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

Exact Algorithms for Mixed-Integer Multilevel Programming Problems

We examine multistage optimization problems, in which one or more decision makers solve a sequence of interdependent optimization problems. In each stage the corresponding decision maker determines values for a set of variables, which in turn parameterizes the subsequent problem by modifying its constraints and objective function. The optimization literature has covered multistage optimization problems in the form of bilevel programs, interdiction problems, robust optimization, and two-stage stochastic programming. One of the main differences among these research areas lies in the relationship between the decision makers. We analyze the case in which the decision makers are self-interested agents seeking to optimize their own objective function (bilevel programming), the case in which the decision makers are opponents working against each other, playing a zero-sum game (interdiction), and the case in which the decision makers are cooperative agents working towards a common goal (two-stage stochastic programming). Traditional exact approaches for solving multistage optimization problems often rely on strong duality either for the purpose of achieving single-level reformulations of the original multistage problems, or for the development of cutting-plane approaches similar to Benders\u27 decomposition. As a result, existing solution approaches usually assume that the last-stage problems are linear or convex, and fail to solve problems for which the last-stage is nonconvex (e.g., because of the presence of discrete variables). We contribute exact finite algorithms for bilevel mixed-integer programs, three-stage defender-attacker-defender problems, and two-stage stochastic programs. Moreover, we do not assume linearity or convexity for the last-stage problem and allow the existence of discrete variables. We demonstrate how our proposed algorithms significantly outperform existing state-of-the-art algorithms. Additionally, we solve for the first time a class of interdiction and fortification problems in which the third-stage problem is NP-hard, opening a venue for new research and applications in the field of (network) interdiction

An investigation of models for identifying critical components in a system.

