Network Interdiction And Stochastic Integer Programming
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Network Interdiction And Stochastic Integer Programming
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Author : David L. Woodruff
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Network Interdiction And Stochastic Integer Programming written by David L. Woodruff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-11 with Mathematics categories.
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.
Decomposition Algorithms In Stochastic Integer Programming
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Author : Babak Saleck Pay
language : en
Publisher:
Release Date : 2017
Decomposition Algorithms In Stochastic Integer Programming written by Babak Saleck Pay and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Decomposition (Mathematics) categories.
In this dissertation we focus on two main topics. Under the first topic, we develop a new framework for stochastic network interdiction problem to address ambiguity in the defender risk preferences. The second topic is dedicated to computational studies of two-stage stochastic integer programs. More specifically, we consider two cases. First, we develop some solution methods for two-stage stochastic integer programs with continuous recourse; second, we study some computational strategies for two-stage stochastic integer programs with integer recourse. We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects in the network. We take a decision-analytic perspective in addressing probabilistic risk over network parameters, assuming that the defender's risk preferences over exogenously given probabilities can be summarized by the expected utility theory. Although the exact form of the utility function is ambiguous to the defender, we assume that a set of historical data on some pairwise comparisons made by the defender is available, which can be used to restrict the shape of the utility function. We use two different approaches to tackle this problem. The first approach conducts utility estimation and optimization separately, by first finding the best fit for a piecewise linear concave utility function according to the available data, and then optimizing the expected utility. The second approach integrates utility estimation and optimization, by modeling the utility ambiguity under a robust optimization framework following \cite{armbruster2015decision} and \cite{Hu}. We conduct extensive computational experiments to evaluate the performances of these approaches on the stochastic shortest path network interdiction problem. In third chapter, we propose partition-based decomposition algorithms for solving two-stage stochastic integer program with continuous recourse. The partition-based decomposition method enhance the classical decomposition methods (such as Benders decomposition) by utilizing the inexact cuts (coarse cuts) induced by a scenario partition. Coarse cut generation can be much less expensive than the standard Benders cuts, when the partition size is relatively small compared to the total number of scenarios. We conduct an extensive computational study to illustrate the advantage of the proposed partition-based decomposition algorithms compared with the state-of-the-art approaches. In chapter four, we concentrate on computational methods for two-stage stochastic integer program with integer recourse. We consider the partition-based relaxation framework integrated with a scenario decomposition algorithm in order to develop strategies which provide a better lower bound on the optimal objective value, within a tight time limit.
Prioritization And Optimization In Stochastic Network Interdiction Problems
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Author : Dennis Paul Michalopoulos
language : en
Publisher:
Release Date : 2008
Prioritization And Optimization In Stochastic Network Interdiction Problems written by Dennis Paul Michalopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Programming (Mathematics) categories.
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.
Two Person Games For Stochastic Network Interdiction
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Author : Michael Victor Nehme
language : en
Publisher:
Release Date : 2009
Two Person Games For Stochastic Network Interdiction written by Michael Victor Nehme and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
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.
Stochastic Network Interdiction
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Author :
language : en
Publisher:
Release Date : 1998
Stochastic Network Interdiction written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
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.
Integration Of Ai And Or Techniques In Constraint Programming For Combinatorial Optimization Problems
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Author : Andrea Lodi
language : en
Publisher: Springer
Release Date : 2010-06-14
Integration Of Ai And Or Techniques In Constraint Programming For Combinatorial Optimization Problems written by Andrea Lodi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-14 with Computers categories.
This book constitutes the refereed proceedings of the 7th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2010, held in Bologna, Italy, in June 2010. The 18 revised full papers and 17 revised short papers presented together with the extended abstracts of 3 invited talks were carefully reviewed and selected from 72 submissions. The papers are focused on both theoretical and practical, application-oriented issues and present current research with a special focus on the integration and hybridization of the approaches of constraint programming, artificial intelligence, and operations research technologies for solving large scale and complex real life combinatorial optimization problems.
Integer Programming And Combinatorial Optimization
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Author : Michel Goemans
language : en
Publisher: Springer
Release Date : 2013-03-12
Integer Programming And Combinatorial Optimization written by Michel Goemans and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Computers categories.
