Logic-based benders decomposition for wildfire suppression

Abstract

In this paper we consider a network interdiction problem where the follower is characterised by a spreading phenomenon. As a case study we consider in detail a wildfire suppression problem. The landscape is modelled as a directed graph, with nodes representing regions of the landscape, and arcs representing adjacency relationships. The fire spread is modelled using the minimum travel time principle. The goal is to locate fire suppression resources in a landscape in order to minimise the total area burned. As previous exact algorithms in this space are intractable on reasonable instances, the literature focuses on heuristics. In this paper we propose a new exact algorithm utilising logic-based Benders decomposition. We benchmark the new approach against mixed-integer programming and metaheuristic approaches. Our approach is able to quickly solve instances from the literature. We are also able to solve larger instances to optimality in a reasonable amount of time.