Lai, Tsz Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 193-207).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Overview --- p.1Chapter 1.2 --- Contributions --- p.2Chapter 1.3 --- Organization --- p.2Chapter 2 --- Literature Review --- p.4Chapter 2.1 --- Taxonomy --- p.4Chapter 2.2 --- Design of Infrastructure --- p.6Chapter 2.2.1 --- Facility Location Models --- p.7Chapter 2.2.1.1 --- Random Breakdowns --- p.7Chapter 2.2.1.2 --- Deliberate Attacks --- p.8Chapter 2.2.2 --- Network Design Models --- p.9Chapter 2.3 --- Protection of Existing Components --- p.10Chapter 2.3.1 --- Interdiction Models --- p.11Chapter 2.3.2 --- Facility Location Models --- p.12Chapter 2.3.2.1 --- Random Breakdowns --- p.12Chapter 2.3.2.2 --- Deliberate Attacks --- p.12Chapter 2.3.3 --- Network Design Models --- p.14Chapter 3 --- Identifying Critical Facilities: Median Problem --- p.16Chapter 3.1 --- Introduction --- p.16Chapter 3.2 --- Problem Formulation --- p.18Chapter 3.2.1 --- The p-Median Problem --- p.18Chapter 3.2.1.1 --- A Toy Example --- p.19Chapter 3.2.1.2 --- Problem Definition --- p.21Chapter 3.2.1.3 --- Mathematical Model --- p.22Chapter 3.2.2 --- The r-Interdiction Median Problem --- p.24Chapter 3.2.2.1 --- The Toy Example --- p.24Chapter 3.2.2.2 --- Problem Definition --- p.27Chapter 3.2.2.3 --- Mathematical Model --- p.28Chapter 3.2.3 --- The r-Interdiction Median Problem with Fortification --- p.29Chapter 3.2.3.1 --- The Toy Example --- p.30Chapter 3.2.3.2 --- Problem Definition --- p.32Chapter 3.2.3.3 --- Mathematical Model --- p.33Chapter 3.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.35Chapter 3.2.4.1 --- Mathematical Model --- p.36Chapter 3.3 --- Solution Methodologies --- p.38Chapter 3.3.1 --- Model Reduction --- p.38Chapter 3.3.2 --- Variable Consolidation --- p.40Chapter 3.3.3 --- Implicit Enumeration --- p.45Chapter 3.4 --- Results and Discussion --- p.48Chapter 3.4.1 --- Data Sets --- p.48Chapter 3.4.1.1 --- Swain --- p.48Chapter 3.4.1.2 --- London --- p.49Chapter 3.4.1.3 --- Alberta --- p.49Chapter 3.4.2 --- Computational Study --- p.50Chapter 3.4.2.1 --- The p-Median Problem --- p.50Chapter 3.4.2.2 --- The r-Interdiction Median Problem --- p.58Chapter 3.4.2.3 --- The r-Interdiction Median Problem with Fortification --- p.63Chapter 3.4.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.68Chapter 3.5 --- Summary --- p.76Chapter 4 --- Hybrid Approaches --- p.79Chapter 4.1 --- Framework --- p.80Chapter 4.2 --- Tabu Assisted Heuristic Search --- p.81Chapter 4.2.1 --- A Tabu Assisted Heuristic Search Construct --- p.83Chapter 4.2.1.1 --- Search Space --- p.84Chapter 4.2.1.2 --- Initial Trial Solution --- p.85Chapter 4.2.1.3 --- Neighborhood Structure --- p.85Chapter 4.2.1.4 --- Local Search Procedure --- p.86Chapter 4.2.1.5 --- Form of Tabu Moves --- p.88Chapter 4.2.1.6 --- Addition of a Tabu Move --- p.88Chapter 4.2.1.7 --- Maximum Size of Tabu List --- p.89Chapter 4.2.1.8 --- Termination Criterion --- p.89Chapter 4.3 --- Hybrid Simulated Annealing Search --- p.90Chapter 4.3.1 --- A Hybrid Simulated Annealing Construct --- p.91Chapter 4.3.1.1 --- Random Selection of Immediate Neighbor --- p.92Chapter 4.3.1.2 --- Cooling Schedule --- p.93Chapter 4.3.1.3 --- Termination Criterion --- p.94Chapter 4.4 --- Hybrid Genetic Search Algorithm --- p.95Chapter 4.4.1 --- A Hybrid Genetic Search Construct --- p.99Chapter 4.4.1.1 --- Search Space --- p.99Chapter 4.4.1.2 --- Initial Population --- p.100Chapter 4.4.1.3 --- Selection --- p.104Chapter 4.4.1.4 --- Crossover --- p.105Chapter 4.4.1.5 --- Mutation --- p.106Chapter 4.4.1.6 --- New Population --- p.108Chapter 4.4.1.7 --- Termination Criterion --- p.109Chapter 4.5 --- Further Assessment --- p.109Chapter 4.6 --- Computational Study --- p.114Chapter 4.6.1 --- Parameter Selection --- p.115Chapter 4.6.1.1 --- Tabu Assisted Heuristic Search --- p.115Chapter 4.6.1.2 --- Hybrid Simulated Annealing Approach --- p.121Chapter 4.6.1.3 --- Hybrid Genetic Search Algorithm --- p.124Chapter 4.6.2 --- Expected Performance --- p.128Chapter 4.6.2.1 --- Tabu Assisted Heuristic Search --- p.128Chapter 4.6.2.2 --- Hybrid Simulated Annealing Approach --- p.138Chapter 4.6.2.3 --- Hybrid Genetic Search Algorithm --- p.146Chapter 4.6.2.4 --- Overall Comparison --- p.150Chapter 4.7 --- Summary --- p.153Chapter 5 --- A Special Case of the Median Problems --- p.156Chapter 5.1 --- Introduction --- p.157Chapter 5.2 --- Problem Formulation --- p.158Chapter 5.2.1 --- The r-Interdiction Covering Problem --- p.158Chapter 5.2.1.1 --- Problem Definition --- p.159Chapter 5.2.1.2 --- Mathematical Model --- p.160Chapter 5.2.2 --- The r-Interdiction Covering Problem with Fortification --- p.162Chapter 5.2.2.1 --- Problem Definition --- p.163Chapter 5.2.2.2 --- Mathematical Model --- p.164Chapter 5.2.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.167Chapter 5.2.3.1 --- Mathematical Model --- p.168Chapter 5.3 --- Theoretical Relationship --- p.170Chapter 5.4 --- Solution Methodologies --- p.172Chapter 5.5 --- Results and Discussion --- p.175Chapter 5.5.1 --- The r-Interdiction Covering Problem --- p.175Chapter 5.5.2 --- The r-Interdiction Covering Problem with Fortification --- p.178Chapter 5.5.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.182Chapter 5.6 --- Summary --- p.187Chapter 6 --- Conclusion --- p.189Chapter 6.1 --- Summary of Our Work --- p.189Chapter 6.2 --- Future Directions --- p.19

