A New Solution Representation for the Firefighter Problem

The firefighter problem (FFP) is used as a model to simulate how a fire breaks out and spreads to its surroundings over a discrete time period. The goal is to deploy a given number of firefighters on strategic points at each time step to contain the fire in a most efficient way, so that as many areas are saved from the fire as possible. In this paper we introduce a new solution representation for the FFP which can be applied in metaheuristic approaches. Compared to the existing approach in the literature, it is more compact in a sense that the solution space is smaller although the complexity for evaluating a solution remains unchanged. We use this representation in conjunction with a variable neighborhood search (VNS) approach to tackle the FFP. To speed up the optimization process, we propose an incremental evaluation technique that omits unnecessary re-calculations. Computational tests were performed on a benchmark instance set containing 120 random graphs of different size and density. Results indicate that our VNS approach is highly competitive with existing state-of-the-art approaches.