Solving Markov decision processes for network-level post-hazard recovery via simulation optimization and rollout

Computation of optimal recovery decisions for community resilience assurance post-hazard is a combinatorial decision-making problem under uncertainty. It involves solving a large-scale optimization problem, which is significantly aggravated by the introduction of uncertainty. In this paper, we draw upon established tools from multiple research communities to provide an effective solution to this challenging problem. We provide a stochastic model of damage to the water network (WN) within a testbed community following a severe earthquake and compute near-optimal recovery actions for restoration of the water network. We formulate this stochastic decision-making problem as a Markov Decision Process (MDP), and solve it using a popular class of heuristic algorithms known as rollout. A simulation-based representation of MDPs is utilized in conjunction with rollout and the Optimal Computing Budget Allocation (OCBA) algorithm to address the resulting stochastic simulation optimization problem. Our method employs non-myopic planning with efficient use of simulation budget. We show, through simulation results, that rollout fused with OCBA performs competitively with respect to rollout with total equal allocation (TEA) at a meagre simulation budget of 5-10% of rollout with TEA, which is a crucial step towards addressing large-scale community recovery problems following natural disasters.Comment: Submitted to Simulation Optimization for Cyber Physical Energy Systems (Special Session) in 14th IEEE International Conference on Automation Science and Engineerin

An approximate dynamic programming approach to food security of communities following hazards

Food security can be threatened by extreme natural hazard events for households of all social classes within a community. To address food security issues following a natural disaster, the recovery of several elements of the built environment within a community, including its building portfolio, must be considered. Building portfolio restoration is one of the most challenging elements of recovery owing to the complexity and dimensionality of the problem. This study introduces a stochastic scheduling algorithm for the identification of optimal building portfolio recovery strategies. The proposed approach provides a computationally tractable formulation to manage multi-state, large-scale infrastructure systems. A testbed community modeled after Gilroy, California, is used to illustrate how the proposed approach can be implemented efficiently and accurately to find the near-optimal decisions related to building recovery following a severe earthquake.Comment: As opposed to the preemptive scheduling problem, which was addressed in multiple works by us, we deal with a non-preemptive stochastic scheduling problem in this work. Submitted to 13th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP13 Seoul, South Korea, May 26-30, 201

OPTIMIZATION MODELS AND METHODOLOGIES TO SUPPORT EMERGENCY PREPAREDNESS AND POST-DISASTER RESPONSE

This dissertation addresses three important optimization problems arising during the phases of pre-disaster emergency preparedness and post-disaster response in time-dependent, stochastic and dynamic environments. The first problem studied is the building evacuation problem with shared information (BEPSI), which seeks a set of evacuation routes and the assignment of evacuees to these routes with the minimum total evacuation time. The BEPSI incorporates the constraints of shared information in providing on-line instructions to evacuees and ensures that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. A mixed-integer linear program is formulated for the BEPSI and an exact technique based on Benders decomposition is proposed for its solution. Numerical experiments conducted on a mid-sized real-world example demonstrate the effectiveness of the proposed algorithm. The second problem addressed is the network resilience problem (NRP), involving an indicator of network resilience proposed to quantify the ability of a network to recover from randomly arising disruptions resulting from a disaster event. A stochastic, mixed integer program is proposed for quantifying network resilience and identifying the optimal post-event course of action to take. A solution technique based on concepts of Benders decomposition, column generation and Monte Carlo simulation is proposed. Experiments were conducted to illustrate the resilience concept and procedure for its measurement, and to assess the role of network topology in its magnitude. The last problem addressed is the urban search and rescue team deployment problem (USAR-TDP). The USAR-TDP seeks an optimal deployment of USAR teams to disaster sites, including the order of site visits, with the ultimate goal of maximizing the expected number of saved lives over the search and rescue period. A multistage stochastic program is proposed to capture problem uncertainty and dynamics. The solution technique involves the solution of a sequence of interrelated two-stage stochastic programs with recourse. A column generation-based technique is proposed for the solution of each problem instance arising as the start of each decision epoch over a time horizon. Numerical experiments conducted on an example of the 2010 Haiti earthquake are presented to illustrate the effectiveness of the proposed approach

Disaster risk management of interdependent infrastructure systems for community resilience planning

This research focuses on developing methodologies to model the damage and recovery of interdependent infrastructure systems under disruptive events for community resilience planning. The overall research can be broadly divided into two parts: developing a model to simulate the post-disaster performance of interdependent infrastructure systems and developing decision frameworks to support pre-disaster risk mitigation and post-disaster recovery planning of the interdependent infrastructure systems towards higher resilience. The Dynamic Integrated Network (DIN) model is proposed in this study to simulate the performance of interdependent infrastructure systems over time following disruptive events. It can consider three different levels of interdependent relationships between different infrastructure systems: system-to-system level, system-to-facility level and facility-to-facility level. The uncertainties in some of the modeling parameters are modeled. The DIN model first assesses the inoperability of the network nodes and links over time to simulate the damage and recovery of the interdependent infrastructure facilities, and then assesses the recovery and resilience of the individual infrastructure systems and the integrated network utilizing some network performance metrics. The recovery simulation result from the proposed model is compared to two conventional models, one with no interdependency considered, and the other one with only system-level interdependencies considered. The comparison results suggest that ignoring the interdependencies between facilities in different infrastructure systems would lead to poorly informed decision making. The DIN model is validated through simulating the recovery of the interdependent power, water and cellular systems of Galveston City, Texas after Hurricane Ike (2008). Implementing strategic pre-disaster risk mitigation plan to improve the resilience of the interdependent infrastructure systems is essential for enhancing the social security and economic prosperity of a community. Majority of the existing infrastructure risk mitigation studies or projects focus on a single infrastructure system, which may not be the most efficient and effective way to mitigate the loss and enhance the overall community disaster resilience. This research proposes a risk-informed decision framework which could support the pre-disaster risk mitigation planning of several interdependent infrastructure systems. The characteristics of the Interdependent Infrastructure Risk Mitigation (IIRM) decision problem, such as objective, decision makers, constraints, etc., are clearly identified. A four-stage decision framework to solve the IIRM problem is also presented. The application of the proposed IIRM decision framework is illustrated using a case study on pre-disaster risk mitigation planning for the interdependent critical infrastructure systems in Jamaica. The outcome of the IIRM problem is useful for the decision makers to allocate limited risk mitigation budget or resources to the most critical infrastructure facilities in different systems to achieve greater community disaster resilience. Optimizing the post-disaster recovery of damaged infrastructure systems is essential to alleviate the adverse impacts of natural disasters to communities and enhance their disaster resilience. As a result of infrastructure interdependencies, the complete functional restoration of a facility in one infrastructure system relies on not only the physical recovery of itself, but also the recovery of the facilities in other systems that it depends on. This study introduces the Interdependent Infrastructure Recovery Planning (IIRP) problem, which aims at optimizing the assignment and scheduling of the repair teams for an infrastructure system with considering the repair plan of the other infrastructure systems during the post-disaster recovery phase. Key characteristics of the IIRP problem are identified and a game theory-based IIRP decision framework is presented. Two recovery time-based performance metrics are introduced and applied to evaluate the efficiency and effectiveness of the post-disaster recovery plan. The IIRP decision framework is illustrated using the interdependent power and water systems of the Centerville virtual community subjected to seismic hazard