Decomposition Algorithms in Stochastic Integer Programming: Applications and Computations.

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\u27s 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

Doctor of Philosophy

dissertationA safe and secure transportation system is critical to providing protection to those who employ it. Safety is being increasingly demanded within the transportation system and transportation facilities and services will need to adapt to change to provide it. This dissertation provides innovate methodologies to identify current shortcomings and provide theoretic frameworks for enhancing the safety and security of the transportation network. This dissertation is designed to provide multilevel enhanced safety and security within the transportation network by providing methodologies to identify, monitor, and control major hazards associated within the transportation network. The risks specifically addressed are: (1) enhancing nuclear materials sensor networks to better deter and interdict smugglers, (2) use game theory as an interdiction model to design better sensor networks and forensically track smugglers, (3) incorporate safety into regional transportation planning to provide decision-makers a basis for choosing safety design alternatives, and (4) use a simplified car-following model that can incorporate errors to predict situational-dependent safety effects of distracted driving in an ITS infrastructure to deploy live-saving countermeasures

Multi-Level Multi-Objective Programming and Optimization for Integrated Air Defense System Disruption

The U.S. military\u27s ability to project military force is being challenged. This research develops and demonstrates the application of three respective sensor location, relocation, and network intrusion models to provide the mathematical basis for the strategic engagement of emerging technologically advanced, highly-mobile, Integrated Air Defense Systems. First, we propose a bilevel mathematical programming model for locating a heterogeneous set of sensors to maximize the minimum exposure of an intruder\u27s penetration path through a defended region. Next, we formulate a multi-objective, bilevel optimization model to relocate surviving sensors to maximize an intruder\u27s minimal expected exposure to traverse a defended border region, minimize the maximum sensor relocation time, and minimize the total number of sensors requiring relocation. Lastly, we present a trilevel, attacker-defender-attacker formulation for the heterogeneous sensor network intrusion problem to optimally incapacitate a subset of the defender\u27s sensors and degrade a subset of the defender\u27s network to ultimately determine the attacker\u27s optimal penetration path through a defended network

Strategic Network Interdiction

We develop a strategic model of network interdiction in a non-cooperative game of flow. An adversary, endowed with a bounded quantity of bads, chooses a flow specifying a plan for carrying bads through a network from a base to a target. Simultaneously, an agency chooses a blockage specifying a plan for blocking the transport of bads through arcs in the network. The bads carried to the target cause a target loss while the blocked arcs cause a network loss. The adversary earns and the agency loses from both target loss and network loss. The adversary incurs the expense of carrying bads. In this model we study Nash equilibria and find a power law relation between the probability and the extent of the target loss. Our model contributes to the literature of game theory by introducing non-cooperative behavior into a Kalai-Zemel (cooperative) game of flow. Our research also advances models and results on network interdiction.Network Interdiction, Noncooperative Game of Flow, Nash Equilibrium, Power Law, Kalai-Zemel Game of Flow

Locating and Protecting Facilities Subject to Random Disruptions and Attacks

Recent events such as the 2011 Tohoku earthquake and tsunami in Japan have revealed the vulnerability of networks such as supply chains to disruptive events. In particular, it has become apparent that the failure of a few elements of an infrastructure system can cause a system-wide disruption. Thus, it is important to learn more about which elements of infrastructure systems are most critical and how to protect an infrastructure system from the effects of a disruption. This dissertation seeks to enhance the understanding of how to design and protect networked infrastructure systems from disruptions by developing new mathematical models and solution techniques and using them to help decision-makers by discovering new decision-making insights. Several gaps exist in the body of knowledge concerning how to design and protect networks that are subject to disruptions. First, there is a lack of insights on how to make equitable decisions related to designing networks subject to disruptions. This is important in public-sector decision-making where it is important to generate solutions that are equitable across multiple stakeholders. Second, there is a lack of models that integrate system design and system protection decisions. These models are needed so that we can understand the benefit of integrating design and protection decisions. Finally, most of the literature makes several key assumptions: 1) protection of infrastructure elements is perfect, 2) an element is either fully protected or fully unprotected, and 3) after a disruption facilities are either completely operational or completely failed. While these may be reasonable assumptions in some contexts, there may exist contexts in which these assumptions are limiting. There are several difficulties with filling these gaps in the literature. This dissertation describes the discovery of mathematical formulations needed to fill these gaps as well as the identification of appropriate solution strategies

DECENTRALIZED ALGORITHMS FOR NASH EQUILIBRIUM PROBLEMS – APPLICATIONS TO MULTI-AGENT NETWORK INTERDICTION GAMES AND BEYOND

Nash equilibrium problems (NEPs) have gained popularity in recent years in the engineering community due to their ready applicability to a wide variety of practical problems ranging from communication network design to power market analysis. There are strong links between the tools used to analyze NEPs and the classical techniques of nonlinear and combinatorial optimization. However, there remain significant challenges in both the theoretical and algorithmic analysis of NEPs. This dissertation studies certain special classes of NEPs, with the overall purpose of analyzing theoretical properties such as existence and uniqueness, while at the same time proposing decentralized algorithms that provably converge to solutions. The subclasses are motivated by relevant application examples

A Synthesis of Optimization Approaches for Tackling Critical Information Infrastructure Survivability

Over the years, Critical Infrastructures (CI) have revealed themselves to be extremely disaster-prone, be the disasters nature-based or man-made. This paper focuses on a specific category of CI: Critical Information Infrastructures (CII), which are commonly deemed to include communication and information net-works. The majority of all the other CI (e.g. electricity, fuel and water supply, transport systems, etc.) are crucially dependent on CII. Therefore, problems associated with CII that disrupt the services they are able to provide (whether to a single end-user or to another CI) are of increasing interest. This paper discusses some recent developments in optimization models regarding CII’s ability to with-stand disruptive events within three main spheres: network survivability assessment, network resource allocation strategy and survivable design

A meta-architecture analysis for a coevolved system-of-systems

Modern engineered systems are becoming increasingly complex. This is driven in part by an increase in the use of systems-of-systems and network-centric concepts to improve system performance. The growth of systems-of-systems allows stakeholders to achieve improved performance, but also presents new challenges due to increased complexity. These challenges include managing the integration of asynchronously developed systems and assessing SoS performance in uncertain environments. Many modern systems-of-systems must adapt to operating environment changes to maintain or improve performance. Coevolution is the result of the system and the environment adapting to changes in each other to obtain a performance advantage. The complexity that engineered systems-of-systems exhibit poses challenges to traditional systems engineering approaches. Systems engineers are presented with the problem of understanding how these systems can be designed or adapted given these challenges. Understanding how the environment influences system-of-systems performance allows systems engineers to target the right set of capabilities when adapting the system for improved performance. This research explores coevolution in a counter-trafficking system-of-systems and develops an approach to demonstrate its impacts. The approach implements a trade study using swing weights to demonstrate the influence of coevolution on stakeholder value, develops a novel future architecture to address degraded capabilities, and demonstrates the impact of the environment on system performance using simulation. The results provide systems engineers with a way to assess the impacts of coevolution on the system-of-systems, identify those capabilities most affected, and explore alternative meta-architectures to improve system-of-systems performance in new environments --Abstract, page iii