Download or read book Stochastic Network Interdiction written by Feng Pan and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Network Interdiction written by and published by . This book was released on 1998 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using limited assets, an interdictor attempts to destroy parts of a capacitated network through which an adversary will subsequently maximize flow. We formulate and solve a stochastic version of the interdictor's problem: Minimize the expected maximum flow through the network when interdiction successes are binary random variables. Extensions are made to handle uncertain arc capacities and other realistic variations. These two-stage stochastic integer programs have applications to interdicting illegal drugs and to reducing the effectiveness of a military force moving material, troops, information, etc., through a network in wartime. Two equivalent model formulations allow Jensen's inequality to be used to compute both lower and upper bounds on the objective, and these bounds are improved within a sequential approximation algorithm. Successful computational results are reported on networks with over 100 nodes, 80 interdictable arcs, and 180 total arcs.

Download or read book Network Interdiction and Stochastic Integer Programming written by David L. Woodruff and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part. A nice overview of the papers is provided in the Foreward written by Roger Wets.

Download or read book Prioritization and Optimization in Stochastic Network Interdiction Problems written by Dennis Paul Michalopoulos and published by . This book was released on 2008 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of a network interdiction problem is to model competitive decision-making between two parties with opposing goals. The simplest interdiction problem is a bilevel model consisting of an 'adversary' and an interdictor. In this setting, the interdictor first expends resources to optimally disrupt the network operations of the adversary. The adversary subsequently optimizes in the residual interdicted network. In particular, this dissertation considers an interdiction problem in which the interdictor places radiation detectors on a transportation network in order to minimize the probability that a smuggler of nuclear material can avoid detection. A particular area of interest in stochastic network interdiction problems (SNIPs) is the application of so-called prioritized decision-making. The motivation for this framework is as follows: In many real-world settings, decisions must be made now under uncertain resource levels, e.g., interdiction budgets, available man-hours, or any other resource depending on the problem setting. Applying this idea to the stochastic network interdiction setting, the solution to the prioritized SNIP (PrSNIP) is a rank-ordered list of locations to interdict, ranked from highest to lowest importance. It is well known in the operations research literature that stochastic integer programs are among the most difficult optimization problems to solve. Even for modest levels of uncertainty, commercial integer programming solvers can have difficulty solving models such as PrSNIP. However, metaheuristic and large-scale mathematical programming algorithms are often effective in solving instances from this class of difficult optimization problems. The goal of this doctoral research is to investigate different methods for modeling and solving SNIPs (optimization) and PrSNIPs (prioritization via optimization). We develop a number of different prioritized and unprioritized models, as well as exact and heuristic algorithms for solving each problem type. The mathematical programming algorithms that we consider are based on row and column generation techniques, and our heuristic approach uses adaptive tabu search to quickly find near-optimal solutions. Finally, we develop a group of hybrid algorithms that combine various elements of both classes of algorithms.

Download or read book Computational Methods for Deterministic and Stochastic Network Interdiction Problems written by Kelly James Cormican and published by . This book was released on 1995 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using limited resources, a network interdictor attempts to disable components of a capacitated network with the objective of minimizing the maximum network flow achievable by the network user. This problem has applications to reducing the importation of illegal drugs and planning wartime air attacks against an enemy's supply lines. A deterministic model using Benders decomposition is developed and improved upon with an original "flow-dispersion heuristic." An extension is made to accommodate probabilistic scenarios, where each scenario is an estimate of uncertain arc capacities in the actual network. A unique sequential- approximation algorithm is utilized to investigate cases where interdiction successes are binary random variables. For a network of 3200 nodes and 6280 arcs, Benders decomposition solves the network interdiction problem in less than one-third of the time required by a direct branch-and-bound method. The flow-dispersion heuristic can decrease solution time to one-fifth or less of that required for the Benders decomposition algorithm alone. With six allowable but uncertain interdictions in a network of 100 nodes and 84 possible interdiction sites among 180 arcs, a stochastic network interdiction problem is solved to optimality in 24 minutes on a IBM RISC/6000 Model 590. With uncertain arc capacities in five scenarios, and three allowable and certain interdictions, a 900 node and 1740 arc network is solved to optimality in 17 minutes on a 60MHZ Pentium PC.