Passenger railway network protection: A model with variable post-disruption demand service

Protecting transportation infrastructures is critical to avoid loss of life and to guard against economic upheaval. This paper addresses the problem of identifying optimal protection plans for passenger rail transportation networks, given a limited budget. We propose a bi-level protection model which extends and refines the model previously introduced by Scaparra et al, (Railway infrastructure security, Springer, New York, 2015). In our extension, we still measure the impact of rail disruptions in terms of the amount of unserved passenger demand. However, our model captures the post-disruption user behaviour in a more accurate way by assuming that passenger demand for rail services after disruptions varies with the extent of the travel delays. To solve this complex bi-level model, we develop a simulated annealing algorithm. The efficiency of the heuristic is tested on a set of randomly generated instances and compared with the one of a more standard exact decomposition algorithm. To illustrate how the modelling approach might be used in practice to inform protection planning decisions, we present a case study based on the London Underground. The case study also highlights the importance of capturing flow demand adjustments in response to increased travel time in a mathematical model

Efficient Algorithms for Solving Facility Problems with Disruptions

This study investigates facility location problems in the presence of facility disruptions. Two types of problems are investigated. Firstly, we study a facility location problem considering random disruptions. Secondly, we study a facility fortification problem considering disruptions caused by random failures and intelligent attacks.We first study a reliable facility location problem in which facilities are faced with the risk of random disruptions. In the literature, reliable facility location models and solution methods have been proposed under different assumptions of the disruption distribution. In most of these models, the disruption distribution is assumed to be completely known, that is, the disruptions are known to be uncorrelated or to follow a certain distribution. In practice, we may have only limited information about the distribution. In this work, we propose a robust reliable facility location model that considers the worst-case distribution with incomplete information. Because the model imposes fewer distributional assumptions, it includes several important reliable facility location problems as special cases. We propose an effective cutting plane algorithm based on the supermodularity of the problem. For the case in which the distribution is completely known, we develop a heuristic algorithm called multi-start tabu search to solve very large instances.In the second part of the work, we study an r-interdiction median problem with fortification that simultaneously considers two types of disruption risks: random disruptions that happen probabilistically and disruptions caused by intentional attacks. The problem is to determine the allocation of limited facility fortification resources to an existing network. The problem is modeled as a bi-level programming model that generalizes the r-interdiction median problem with probabilistic fortification. The lower level problem, that is, the interdiction problem, is a challenging high-degree non-linear model. In the literature, only the enumeration method is applied to solve a special case of the problem. By exploring the special structure property of the problem, we propose an exact cutting plane method for the problem. For the fortification problem, an effective logic based Benders decomposition algorithm is proposed

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

Optimization Approaches for Improving Mitigation and Response Operations in Disaster Management