This book constitutes the proceedings of the 16th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2013, held in Valparaíso, Chile, in March 2013. The 33 full papers presented were carefully reviewed and selected from 98 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization with the aim to present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
Computational Stochastic Programming
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Author : Lewis Ntaimo
language : en
Publisher: Springer Nature
Release Date :
Computational Stochastic Programming written by Lewis Ntaimo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Formulations And Valid Inequalities For Network Interdiction Problems And Reverse Convex Sets
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Author : Eli Towle
language : en
Publisher:
Release Date : 2019
Formulations And Valid Inequalities For Network Interdiction Problems And Reverse Convex Sets written by Eli Towle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
We consider two research projects related to mixed-integer and nonconvex programming. We begin by presenting new solution approaches for the maximum-reliability stochastic network interdiction problem (SNIP). In SNIP, a defender interdicts arcs on a directed graph, reducing the probability of an attacker's undetected traversal through those arcs. The attacker's origin and destination are unknown to the defender. The attacker then selects the maximum-reliability path through the network. The defender seeks to minimize the expected reliability of this path. SNIP can be formulated as a deterministic mixed-integer linear program. Current approaches to solving SNIP rely on modifications of Benders decomposition. We reformulate the existing extensive formulation to be significantly more compact. We then present a new path-based formulation of SNIP. We introduce valid inequalities to embed in a branch-and-cut (BC) algorithm to solve this path-based formulation. Directly solving the compact SNIP formulation and this BC algorithm demonstrate improvement over a state-of-the-art Benders implementation for SNIP. Next, we present new approaches to obtain valid inequalities for a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are motivated by cases where the closure of the convex set is either non-polyhedral, or is defined by too many inequalities to directly apply disjunctive programming. Reverse convex sets arise in many models, including bilevel optimization and polynomial optimization. Intersection cuts are a well-known method for generating valid inequalities for a reverse convex set. Intersection cuts are generated from a basic solution that lies within the convex set. Our contribution is a framework for deriving valid inequalities for the reverse convex set from basic solutions that lie outside the convex set. We begin by proposing an extension to intersection cuts that defines a two-term disjunction for a reverse convex set. We refer to such a disjunction as an intersection disjunction. Next, we generalize this analysis to a multi-term disjunction by considering the convex set's recession directions. These disjunctions can be used in a cut-generating linear program to obtain valid inequalities for the reverse convex set. We continue investigating valid inequalities for optimization problems containing a reverse convex structure. So far, we have only considered methods for generating valid inequalities for such problems that rely on pointed relaxations of the polyhedron defining the reverse convex set that are formed by exactly n constraints. We present a framework to obtain valid inequalities for these problems from non-pointed relaxations of the polyhedron. We start by deriving a two-term disjunction for the reverse convex set using non-pointed relaxations formed by n constraints. We then generalize this and a previously presented two-term disjunction to relaxations of the polyhedron that are formed by more than n constraints. Finally, we present a two-term disjunction for the reverse convex set that is generated by a relaxation of the polyhedron formed by less than n constraints. We present a valid inequality for each disjunctive term and show that it defines the convex hull of the disjunctive term. We conclude by briefly investigating topics related to the convergence of intersection cuts for reverse convex sets. It is currently unknown whether cutting plane algorithms that are based purely on standard intersection cuts can be guaranteed to converge in a finite number of iterations to optimal solutions of optimization problems defined by reverse convex sets. Such a result has practical algorithmic consequences. If the result does hold, certain cutting plane algorithms could be proven to finitely converge to an optimal solution for problems with a reverse convex structure. We show that cutting plane algorithms based on standard intersection cuts can converge to the optimal solution of reverse convex optimization problems set in two dimensions. We then show that this does not hold in general for problems in three dimensions. To conclude, we conjecture that cutting plane algorithms for reverse convex optimization that add all possible intersection cuts at each iteration converge to the optimal solution of the problem in the limit. We show that this conjecture holds if the sequence of relaxations produced by such cutting plane algorithms converges to a polyhedron.
Pareto Optimality Game Theory And Equilibria
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Author : Panos M. Pardalos
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-02
Pareto Optimality Game Theory And Equilibria written by Panos M. Pardalos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-02 with Mathematics categories.
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.