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Evacuation planning is a crucial part of disaster management. However, joint optimization of its two essential components, routing and scheduling, with objectives such as minimizing average evacuation time or evacuation completion time, is a computationally hard problem. To approach it, we present MIP-LNS, a scalable optimization method that utilizes heuristic search with mathematical optimization and can optimize a variety of objective functions. We also present the method MIPLNS-SIM, where we combine agent-based simulation with MIP-LNS to estimate delays due to congestion, as well as, find optimized plans considering such delays. We use Harris County in Houston, Texas, as our study area. We show that, within a given time limit, MIP-LNS finds better solutions than existing methods in terms of three different metrics. However, when congestion dependent delay is considered, MIP-LNS-SIM outperforms MIP-LNS in multiple performance metrics. In addition, MIP-LNS-SIM has a significantly lower percent error in estimated evacuation completion time compared to MIP-LNS. 

ABSTRACT Evacuation plans are designed to move people to safety in case of a disaster. It mainly consists of two components: routing and scheduling. Joint optimization of these two components with the goal of minimizing total evacuation time is a computationally hard problem, specifically when the problem instance is large. Moreover, often in disaster situations, there is uncertainty regarding the passability of roads throughout the evacuation time period. In this paper, we present a way to model the time-varying risk associated with roads in disaster situations. We also design a heuristic method based on the well known Large Neighborhood Search framework to perform the joint optimization task. We use real-world road network and population data from Harris County in Houston, Texas and apply our heuristic to find evacuation routes and schedules for the area. We show that the proposed method is able to find good solutions within a reasonable amount of time. We also perform agent-based simulations of the evacuation using these solutions to evaluate their quality and efficacy. 

Graph cut problems are fundamental in combinatorial optimization, and are a central object of study in both theory and practice. Further, the study of fairness in Algorithmic Design and Machine Learning has recently received significant attention, with many different notions proposed and analyzed for a variety of contexts. In this paper we initiate the study of fairness for graph cut problems by giving the first fair definitions for them, and subsequently we demonstrate appropriate algorithmic techniques that yield a rigorous theoretical analysis. Specifically, we incorporate two different notions of fairness, namely demographic and probabilistic individual fairness, in a particular cut problem that models disaster containment scenarios. Our results include a variety of approximation algorithms with provable theoretical guarantees. 

In response to COVID-19, many countries have mandated social distancing and banned large group gatherings in order to slow down the spread of SARS-CoV-2. These social interventions along with vaccines remain the best way forward to reduce the spread of SARS CoV-2. In order to increase vaccine accessibility, states such as Virginia have deployed mobile vaccination centers to distribute vaccines across the state. When choosing where to place these sites, there are two important factors to take into account: accessibility and equity. We formulate a combinatorial problem that captures these factors and then develop efficient algorithms with theoretical guarantees on both of these aspects. Furthermore, we study the inherent hardness of the problem, and demonstrate strong impossibility results. Finally, we run computational experiments on real-world data to show the efficacy of our methods. 

The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinInfEdge problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most B edges; similarly the MinInfNode problem involves removing at most B vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of these problems remains generally open. In this paper, we present two bicriteria approximation algorithms for MinInfEdge, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result of Karger, and works when the transmission probabilities are not too small. The second is a Sample Average Approximation--based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results to tackle the MinInfNode problem.