Resilience-Driven Post-Disruption Restoration of Interdependent Critical Infrastructure Systems Under Uncertainty: Modeling, Risk-Averse Optimization, and Solution Approaches

Critical infrastructure networks (CINs) are the backbone of modern societies, which depend on their continuous and proper functioning. Such infrastructure networks are subjected to different types of inevitable disruptive events which could affect their performance unpredictably and have direct socioeconomic consequences. Therefore, planning for disruptions to CINs has recently shifted from emphasizing pre-disruption phases of prevention and protection to post-disruption studies investigating the ability of critical infrastructures (CIs) to withstand disruptions and recover timely from them. However, post-disruption restoration planning often faces uncertainties associated with the required repair tasks and the accessibility of the underlying transportation network. Such challenges are often overlooked in the CIs resilience literature. Furthermore, CIs are not isolated from each other, but instead, most of them rely on one another for their proper functioning. Hence, the occurrence of a disruption in one CIN could affect other dependent CINs, leading to a more significant adverse impact on communities. Therefore, interdependencies among CINs increase the complexity associated with recovery planning after a disruptive event, making it a more challenging task for decision makers. Recognizing the inevitability of large-scale disruptions to CIs and their impacts on societies, the research objective of this work is to study the recovery of CINs following a disruptive event. Accordingly, the main contributions of the following two research components are to develop: (i) resilience-based post-disruption stochastic restoration optimization models that respect the spatial nature of CIs, (ii) a general framework for scenario-based stochastic models covering scenario generation, selection, and reduction for resilience applications, (iii) stochastic risk-related cost-based restoration modeling approaches to minimize restoration costs of a system of interdependent critical infrastructure networks (ICINs), (iv) flexible restoration strategies of ICINs under uncertainty, and (v) effective solution approaches to the proposed optimization models. The first research component considers developing two-stage risk-related stochastic programming models to schedule repair activities for a disrupted CIN to maximize the system resilience. The stochastic models are developed using a scenario-based optimization technique accounting for the uncertainties of the repair time and travel time spent on the underlying transportation network. To assess the risks associated with post-disruption scheduling plans, a conditional value-at-risk metric is incorporated into the optimization models through the scenario reduction algorithm. The proposed restoration framework is illustrated using the French RTE electric power network. The second research component studies the restoration problem for a system of ICINs following a disruptive event under uncertainty. A two-stage mean-risk stochastic restoration model is proposed to minimize the total cost associated with ICINs unsatisfied demands, repair tasks, and flow. The model assigns and schedules repair tasks to network-specific work crews with consideration of limited time and resources availability. Additionally, the model features flexible restoration strategies including a multicrew assignment for a single component and a multimodal repair setting along with the consideration of full and partial functioning and dependencies between the multi-network components. The proposed model is illustrated using the power and water networks in Shelby County, Tennessee, United States, under two hypothetical earthquakes. Finally, some other topics are discussed for possible future work

The State-of-the-Art Survey on Optimization Methods for Cyber-physical Networks

Cyber-Physical Systems (CPS) are increasingly complex and frequently integrated into modern societies via critical infrastructure systems, products, and services. Consequently, there is a need for reliable functionality of these complex systems under various scenarios, from physical failures due to aging, through to cyber attacks. Indeed, the development of effective strategies to restore disrupted infrastructure systems continues to be a major challenge. Hitherto, there have been an increasing number of papers evaluating cyber-physical infrastructures, yet a comprehensive review focusing on mathematical modeling and different optimization methods is still lacking. Thus, this review paper appraises the literature on optimization techniques for CPS facing disruption, to synthesize key findings on the current methods in this domain. A total of 108 relevant research papers are reviewed following an extensive assessment of all major scientific databases. The main mathematical modeling practices and optimization methods are identified for both deterministic and stochastic formulations, categorizing them based on the solution approach (exact, heuristic, meta-heuristic), objective function, and network size. We also perform keyword clustering and bibliographic coupling analyses to summarize the current research trends. Future research needs in terms of the scalability of optimization algorithms are discussed. Overall, there is a need to shift towards more scalable optimization solution algorithms, empowered by data-driven methods and machine learning, to provide reliable decision-support systems for decision-makers and practitioners

Project Network Implementation of Infrastructure System Restoration

Infrastructure system restoration at shortest time became a paramount demand to retain system’s functionality to normal performance and avoid services from being ceased for a long time. Enormous studies elucidated the effect of project planning in the restoration problem, aspect studied as schedule, cost, and quality helped in organizing the efforts to restore disrupted networks efficiently with lowest time and costs. However, urging necessities to expedite system restoration affects the validity of normal restoration plans, post optimization model is needed to compress restoration schedule. Method presented in this work is applying crashing on network restoration as a schedule compression technique, this is attained by allocating more resources to recover the network, thus adding additional costs to restoration activities. Two cases were studied, first is allocating the same available human resources for additional working units, second is allocating external human resources to restore the network, both cases resulted in partial crashing, additional costs, and time reduction. Implications of crashing the network are represented by a cost benefit analysis for a set of solutions, these solutions provide decision makers with the tradeoffs between time and cost to adjust their plans according to project priorities and available budget. Example presented in this work used Shelby County, Tennessee USA data

Interdependent Scheduling Games

We propose a model of interdependent scheduling games in which each player controls a set of services that they schedule independently. A player is free to schedule his own services at any time; however, each of these services only begins to accrue reward for the player when all predecessor services, which may or may not be controlled by the same player, have been activated. This model, where players have interdependent services, is motivated by the problems faced in planning and coordinating large-scale infrastructures, e.g., restoring electricity and gas to residents after a natural disaster or providing medical care in a crisis when different agencies are responsible for the delivery of staff, equipment, and medicine. We undertake a game-theoretic analysis of this setting and in particular consider the issues of welfare maximization, computing best responses, Nash dynamics, and existence and computation of Nash equilibria.Comment: Accepted to IJCAI 201

