) models is investigated. All the models developed are demonstrated on notional examples and were tested on a range of sample problem sets

Solving Defender-Attacker-Defender Models for Infrastructure Defense

In Operations Research, Computing, and Homeland Defense, R.K. Wood and R.F. Dell, editors, INFORMS, Hanover, MD, pp. 28-49.The article of record as published may be located at http://dx.doi.org10.1287/ics.2011.0047This paper (a) describes a defender-attacker-defender sequential game model (DAD) to plan defenses for an infrastructure system that will enhance that system's resilience against attacks for an intelligent adversary, (b) describes a realistic formulation of DAD for defending a transportation network, (c) develops a decomposition algorithm for solving this instance of DAD and others, and (d) demonstrates the solution of a small transportation-network example. A DAD model generally evaluates system operation through the solution of an optimization model, and the decomposition algorithm developed here requires only that this system-operation model be continuous and convex. For example, our transportation-network example incorporates a congestion model with a (convex) nonlinear objective function and linear constraints

Vulnerability Assessment and Re-routing of Freight Trains Under Disruptions: A Coal Supply Chain Network Application

In this paper, we present a two-stage mixed integer programming (MIP) interdiction model in which an interdictor chooses a limited amount of elements to attack first on a given network, and then an operator dispatches trains through the residual network. Our MIP model explicitly incorporates discrete unit flows of trains on the rail network with time-variant capacities. A real coal rail transportation network is used in order to generate scenarios to provide tactical and operational level vulnerability assessment analysis including rerouting decisions, travel and delay costs analysis, and the frequency of interdictions of facilities for the dynamic rail system

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

An Implicit Optimization Approach for Survivable Network Design

We consider the problem of designing a network of minimum cost while satisfying a prescribed survivability criterion. The survivability criterion requires that a feasible flow must still exists (i.e. all demands can be satisfied without violating arc capacities) even after the disruption of a subset of the network's arcs. Specifically, we consider the case in which a disruption (random or malicious) can destroy a subset of the arcs, with the cost of the disruption not to exceed a disruption budget. This problem takes the form of a tri-level, two-player game, in which the network operator designs (or augments) the network, then the attacker launches a disruption that destroys a subset of arcs, and then the network operator attempts to find a feasible flow over the residual network. We first show how this can be modeled as a two-stage stochastic program from the network operator's perspective, with each of the exponential number of potential attacks considered as a disruption scenario. We then reformulate this problem, via a Benders decomposition, to consider the recourse decisions implicitly, greatly reducing the number of variables but at the expense of an exponential increase in the number of constraints. We next develop a cut-generation based algorithm. Rather than \emph{explicitly} considering each disruption scenario to identify these Benders cuts, however, we develop a bi-level program and corresponding separation algorithm that enables us to \emph{implicitly} evaluate the exponential set of disruption scenarios. Our computational results demonstrate the efficacy of this approach

RUNTIME ANALYSIS OF BENDERS DECOMPOSITION AND DUAL ILP ALGORITHMS AS APPLIED TO COMMON NETWORK INTERDICTION PROBLEMS

Attacker-defender models help practitioners understand a network’s resistance to attack. An assailant interdicts a network, and the operator responds in such a way as to optimally utilize the degraded network. This thesis analyzes two network interdiction algorithms, Benders decomposition and a dual integer linear program approach, to compare their computational efficiency on the shortest path and maximum flow interdiction problems. We construct networks using two operationally meaningful structures: a grid structure designed to represent an urban transportation network, and a layered network designed to mimic a supply chain. We vary the size of the network and the attacker's budget and we record each algorithm’s runtime. Our results indicate that Benders decomposition performs best when solving the shortest path interdiction problem on a grid network, the dual integer linear program performs better for the maximum flow problem on both the grid and layered network, and the two approaches perform comparably when solving the shortest path interdiction problem on the layered network.Lieutenant Commander, United States NavyApproved for public release. Distribution is unlimited

Bilevel Network Design

This chapter is devoted to network design problems involving conflicting agents, referred to as the designer and the users, respectively. Such problems are best cast into the framework of bilevel programming, where the designer anticipates the reaction or rational users to its course of action, and fits many situations of interest. In this chapter, we consider four applications of very different nature, with a special focus on algorithmic issues