In this thesis, we presented the first reported exact algorithms for the Geometric Firefighter Problem. In Chapter 4 we include our earliest algorithm whose major contributions are a barrier discarding algorithm and ip model. In that paper, we proposed, and reported on experimental results on the first set of instances for the gfp. In the article within Chapter 5, our ip model went through a complete rework. We also described significant improvements to the barrier discarding algorithm and were able to present in greater detail all the preprocessing algorithms required to build the ip model and primal algorithms.
Moreover, we adapted the algorithm to solve the Disjoint Geometric Firefighter Problem.
Finally, a new, more challenging, set of instances was proposed after we realized that we were able to solve all the instances from the previous benchmark within seconds. We reported extensive experimental results for both the gfp and the dgfp.
In the research paper in Chapter 6 we decided it would be interesting to lift restrictions from the gfp in order to better model realistic settings. Relaxing the linearity condition imposed in the gfp, we formulated the Geometric Firefighter Routing Problem and its sub-variant the 1-gfrp. We detailed a complete exact algorithm, including barrier discarding algorithms, primal heuristics and ip models for both problems. We also constructed two large sets of instances, designed to thoroughly test our algorithms, and reported on comprehensive experimental results.
Moreover, all sets of instances as well as their best known bounds have been made publicly available for future works ([28, 27]).
7.1 Future works
Although the gfrp made the gfp considerably more general, many aspects remain to be improved that can help bring the problem closer to real life situations. The most challenging aspect to be considered are dynamic deadlines. So far, we only considered deadlines that portray the worst possible scenario regarding fire expansion. In a more realistic setting, the fire could be diverted by fully constructed barriers, or even by partially constructed ones, thus possibly delaying the fire as it progresses towards another set of barriers.
Other aspects that were not considered in our solutions and would require a significant
effort to be implemented are:
• Dynamic speeds such as:
– increasing/decreasing the fire rate of spreading as a function of time;
– increasing/decreasing the barrier construction speed as a function of the path cost;
– increasing/decreasing the barrier construction speed based on the proximity to the boundary of nearest burned region.
• In the gfrp we allowed each barrier to be constructed at most once in each direction.
In order to relax this restriction, one could allow a barrier to be constructed at most k times or be allowed to be traversed after being constructed. This traversal could be done at a higher speed than the construction speed.
Many other scenarios are possible and could lead to challenging problems.
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