Disasters are calamitous events that severely affect the life conditions of an entire community, being the disasters either nature-based (e.g., earthquake) or man-made (e.g., terroristic attack). Disaster-related issues are usually dealt with according to the Disaster Operations Management (DOM) framework, which is composed of four phases: mitigation and preparedness, which address pre-disaster issues, and response and recovery, which tackle problems arising after the occurrence of a disaster. The ultimate scope of this dissertation is to present novel optimization models and algorithms aimed at improving operations belonging to the mitigation and response phases of the DOM. On the mitigation side, this thesis focuses on the protection of Critical Information Infrastructures (CII), which are commonly deemed to include communication and information networks. The majority of all the other Critical Infrastructures (CI), such as electricity, fuel and water supply as well as transportation systems, 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 dissertation reviews several issues emerging in the Critical Information Infrastructures Protection (CIIP), field such as: how to identify the most critical components of a communication network whose disruption would affect the overall system functioning; how to mitigate the consequences of such calamitous events through protection strategies; and how to design a system which is intrinsically able to hedge against disruptions. To this end, this thesis provides a description of the seminal optimization models that have been developed to address the aforementioned issues in the general field of Critical Infrastructures Protection (CIP). Models are grouped in three categories which address the aforementioned issues: survivability-oriented interdiction, resource allocation strategy, and survivable design models; existing models are reviewed and possible extensions are proposed. In fact, some models have already been developed for CII (i.e., survivability-interdiction and design models), while others have been adapted from the literature on other CI (i.e., resource allocation strategy models). The main gap emerging in the CII field is that CII protection has been quite overlooked which has led to review optimization models that have been developed for the protection of other CI. Hence, this dissertation contributes to the literature in the field by also providing a survey of the multi-level programs that have been developed for protecting supply chains, transportation systems (e.g., railway infrastructures), and utility networks (e.g., power and water supply systems), in order to adapt them for CII protection. Based on the review outcomes, this thesis proposes a novel linear bi-level program for CIIP to mitigate worst-case disruptions through protection investments entailing network design operations, namely the Critical Node Detection Problem with Fortification (CNDPF), which integrates network survivability assessment, resource allocation strategies and design operations. To the best of my knowledge, this is the first bi-level program developed for CIIP. The model is solved through a Super Valid Inequalities (SVI) decomposition approach and a Greedy Constructive and Local Search (GCLS) heuristic. Computational results are reported for real communication networks and for different levels of both disaster magnitude and protection resources. On the response side, this thesis identifies the current challenges in devising realistic and applicable optimization models in the shelter location and evacuation routing context and outlines a roadmap for future research in this topical area. A shelter is a facility where people belonging to a community hit by a disaster are provided with different kinds of services (e.g., medical assistance, food). The role of a shelter is fundamental for two categories of people: those who are unable to make arrangements to other safe places (e.g., family or friends are too far), and those who belong to special-needs populations (e.g., disabled, elderly). People move towards shelter sites, or alternative safe destinations, when they either face or are going to face perilous circumstances. The process of leaving their own houses to seek refuge in safe zones goes under the name of evacuation. Two main types of evacuation can be identified: self-evacuation (or car-based evacuation) where individuals move towards safe sites autonomously, without receiving any kind of assistance from the responder community, and supported evacuation where special-needs populations (e.g., disabled, elderly) require support from emergency services and public authorities to reach some shelter facilities. This dissertation aims at identifying the central issues that should be addressed in a comprehensive shelter location/evacuation routing model. This is achieved by a novel meta-analysis that entail: (1) analysing existing disaster management surveys, (2) reviewing optimization models tackling shelter location and evacuation routing operations, either separately or in an integrated manner, (3) performing a critical analysis of existing papers combining shelter location and evacuation routing, concurrently with the responses of their authors, and (4) comparing the findings of the analysis of the papers with the findings of the existing disaster management surveys. The thesis also provides a discussion on the emergent challenges of shelter location and evacuation routing in optimization such as the need for future optimization models to involve stakeholders, include evacuee as well as system behaviour, be application-oriented rather than theoretical or model-driven, and interdisciplinary and, eventually, outlines a roadmap for future research. Based on the identified challenges, this thesis presents a novel scenario-based mixed-integer program which integrates shelter location, self-evacuation and supported-evacuation decisions, namely the Scenario-Indexed Shelter Location and Evacuation Routing (SISLER) problem. To the best of my knowledges, this is the second model including shelter location, self-evacuation and supported-evacuation however, SISLER deals with them based on the provided meta-analysis. The model is solved through a Branch-and-Cut algorithm of an off-the-shelf software, enriched with valid inequalities adapted from the literature. Computational results are reported for both testbed instances and a realistic case study

Passenger railway network protection: A model with variable post-disruption demand service

Protecting transportation infrastructures is critical to avoid loss of life and to guard against economic upheaval. This paper addresses the problem of identifying optimal protection plans for passenger rail transportation networks, given a limited budget. We propose a bi-level protection model which extends and refines the model previously introduced by Scaparra et al, (Railway infrastructure security, Springer, New York, 2015). In our extension, we still measure the impact of rail disruptions in terms of the amount of unserved passenger demand. However, our model captures the post-disruption user behaviour in a more accurate way by assuming that passenger demand for rail services after disruptions varies with the extent of the travel delays. To solve this complex bi-level model, we develop a simulated annealing algorithm. The efficiency of the heuristic is tested on a set of randomly generated instances and compared with the one of a more standard exact decomposition algorithm. To illustrate how the modelling approach might be used in practice to inform protection planning decisions, we present a case study based on the London Underground. The case study also highlights the importance of capturing flow demand adjustments in response to increased travel time in a mathematical model

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

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application