Download or read book Computational Methods for Deterministic and Stochastic Network Interdiction Problems written by Kelly James Cormican and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using limited resources, a network interdictor attempts to disable components of a capacitated network with the objective of minimizing the maximum network flow achievable by the network user. This problem has applications to reducing the importation of illegal drugs and planning wartime air attacks against an enemy's supply lines. A deterministic model using Benders decomposition is developed and improved upon with an original "flow-dispersion heuristic." An extension is made to accommodate probabilistic scenarios, where each scenario is an estimate of uncertain arc capacities in the actual network. A unique sequential- approximation algorithm is utilized to investigate cases where interdiction successes are binary random variables. For a network of 3200 nodes and 6280 arcs, Benders decomposition solves the network interdiction problem in less than one-third of the time required by a direct branch-and-bound method. The flow-dispersion heuristic can decrease solution time to one-fifth or less of that required for the Benders decomposition algorithm alone. With six allowable but uncertain interdictions in a network of 100 nodes and 84 possible interdiction sites among 180 arcs, a stochastic network interdiction problem is solved to optimality in 24 minutes on a IBM RISC/6000 Model 590. With uncertain arc capacities in five scenarios, and three allowable and certain interdictions, a 900 node and 1740 arc network is solved to optimality in 17 minutes on a 60MHZ Pentium PC.

Download or read book Two person Games for Stochastic Network Interdiction written by Michael Victor Nehme and published by . This book was released on 2009 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a stochastic network interdiction problem in which an interdictor, subject to limited resources, installs radiation detectors at border checkpoints in a transportation network in order to minimize the probability that a smuggler of nuclear material can traverse the residual network undetected. The problems are stochastic because the smuggler's origin-destination pair, the mass and type of material being smuggled, and the level of shielding are known only through a probability distribution when the detectors are installed. We consider three variants of the problem. The first is a Stackelberg game which assumes that the smuggler chooses a maximum-reliability path through the network with full knowledge of detector locations. The second is a Cournot game in which the interdictor and the smuggler act simultaneously. The third is a "hybrid" game in which only a subset of detector locations is revealed to the smuggler. In the Stackelberg setting, the problem is NP-complete even if the interdictor can only install detectors at border checkpoints of a single country. However, we can compute wait-and-see bounds in polynomial time if the interdictor can only install detectors at border checkpoints of the origin and destination countries. We describe mixed-integer programming formulations and customized branch-and-bound algorithms which exploit this fact, and provide computational results which show that these specialized approaches are substantially faster than more straightforward integer-programming implementations. We also present some special properties of the single-country case and a complexity landscape for this family of problems. The Cournot variant of the problem is potentially challenging as the interdictor must place a probability distribution over an exponentially-sized set of feasible detector deployments. We use the equivalence of optimization and separation to show that the problem is polynomially solvable in the single-country case if the detectors have unit installation costs. We present a row-generation algorithm and a version of the weighted majority algorithm to solve such instances. We use an exact-penalty result to formulate a model in which some detectors are visible to the smuggler and others are not. This may be appropriate to model "decoy" detectors and detector upgrades.

Download or read book Stochastic Network Interdiction for Optimizing Defensive Counter Air Operations Planning written by Charalampos I. Tsamtsaridis and published by . This book was released on 2011 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a stochastic, network interdiction optimization model to guide defensive, counter-air (DCA) operations planning. We model a layered, integrated air-defense system, which consists of fighter and missile engagement zones. We extend an existing two-stage, stochastic, generalized-network interdiction model by Pan, Charlton and Morton, and adapt it to DCA operations planning. The extension allows us to handle multiple-type interdiction assets, and constrain the attacker's flight path by the maximum allowable traveled distance. The defender selects the locations to install multiple interceptor types, with uncertainty in the attacker's origin and destination, in order to minimize the probability of evasion, or the expected target value collected by the evader. Then, the attacker reveals an origin-destination pair (independent of the defender's decision), and sends a strike package along a path (through the interdicted network) that maximizes his probability of evasion. By adding a small persistence penalty we ensure the plans are consistent in presence of minor variations in the number of interceptors. We present computational results for several instances of a test case consisting of the airspace over a 360-by-360 nautical miles area. The computational time ranges from some seconds to ten minutes, which is acceptable for operational use of this model.

