AndrĂ©s David GonzĂˇlez Huertas
Critical infrastructure systems such as water, gas, power, telecommunications, and transportation networks, among others, are constantly stressed by aging and natural disasters. Just since 2001, adverse events such as earthquakes, landslides, and floods, have accounted for economic losses exceeding USD 1.68 trillion (UNISDR,2013). Thus, governments and other stakeholders are giving priority to mitigate the effects of natural disasters over such critical infrastructure systems, especially when considering their increasing vulnerability to interconnectedness. Studying the failure and recovery dynamics of networked systems is an important but complex task, especially when considering the emerging multiplex of networks with underlying interdependencies. In particular, designing optimal mitigation and recovery strategies for networked systems while considering their interdependencies is imperative to enhance their resilience, thus reducing the negative effects of damaging events.
Considering this, the present thesis describes a comprehensive body of work that focuses on modeling, understanding, and optimizing the resilience of systems of interdependent networks. To approach these concepts, we have introduced a problem denominated the Interdependent Network Design Problem (INDP), which focuses on optimizing the resource allocation and recovery strategies of interdependent networks after a destructive event, while considering limited resources and operational constraints. To solve the INDP, we describe a mathematical model denominated the time-dependent INDP (td-INDP), which finds the least-cost recovery strategy for a system of physically and geographically interdependent systems, while accounting for realistic operational constraints associated with the limited availability of resources and the finite capacity of the system's elements, among others. Additional analytical and heuristic solution strategies are also introduced, in order to extend and enhance the td-INDP solving capabilities. Additionally, we propose diverse methodological approaches to incorporate uncertainty in the modeling and optimization processes. Particularly, we present the stochastic INDP (sINDP), which can be seen as an extension of the td-INDP that considers uncertainty in parameters of the model, such as the costs, demands, and resource availability, among others. Finally, we explore different multidisciplinary techniques to allow modeling decentralized systems, as well as to enable compressing the main recovery dynamics of a system of interdependent networks by using a time-invariant linear recovery operator.
The proposed methodologies enable studying and optimizing pre- and post-event decisions, to improve the performance, reliability, and resilience of systems of coupled infrastructure networks, such that they can better withstand normal demands and damaging hazards. To illustrate each of these methodologies, we study a realistic system of interdependent networks, composed of streamlined versions of the water, power, and gas networks in Shelby County, TN. This problem is of interest, since it does not only describe physical and geographical interdependencies, but is also subject to earthquake hazards due to its proximity to the New Madrid Seismic Zone (NMSZ). We show that the proposed methodologies represent useful tools for decision makers and stakeholders, which can support optimal mitigation and recovery planning.