Wildfire Suppression: Complexity, Models, and Instances

TL;DR

This paper analyzes wildfire suppression strategies using graph models, proving NP-completeness, proposing a new MIP formulation, and introducing realistic benchmarks for evaluating algorithms.

Contribution

It provides theoretical complexity results, a competitive optimization approach, and realistic test instances for wildfire suppression modeling.

Findings

NP-completeness of suppression resource allocation problems

MIP formulation achieves state-of-the-art results

New realistic benchmark instances reveal algorithm strengths and weaknesses

Abstract

Wildfires cause major losses worldwide, and the frequency of fire-weather conditions is likely to increase in many regions. We study the allocation of suppression resources over time on a graph-based representation of a landscape to slow down fire propagation. Our contributions are theoretical and methodological. First, we prove that this problem and related variants in the literature are NP-complete, including cases without resource-timing constraints. Second, we propose a new mixed-integer programming (MIP) formulation that obtains state-of-the-art results, showing that MIP is a competitive approach contrary to earlier findings. Third, showing that existing benchmarks lack realism and difficulty, we introduce a physics-grounded instance generator based on Rothermel's surface fire spread model. We use these diverse instances to benchmark the literature, identifying the specific conditions where each algorithm succeeds or fails.