A robust optimisation approach for the placement of forest fire suppression resources

Abstract

This research develops an initial attack plan for combating forest fires in any wildland areas susceptible to fire outbreaks. To be eligible for such a plan, the landscape must have been previously mapped and modelled concerning spatial and topographic data and fuel levels. Thus, when ignition occurs, one can predict the expected fire behaviour in terms of spread direction and rate of spread. With such information, decisions can be taken on where and when to position the suppression resources. This paper extends a recent contribution to this subject, generalising each node's resource requirement, allowing a more precise modelling of non-homogeneous landscapes. Moreover, we treat the cases where the estimated number of resources may not be sufficient to deal with the fire intensity, which becomes revealed only at the fire scene. In such cases, additional resources may be needed to contain the fire effectively. This worst-case approach is modelled with the support of the robust optimisation paradigm. We propose a deterministic mathematical programming model, a robust optimisation counterpart, and a robust tabu search (RoTS) algorithm. We adapt instances from the literature, which are optimally solved by a commercial solver and used for assessing the quality of the RoTS. The proposed algorithm could optimally solve 94 of 96 instances. Finally, we conducted a Monte Carlo simulation as part of a risk analysis assessment of the generated solutions.