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Infrastructure networks serve communities by providing essential goods and services, for example, transportation, power and water. Natural hazard events, such as earthquakes, can damage network elements that disrupt operations on the network, leading to potentially significant economic and social losses. Simultaneous and instantaneous restoration of all damaged network elements is an ideal restoration action following the occurrence of a hazard event; however, the scale of the disruption and limitations on available physical and financial resources preclude this restoration solution. Instead, restoration actions must be prioritized preferably in a way that accounts for broader considerations, such as indirect economic losses and social impacts. Although optimal restoration design of disrupted infrastructure networks has been studied in the past, these studies focused solely on recovering the physical infrastructure as rapidly as possible within the financial constraints. In this research, the restoration problem is formulated in such a way that broader considerations such as indirect economic losses and social impacts can be factored into the decision-making.

The restoration problem is solved through a framework that is adopted from “Design by shopping” paradigm where simulation, many-objective, that is, four or more objectives, optimization and data visualization are combined. In order to expedite decision-making, a data visualization technique that reduce the cognitive efforts required to explore the solution set of a many-objective optimization problem is developed.  The novel data visualization technique enables efficient exploration of the solution set by quickly revealing those objectives that have significant tradeoffs for further exploration, thus reducing the number of 2D representations that must be generated and interpreted while allowing preferences to be applied when selecting a solution. The utility of the framework for restoration design is demonstrated through two case study transportation network applications. The results of the case studies demonstrated that a clear tradeoff exists between the restoration costs and the indirect economic and social losses and that a marginal increase in restoration costs with a different allocation of resources could yield significant gains in indirect economic and social losses.

Table of Contents


List of Figures                                                                                                                     vii

List of Tables                                                                                                                       xi

Acknowledgements                                                                                                             xii

Chapter 1    Introduction                                                                                                        1

1.1  Background and Motivation                                                                                         1

1.2  Goals                                                                                                                          4

1.3  Methodology                                                                                                              5

1.4  Contributions of the Research                                                                                      5

1.5  Organization of the Dissertation                                                                                   6

Chapter 2    Literature review                                                                                                 7

2.1  Overview                                                                                                                    7

2.2  Infrastructure disruption and its consequences                                                               7

2.3  Restoration design of disrupted infrastructure networks                                               10

2.4  Design decision-making with multiple considerations                                                  13

2.5  Many-objective optimization                                                                                     14

2.6  Many-objective data visualization                                                                              16

Chapter 3    A Design by Shopping Framework for Restoration of Infrastructure Networks      25

3.1  Overview                                                                                                                  25

3.2  Development of the design by shopping framework                                                     25

3.3  Simulation component                                                                                               26

3.4  Many-objective optimization component                                                                    27

3.5  Data visualization component                                                                                    28

Chapter 4      A New Data Visualization Technique                                                               30

4.1  Overview                                                                                                                  30

4.2  Definition of the tradeoff index and graphical representation                                        31

4.3  The homogenized tradeoff index and graphical representation                                      34

4.4  Quantifying the degree of diminishing returns                                                             37

4.5  Overview of the new data visualization technique                                                       42

4.6  Application of the data visualization technique to complex engineered systems             43

4.6.1  Four-objective application:  Knapsack problems                                                   43

4.6.2  Ten-objective application: General Aviation Aircraft (GAA) design problem         48

4.7  Utility of the tradeoff index as a tool to reduce the dimensionality of complex problems                                                                                                                                                   58 4.7.1  Overview                                                                                                                       58

4.7.2  Application of the data visualization technique to Van Veldhuizen’s benchmark problem           59

4.7.3  Application of other common data visualization techniques to Van Veldhuzien’s problem          72

4.7.4  Comparison of selected solutions from the various techniques                               77

4.7.5  Discussion                                                                                                          79

Chapter 5      Application of the Design by Shopping Framework to Transportation Networks  81 5.1  Overview   81

5.2  Case study 1: Lehigh Valley Network                                                                         81

5.2.1  Description of the network characteristics and hazard scenario                              81

5.2.2  The simulation                                                                                                    83

5.2.3  Many-objective optimization                                                                               87

5.2.4  Many-objective optimization results                                                                    93

5.2.5  Many-objective data visualization and down-selected solutions                             95

5.2.6  Single-objective and two-objective optimization                                                 101

5.2.7  Comparison of identified solutions                                                                     102

5.3  Case Study 2: Sioux Falls Network                                                                          103

5.3.1  Description of the network characteristics and hazard scenario                            103

5.3.2  Simulation                                                                                                        104

5.3.3  Formulation of objectives                                                                                  105

5.3.4  Many-objective optimization results                                                                  106

5.3.5  Many-objective data visualization                                                                      108

5.3.6  Single-objective formulation using goal programming                                        113

5.3.7  Solution selection without data visualization                                                                       115

