Bi-level optimization for risk-based regional hurricane evacuation planning

Abstract

Almost all engineering evacuation models define the objective as minimizing the time required to clear the region or total travel time, thus making an implicit assumption that who will or should evacuate is known. Conservatively evacuating everyone who may be affected may be the best strategy for a given storm, but there is a growing recognition that in some places that strategy is no longer viable and in any case, may not be the best alternative by itself. Here, we introduce a new bi-level optimization that reframes the decision more broadly. The upper level develops an evacuation plan that describes, as a hurricane approaches, who should stay and who should leave and when, so as to minimize both risk and travel time. The lower level is a dynamic user equilibrium (DUE) traffic assignment model. The model includes four novel features: (1) it refocuses the decision on the objectives of minimizing both risk and travel time; (2) it allows direct comparison of more alternatives, including for the first time, sheltering-in-place; (3) it uses a hurricane-scenario-based analysis that explicitly represents the critically important uncertainty in hurricane track, intensity, and speed; and (4) it includes a new DUE algorithm that is efficient enough for full-scale hurricane evacuation applications. The model can be used both to provide an evacuation plan and to evaluate a plan's performance in terms of risk and travel time, assuming the plan is implemented and a specified hurricane scenario then actually occurs. We demonstrate the model with a full-scale case study for Eastern North Carolina.

Optimization of the issuance of evacuation orders under evolving hurricane conditions

“…They use a cell transmission model (Daganzo, 1995(Daganzo, , 1994 to represent the traffic flow. Apivatanagul et al (2011) integrates the decision of who should leave and who should shelter in place to optimize the trade-off between total risk, total travel time and total time away from home from a societal perspective. Using a bi-level two-stage stochastic programming model, they also explicitly include uncertainty in the hurricane evolution but require all of the decisions to be made prior to any resolution of the uncertainly associated with the hurricane evolution.…”

“…As stated previously, we focus on the issuance of aggregate orders (as in Bish and Sherali, 2013, Chen and Zhan, 2004, Wolshon et al, 2015and Zhang et al, 2014 and the explicit incorporation of the rich behavioral modeling developed in a number of papers so as to represent compliance and noncompliance with evacuation orders including shadow evacuation. We also integrate the concept of optimizing the issuance of orders to achieve region-wide risk reduction and to control congestion as developed in Apivatanagul et al (2011). Further, we explicitly include a probabilistic representation of the evolution of the hurricane yielding a multi-stage stochastic program (MSP).…”

“…Complexity explodes in the number of stages when this single-shot assumption is relaxed. Some examples of TSP applied to disaster management are An et al (2015), Apivatanagul et al (2011), Li et al (2011), Li et al (2012), and Prentiss (2014). Faturechi and Miller-Hooks (2014) develops a three stage stochastic programming formulation that includes mitigation, preparedness and response stages, where evacuation, corresponding to preparedness, is treated as a single stage.…”

Integrating disciplinary contributions to achieve community resilience to natural disasters

“…Similarly, while in a general sense, all hurricane and storm surge models produce assessments of the wind and storm surge flooding hazards, without collaboration from the start, they will not necessarily be supplied in the format required by an evacuation decision support model. The evacuation model in Apivatanagul, Davidson, and Nozick (2012) uses stochastic programming to represent the hurricane uncertainty, and thus requires that the hazard be represented using probabilistic hurricane scenarios, not the typical result that hazards models produce. Another example relates to the basic question of how risk is defined and measured.…”

Modeling geospatial events during flood disasters for response decision-making

“…For example, the time required to evacuate residents from wildfires along road networks including the number of lead hours required to handle the evacuation traffic, the establishment of evacuation zones (Cova andJohnson 2002, Shekhar et al 2012) and the development of temporal trigger buffers (Cova et al 2005, Dennison et al, 2007, Larsen et al, 2011 have been discussed. The travel times and level of risk have been used to construct regional public hurricane evacuations (Apivatanagul et al 2012) and network route times during hurricane evacuations have also been examined (Shekhar et al 2012), as well as models for the evacuation of people within buildings during a fire (Luh et al 2012). In each of these works, an integral part of the modeling approach is to compute the length of time required to evacuate individuals from these disasters.…”