Download or read book A Stochastic Network interdiction Model for Cyber Security written by and published by . This book was released on 2014 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a general defender-attacker model for security of computer networks, using attack graphs to represent the possible attacker strategies and defender options. The defender's objective is to maximize the security of the network under a limited budget. In the literature, most network-interdiction models allow the attacker only one attempt; other models allow multiple attempts, but assume that any subsequent attempt begins at the point where the previous attempt failed. By contrast, in computer security, the attacker could be operating from the safety of a foreign country, and the cost of changing attack strategies may be quite low, so a new model is needed. To capture the ability of the attacker to launch multiple attempts, we represent the attacker's success on each arc of the attack graph probabilistically, and formulate the resulting problem as a multiple-stage stochastic network-interdiction problem. In the resulting game, the defender anticipates both the attacker's strategy choices, and their probabilities of success, and chooses which arcs in the attack graph to protect in order to defend against multiple attempted attacks. The attacker then launches an optimal attack against the system, knowing which arcs have been protected. If the attacker fails at the first attempt, a second-stage optimal strategy is chosen, based on a revised attack graph showing which arcs have been successfully traversed (with success probabilities of 1), and which arc failed (assumed to have success probability 0). We solve the resulting problem using multi-stage stochastic optimization with recourse, and explore the attacker's strategies.

Download or read book Risk averse Bi level Stochastic Network Interdiction Model for Cyber security Risk Management written by Tanveer Hossain Bhuiyan and published by . This book was released on 2018 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research presents a bi-level stochastic network interdiction model on an attack graph to enable a risk-averse resource constrained cyber network defender to optimally deploy security countermeasures to protect against attackers having an uncertain budget. This risk-averse conditional-value-at-risk model minimizes a weighted sum of the expected maximum loss over all scenarios and the expected maximum loss from the most damaging attack scenarios. We develop an exact algorithm to solve our model as well as several acceleration techniques to improve the computational efficiency. Computational experiments demonstrate that the application of all the acceleration techniques reduces the average computation time of the basic algorithm by 71% for 100-node graphs. Using metrics called mean-risk value of stochastic solution and value of risk-aversion, numerical results suggest that our stochastic risk-averse model significantly outperforms deterministic and risk-neutral models when 1) the distribution of attacker budget is heavy-right-tailed and 2) the defender is highly risk-averse.

Download or read book Risk averse Bi level Stochastic Network Interdiction Model for Cyber security Risk Management written by and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This research presents a bi-level stochastic network interdiction model on an attack graph to enable a risk-averse resource constrained cyber network defender to optimally deploy security countermeasures to protect against attackers having an uncertain budget. This risk-averse conditional-value-at-risk model minimizes a weighted sum of the expected maximum loss over all scenarios and the expected maximum loss from the most damaging attack scenarios. We develop an exact algorithm to solve our model as well as several acceleration techniques to improve the computational efficiency. Computational experiments demonstrate that the application of all the acceleration techniques reduces the average computation time of the basic algorithm by 71% for 100-node graphs. Using metrics called mean-risk value of stochastic solution and value of risk-aversion, numerical results suggest that our stochastic risk-averse model significantly outperforms deterministic and risk-neutral models when 1) the distribution of attacker budget is heavy-right-tailed and 2) the defender is highly risk-averse.

Download or read book Stochastic Programming written by Horand Gassmann and published by World Scientific. This book was released on 2013 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.

Download or read book Why Stochastic Modeling is Essential in Analyzing Interdicted Transportation Network Performance written by Byung Kwon Choi and published by . This book was released on 1989 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.

Download or read book Pareto Optimality Game Theory and Equilibria written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2008-07-02 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.

Download or read book Bilevel Optimization written by Stephan Dempe and published by Springer Nature. This book was released on 2020-11-23 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.

Download or read book Network Design with Applications to Transportation and Logistics written by Teodor Gabriel Crainic and published by Springer Nature. This book was released on 2021-07-16 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the methodological and application developments of network design in transportation and logistics. It identifies trends, challenges and research perspectives in network design for these areas. Network design is a major class of problems in operations research where network flow, combinatorial and mixed integer optimization meet. The analysis and planning of transportation and logistics systems continues to be one of the most important application areas of operations research. Networks provide the natural way of depicting such systems, so the optimal design and operation of networks is the main methodological area of operations research that is used for the analysis and planning of these systems. This book defines the current state of the art in the general area of network design, and then turns to its applications to transportation and logistics. New research challenges are addressed. Network Design with Applications to Transportation and Logistics is divided into three parts. Part I examines basic design problems including fixed-cost network design and parallel algorithms. After addressing the basics, Part II focuses on more advanced models. Chapters cover topics such as multi-facility network design, flow-constrained network design, and robust network design. Finally Part III is dedicated entirely to the potential application areas for network design. These areas range from rail networks, to city logistics, to energy transport. All of the chapters are written by leading researchers in the field, which should appeal to analysts and planners.