5.4  Discussion                                                                                                              116

Chapter 6  Summary and Conclusions                                                                                 117

6.1  Summary                                                                                                                117

6.2  Specific conclusions                                                                                                118

6.3  Recommendations for future research                                                                       120

References                                                                                                                        122

Appendix A MATLAB scripts to compute tradeoff indices and generate mosaic plot   130

Chapter 1  Introduction

1.1 Background and Motivation

Communities and regional economies are dependent on infrastructure networks for essential services, for example, transportation, electric power and water. However, infrastructure networks are composed of elements (links and nodes) that are vulnerable to natural hazard events, such as earthquakes, hurricanes and floods. Following the occurrence of a hazard event, some of the elements can become damaged resulting in disruption to the operations on the network that translates into economic and social losses (Schiff 1995, Gordon et al. 1998, French et al. 2010). In recent years, the notion of reducing disruption due to natural hazards and restoring infrastructure networks as rapidly as possible have received significant attention (Presidential Policy Directive on Critical Infrastructure Security and Resilience 2013) in an effort to increase the nation’s disaster resilience. While definitions for resilience continue to evolve and emerge (e.g., Bruneau et al. 2003, Chang and Shinozuka 2004, Vugrin et al. 2010), a recent report by the National Research Council (NRC 2012) has offered the following definition for disaster resilience: “the ability to prepare and plan for, absorb, recover from and more successfully adapt to actual or potential adverse events.”

According to the NRC’s definition, the resilience of a community or region can be increased by investing in preparedness and planning activities and reducing the vulnerability of the network elements, for example, through retrofit and new technologies. With respect to reducing vulnerability, it is unlikely to expect that the vulnerability of the infrastructure network elements can be altogether eliminated. Thus, some level of disruption can be expected following a natural hazard event. The ideal restoration action for infrastructure networks following the occurrence of a hazard event would be to restore all damaged elements simultaneously and instantaneously; however, this action is unrealistic, due in part, to the severity of the damage, geographic distribution, and the limitations on the available physical and financial resources.  Instead, restoration actions throughout the network must be designed to restore the network as rapidly as possible and minimize indirect economic losses and social impacts, by prioritizing the restoration of damaged elements and effectively allocating the available resources within limits. Such a restoration design is necessarily complex since tradeoffs are likely to exist among conflicting objectives, for example, minimizing both network recovery time and restoration costs. Furthermore, the restoration design should be chosen to minimize the broader impacts to the community by factoring broad considerations into the design, for example, minimizing indirect economic losses and social impacts.

Optimal restoration design, that is, restoration actions for disrupted transportation networks has been studied in the past (for example, Cagnan and Davidson 2004, Luna et al. 2011, Mehlhorn et al. 2011, Bocchini and Frangopol 2012a-b, Chen and Miller-Hooks 2012, Vugrin et al. 2013, Chang 2013, among others). Most of these studies designed the restoration solely based on recovering the physical infrastructure as rapidly as possible within the financial constraints. To quantify the efficiency of the restoration process, most of these studies consider single technical performance objectives such as maximizing network resilience where resilience is defined by the area under network functionality vs. time curve (Bruneau et al. 2003). However, as acknowledged by Bruneau and Reinhorn (2007), restoration is necessarily complex and basing the restoration on a single performance objective does not provide decision-makers with broader impacts of the restoration design such as economic losses or social impacts. For example, consider the hypothetical restoration processes shown in Figure 1-1. Both processes have the same resilience (as defined by Bruneau et al. 2003) yet distinctly different functionality vs. time curves. These two restoration processes involve different allocation of physical and financial resources and might result in inequitable impact among those affected by the disrupted transportation network. For example, the restoration process in Figure 1-1a is likely to involve more efficient allocation of physical resources, that is, construction workers, which is likely to be favored by infrastructure agencies and government officials. The restoration activities also start immediately in Figure 1-1a, which is likely to minimize the cascading consequences of extreme events such as indirect economic losses for business, in comparison to the solution in Figure 1-1b. However, the restoration process shown in Figure 1-1b returns the network to the pre-event functionality in a shorter period of time which could lessen, by comparison to Figure 1-1a, social impact and lost opportunity as more people have full service in a shorter period of time. From this expository example, it is evident that restoration is complex, and designing the restoration solely based on a technical objective is unlikely to accommodate the preferences of the various users of a regional infrastructure network.


