618 research outputs found
Robust optimization with incremental recourse
In this paper, we consider an adaptive approach to address optimization
problems with uncertain cost parameters. Here, the decision maker selects an
initial decision, observes the realization of the uncertain cost parameters,
and then is permitted to modify the initial decision. We treat the uncertainty
using the framework of robust optimization in which uncertain parameters lie
within a given set. The decision maker optimizes so as to develop the best cost
guarantee in terms of the worst-case analysis. The recourse decision is
``incremental"; that is, the decision maker is permitted to change the initial
solution by a small fixed amount. We refer to the resulting problem as the
robust incremental problem. We study robust incremental variants of several
optimization problems. We show that the robust incremental counterpart of a
linear program is itself a linear program if the uncertainty set is polyhedral.
Hence, it is solvable in polynomial time. We establish the NP-hardness for
robust incremental linear programming for the case of a discrete uncertainty
set. We show that the robust incremental shortest path problem is NP-complete
when costs are chosen from a polyhedral uncertainty set, even in the case that
only one new arc may be added to the initial path. We also address the
complexity of several special cases of the robust incremental shortest path
problem and the robust incremental minimum spanning tree problem
Network Interdiction Using Adversarial Traffic Flows
Traditional network interdiction refers to the problem of an interdictor
trying to reduce the throughput of network users by removing network edges. In
this paper, we propose a new paradigm for network interdiction that models
scenarios, such as stealth DoS attack, where the interdiction is performed
through injecting adversarial traffic flows. Under this paradigm, we first
study the deterministic flow interdiction problem, where the interdictor has
perfect knowledge of the operation of network users. We show that the problem
is highly inapproximable on general networks and is NP-hard even when the
network is acyclic. We then propose an algorithm that achieves a logarithmic
approximation ratio and quasi-polynomial time complexity for acyclic networks
through harnessing the submodularity of the problem. Next, we investigate the
robust flow interdiction problem, which adopts the robust optimization
framework to capture the case where definitive knowledge of the operation of
network users is not available. We design an approximation framework that
integrates the aforementioned algorithm, yielding a quasi-polynomial time
procedure with poly-logarithmic approximation ratio for the more challenging
robust flow interdiction. Finally, we evaluate the performance of the proposed
algorithms through simulations, showing that they can be efficiently
implemented and yield near-optimal solutions
An O(1)-Approximation for Minimum Spanning Tree Interdiction
Network interdiction problems are a natural way to study the sensitivity of a
network optimization problem with respect to the removal of a limited set of
edges or vertices. One of the oldest and best-studied interdiction problems is
minimum spanning tree (MST) interdiction. Here, an undirected multigraph with
nonnegative edge weights and positive interdiction costs on its edges is given,
together with a positive budget B. The goal is to find a subset of edges R,
whose total interdiction cost does not exceed B, such that removing R leads to
a graph where the weight of an MST is as large as possible. Frederickson and
Solis-Oba (SODA 1996) presented an O(log m)-approximation for MST interdiction,
where m is the number of edges. Since then, no further progress has been made
regarding approximations, and the question whether MST interdiction admits an
O(1)-approximation remained open.
We answer this question in the affirmative, by presenting a 14-approximation
that overcomes two main hurdles that hindered further progress so far.
Moreover, based on a well-known 2-approximation for the metric traveling
salesman problem (TSP), we show that our O(1)-approximation for MST
interdiction implies an O(1)-approximation for a natural interdiction version
of metric TSP
Optimization Approaches To Protect Transportation Infrastructure Against Strategic and Random Disruptions
Past and recent events have proved that critical infrastructure are vulnerable to natural catastrophes, unintentional accidents and terrorist attacks. Protecting these systems is critical to avoid loss of life and to guard against economical upheaval. A systematic approach to plan security investments is paramount to guarantee that limited protection resources are utilized in the most effcient manner. This thesis provides a detailed review of the optimization models that have been introduced in the past to identify vulnerabilities and protection plans for critical infrastructure. The main objective of this thesis is to study new and more realistic models to protect transportation infrastructure such as railway and road systems against man made and natural disruptions. Solution algorithms are devised to effciently solve the complex formulations proposed. Finally, several illustrative case studies are analysed to demonstrate how solving these models can be used to support effcient protection decisions
Prioritizing Interdictions on a Shortest Path Network
We consider a variant to the shortest path network interdiction problem with symmetric information from Israeli and Wood (Networks 40, 97-111,2002) which arises in the context of nuclear smuggling prevention. In the basic shortest path interdiction problem, an interdictor has a limited number of interdictions with which he can lengthen arcs in a network in order to maximize the length of the network’s shortest path. This thesis considers the case in which the interdictor does not make all of the interdictions at once. Rather, the interdictor must make the interdictions over a set number of periods. Each period has a budget for the number of interdictions that can be placed during the period. The interdictor must prioritize the interdictions and decide the order in which the interdictions should take place. This problem is formulated as an integer program with an objective to maximize the average of the shortest paths across all periods
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
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
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