Community Vulnerability Perspectives on Infrastructure Network Resilience Decision Making

Critical interdependent infrastructure networks such as water distribution, natural gas pipeline, electricity power, communication and transportation systems provide the essential necessities for societies and their utilization is the backbone of everyday processes such as production, health, convenience and many more. Often cascading dysfunctionality or disruption in these critical infrastructure networks triggers chain reactions of blackouts or blockages through the system of highly interconnected infrastructure networks and the inevitable collapse of surrounding societies. For the planning of restoration processes and resilience of these, social aspects and demographics should also be considered to assign and mitigate the possible social risks associated with these disruptions. Additionally, it is crucial to identify the most critical components of these networks which are the components that have the largest impact on the performance of both their and other networks that are operationally dependent. These critical components have the largest impact on society in terms of serving its needs so that its recovery can be completed in a timely manner after a disruption. This research studies the restoration planning of critical interdependent infrastructure networks after a possible disruptive event by mainly emphasizing on the vulnerability indices of interacting society. The methodology integrates (i) a resilience-driven multi-objective mixed-integer programming formulation to schedule the restoration process of disrupted network components in each network, and (ii) a component importance measure that quantifies the impact of equitable restoration activities on components with (iii) an index of social vulnerability that is geographically distributed. An illustrative example of the proposed integrated model that focuses on studying the community resilience in Shelby County, TN, United States is also represented

Data Processing on Large Interdependent Networks: An Application for Infrastructure Preparedness, and Restoration

This paper presents a method for validating and transforming data for use in interdependent infrastructure network analysis. Critical infrastructure are interdependent on each other for delivery of services and execution of restoration activities.  These interdependencies make infrastructure systems vulnerable to extreme events and highlights the needs for preparedness and response plans.  Optimization models have been used to create effective plans using interdependent infrastructure networks.  These models require accurate input data.  However, many data sources have inconsistencies or errors which inhibit the ability to use such optimization models.   This work identifies common errors in input network data and provides a method for processing and correcting these errors.  We demonstrate the effectiveness of this method on data representing the transportation network in Juan Diaz town, in Panama. Keywords: Data processing, network, infrastructure, interdependence

Modeling and Solution Approaches for Non-traditional Network Flow Problems with Complicating Constraints

In this dissertation, we model three network-based optimization problems. Chapter 2 addresses the question of what the operation plan should be for interdependent infrastructure systems in resource-constrained environments so that they collectively operate at the highest level. We develop a network-based operation model of these systems that accounts for interdependencies among them. To solve this large-scale model, a solution approach is proposed that relatively quickly generates high-quality solutions to the problem. Chapter 3 presents a routing model for a single train within a railyard with the objective of minimizing the total length traveled by train. The difference between this problem and the traditional shortest path is that the route must accommodate the length of the train at any time, subject to yard tracks’ configuration. This problem has application in the railway industry where they need to solve the single-train routing problem repeatedly for simulations of train movements in large complex yards. We develop an optimal polynomial-time algorithm that solves an important special case of the problem. Chapter 4 extends the problem defined in Chapter 3 to a two-train routing problem with the objective of minimizing the overall time possible to schedule the routes in a conflict-free manner. We propose a routing problem that indirectly aims to decrease the overall scheduling time for the two trains. We develop a scheduling model that compares the performance of the solution obtained by the proposed routing model with the solutions obtained by solving the problem as two separate single-train yard routing problems. The comparison indicates a better performance obtained by the proposed routing model for specific problems

Incremental Network Design with Minimum Spanning Trees

Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where $w(X_t)$ is the weight of a minimum spanning tree $X_t$ for the subgraph $(V,E_0\cup\{e'_1,\ldots,e'_t\})$ and $T=\lvert E\setminus E_0\rvert$. We prove that this problem can be solved by a greedy algorithm.Comment: 9 pages, minor revision based on reviewer comment

Recovery Optimization of Interdependent Infrastructure: A Multi-Scale Approach

2) modeling the associated service recoveryand 3) developing a computationally manageable approach for the recovery modeling and optimization. This paper presents a novel multi-scale approach for the post-disaster recovery modeling and optimization of interdependent infrastructure. The multi-scale approach facilitates the recovery modeling and enables developing recovery strategies that are feasible to implement and easy to communicate. To enhance regional resilience, the paper integrates the recovery modeling into a multi-objective optimization problem. The optimization problem aims to schedule the required recovery activities such that disrupted services are restored as fast as possible, while minimizing the incurred cost. In the optimization problem, resilience metrics are introduced to monitor and quantify service recovery. The optimization problem is subject to recovery scheduling and network flow constraints, where each is formulated as a nested optimization. The multi-scale approach to the recovery optimization highlights the role of infrastructure at multiple scales to achieve selected recovery objective(s). As an illustration, the proposed approach is used to optimize the post-disaster recovery of interdependent infrastructure in a virtual community testbed.Rapid post-disaster recovery of infrastructure is necessary for prompt societal recovery. Regional resilience analysis can promote mitigation and recovery strategies that reduce the spatial extent and duration of infrastructure disruptions. Three significant challenges in regional resilience analysis are 1) modeling the physical recovery of infrastructureThis work was supported in part by the National Institute of Standards and Technology (NIST) through the Center for Risk-based Community Resilience Planning under Award No. 70NANB15H044 and by the National Science Foundation (NSF) under Award No. 1638346. Opinions and findings presented are those of the authors and do not necessarily reflect the views of the sponsors