Figure 1-1: Illustration of two different restoration solutions that have same resilience as defined by

Bruneau et al. (2003), (R1=R2)

Design decision-making of complex systems has been studied in various engineering fields, such as automotive, aerospace and industrial engineering (Stump et al. 2009, Miller et al. 2013). An emerging approach that is used in these studies is the “design by shopping” paradigm which was introduced by Balling (1999). In the design by shopping paradigm, a many-objective optimization approach, that is, optimization of four or more objectives, (Fleming et al. 2005) is used to produce a rich solution set in which the decision-makers can “shop” to select solutions that best satisfy the preferences of various stakeholders involved in the decision-making process. In contrast to traditional optimization where a problem is formulated with aggregated and simplified functions, and preferences between different aspects of the problem are formed and articulated a priori, a many-objective approach allows a posteriori preference articulation by exploring the design space to learn about the relationships and feasibility to form preferences and make a final choice (Stump et al. 2009). The design by shopping paradigm can be an alternative approach for the restoration design of infrastructure networks because with this approach, decision-makers can explore all possible restoration actions, learn about the impacts of each restoration action on the community in terms of the broad considerations of the recovery, such as network recovery time, restoration costs, indirect losses and social impacts and identify a design that is preferred by the majority of the infrastructure users.

Design by shopping paradigm has been adopted for various complex design problems with many conflicting objectives (Stump et al. 2009). However, as the number of objectives increases, the effort required to visualize and explore the resulting solution set increases. Although data visualization techniques exist to facilitate analytical reasoning for exploring high-dimensional solution sets through graphical interfaces (Woodruff et al. 2013), these techniques often rely on exhaustive two-dimensional representations to identify all tradeoffs. The knowledge of the tradeoffs among competing objectives is important for decision-making because it fosters learning from the solution set and hence aids preference formation. Therefore, identifying objectives that possess tradeoff, and then focusing cognitive efforts only on those objectives can expedite the process of selecting designs.

1.2 Goals

The overarching goal of this research is to formulate the problem of infrastructure network restoration to account for broader considerations, such as indirect economic losses and social impacts. In order to achieve this goal, “design by shopping” paradigm is adopted in a framework that combines simulation, many-objective optimization and data visualization. To overcome the cognitive challenges associated with selecting a final design from a many-objective search, a data visualization technique is developed that facilitates learning about the tradeoffs through quantification and allows decision-makers to form and apply preferences along the way.

1.3 Methodology

The research progresses from reviewing literature on impacts of infrastructure disruption on the communities and restoration of the infrastructure networks. The literature review includes evidence of disruption and losses from past natural hazard events, past studies on restoration design and important considerations in restoration decision-making process. Following the literature review, a framework to support restoration decision-making is developed based on design by shopping paradigm that combines simulation, many-objective optimization and data visualization. In order to develop the design by shopping framework, first, modeling and optimization techniques are explored that facilitate solving the restoration problem with many objectives with a reasonable computational effort. Second, a novel data visualization technique is developed to facilitate efficient exploration of the results of many-objective optimization and expedite final design selection. The utility of the data visualization technique is illustrated with optimization applications from different engineering disciplines. Finally, the utility of the design by shopping framework for restoration design is demonstrated through two case study transportation network applications and the feasibility of the restoration designs obtained from the casestudies are assessed and justified.

1.4 Contributions of the Research

The design by shopping framework presented in this dissertation facilitates accounting for broader considerations of community’s recovery and resilience, such as indirect economic losses and social impacts, in the restoration design of disrupted infrastructure networks in contrast to previous studies (Bocchini and Frangopol 2011, 2012a, Chen and Miller-Hooks 2012, Vugrin et al. 2013) that have focused purely on the technical and direct economic aspects. The novel data visualization technique developed in this study to visualize tradeoffs and overcome the cognitive challenges in identifying preferred solutions is general and scalable so that it could be broadly applied to the design of any engineered systems with many, especially conflicting, objectives.

1.5 Organization of the Dissertation

The dissertation is divided into six chapters. Following a brief introduction in Chapter 1, Chapter 2 provides a summary of literature discussing impacts of natural hazard events on infrastructure networks, and the consequences of these impacts on the community. This chapter also presents a review of key studies on many-objective optimization and data visualization techniques that would be a background for the design by shopping framework proposed in this dissertation. Chapter 3 presents the design by shopping framework to support restoration decision-making of disrupted infrastructure networks. The general details of each component of the framework are presented and discussed. Chapter 4 presents the novel data visualization technique developed to facilitate the visualization of tradeoffs between conflicting objectives and efficient exploration of complex solution sets. The utility and the efficiency of the data visualization technique are demonstrated through different engineering applications. Chapter 5 illustrates the utility of the design by shopping framework through the restoration of two transportation network case-studies. The final restoration designs obtained from the framework are compared and justified. Finally, Chapter 6 provides a brief summary of the dissertation, key findings, conclusions, and recommendations for future research.


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