Use of graph theory and a genetic algorithm for finding optimal fuel treatment locations.

Fuel treatments are intended to modify the effects and behavior of wildland fires. In low-elevation forests of the western US (e.g. ponderosa pine), combinations of prescribed burning and thinning are typically applied in discrete units of 100’s to 1000’s of hectares. Since wildland fires are generally large compared to the practical sizes and numbers of such fuel treatment units, the pattern and location of treatment units across a landscape has important bearing on their effectiveness and efficiency in changing fire growth and behavior. For example, the fuel-age mosaic created by natural fires is essentially random but the large numbers and sizes of these burns has a strong influence on the patterns and behaviors of subsequent wildland fires. By contrast, fuel treatment units that are small and isolated from other units have little net effect on the growth and behavior of large wildland fires which merely circumvent the units. In fuel treatment planning, theoretical patterns of treatment units can be designed to efficiently disrupt fire growth for simple conditions (Finney 2001). Such patterns are optimal in terms of efficiency and effectiveness in reducing overall fire growth rates compared to random fuel patterns. However, there are no analytical solutions to the optimization of fuel treatment locations on real landscapes that are complex in terms of fuels, topography, and weather. To attempt optimization on complex landscapes for the purposes of disrupting large fire growth, the search for optimal fuel treatment locations is approached using graph theory to compute fire growth and a genetic algorithm to improve the spatial fuel treatment patterns. The solutions accommodate constraints on total treatment area (or treatment fraction) and treatment location and suggest locations, sizes, and orientations of fuel treatments that are efficient and effective at changing large fire growth.