# Evolutionary learning of fire fighting strategies

## TL;DR

This paper explores using evolutionary algorithms to learn fire fighting strategies in a grid model, aiming to approximate critical thresholds for success and gain insights into evolutionary methods for geometric threshold problems.

## Contribution

It demonstrates the potential of evolutionary strategies to approach critical thresholds in fire fighting problems and uncovers strategic paradigms in highway protection scenarios.

## Key findings

- Evolutionary algorithms can approximate critical thresholds for fire containment.
- Identified strategic paradigms for highway protection.
- Insights into the effectiveness of evolutionary strategies in geometric threshold problems.

## Abstract

The dynamic problem of enclosing an expanding fire can be modelled by a discrete variant in a grid graph. While the fire expands to all neighbouring cells in any time step, the fire fighter is allowed to block $c$ cells in the average outside the fire in the same time interval. It was shown that the success of the fire fighter is guaranteed for $c>1.5$ but no strategy can enclose the fire for $c\leq 1.5$. For achieving such a critical threshold the correctness (sometimes even optimality) of strategies and lower bounds have been shown by integer programming or by direct but often very sophisticated arguments. We investigate the problem whether it is possible to find or to approach such a threshold and/or optimal strategies by means of evolutionary algorithms, i.e., we just try to learn successful strategies for different constants $c$ and have a look at the outcome. The main general idea is that this approach might give some insight in the power of evolutionary strategies for similar geometrically motivated threshold questions. We investigate the variant of protecting a highway with still unknown threshold and found interesting strategic paradigms. Keywords: Dynamic environments, fire fighting, evolutionary strategies, threshold approximation