Simulation-Assisted Optimization for Large-Scale Evacuation Planning with Congestion-Dependent Delays

TL;DR

The paper tackles joint routing and scheduling for large-scale evacuations under congestion-dependent delays. It introduces MIP-LNS, a scalable Large Neighborhood Search hybrid with a time-expanded graph, to optimize objectives such as the average evacuation time $\min \frac{1}{|W|}\sum_{i\in W} t_i$ and evacuation completion time, and extends it with MIP-LNS-SIM to account for congestion via agent-based simulation using edge travel-time parameters learned by QueST. Empirical results on Harris County show MIP-LNS outperforms baselines across key metrics, while MIP-LNS-SIM yields further improvements when delays are modeled and substantially reduces estimation error from simulation. The work demonstrates a practical, simulation-assisted optimization framework for realistic, large-scale evacuation planning with tangible applications in disaster management and vulnerability assessment.

Abstract

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 MIP-LNS-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.

Figures (9)

• Figure 1: Sample Problem Instance
• Figure 2: Harris County Problem Instance
• Figure 3: Comparison of MIP-LNS, MIP-LNS-SIM-$5\%$, and MIP-LNS-SIM-$10\%$ in terms of departure rate from sources and arrival rate at safe nodes. Even though MIP-LNS-SIM-$5\%$, and MIP-LNS-SIM-$10\%$ regulates the departure of evacuees, they evacuate everyone faster than MIP-LNS.
• Figure 4: Congestion on the roads in terms of traffic density and time spent on the road by evacuees.
• Figure 5: Sample Problem Instance

Theorems & Definitions (10)

• Definition 3.1
• Definition 3.2
• Definition 3.3
• Definition 3.4
• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• proof : Proof of Theorem \ref{['hardconst']}
• proof : Proof of Theorem \ref{['thm:gridhard']}