A Scalable Game-theoretic Approach to Urban Evacuation Routing and Scheduling

Evacuation planning is an essential part of disaster management where the goal is to relocate people under imminent danger to safety. However, finding jointly optimal evacuation routes and a schedule that minimizes the average evacuation time or evacuation completion time, is a computationally hard problem. As a result, large-scale evacuation routing and scheduling continues to be a challenge. In this paper, we present a game-theoretic approach to tackle this problem. We start by formulating a strategic routing and scheduling game, named the Evacuation Game: Routing and Scheduling (EGRES), where players choose their route and time of departure. We show that: (i) every instance of EGRES has at least one pure strategy Nash equilibrium, and (ii) an optimal outcome in an instance will always be an equilibrium in that instance. We then provide bounds on how bad an equilibrium can be compared to an optimal outcome. Additionally, we present a polynomial-time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance under a special condition. We use Virginia Beach City in Virginia, and Harris County in Houston, Texas as study areas and construct two EGRES instances. Our results show that, by utilizing SAA, we can efficiently find equilibria in these instances that have social objective close to the optimal value.