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

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.