Optimal Control of Emergency Evacuations Leveraging Equivalent Circuit Models

Abstract Emergency evacuation planning is a critical task that ensures individuals’ swift and safe movement from hazardous locations to designated safe zones. This article proposes a novel controllable equivalent circuit model (cECM) to capture the flow of traffic in a network. The model includes switches for flow routing and additional circuit elements to represent the time lost due to recharging, which is critical for (electric) vehicles with the limited driving range. We embed this cECM into a mixed-integer linear program (MILP) that determines optimal evacuation routes and recharging strategies to minimize evacuation time while considering road capacity, limited vehicle energy, and the availability of charging stations. The effectiveness of the proposed approach is demonstrated through simulations based on an evacuation case study using the Sioux Falls and Anaheim networks.