Spatial Forest Plan Development Using Heuristic Processes Seeded with a Relaxed Linear Programming Solution

Abstract

Linear programming is often used for the development of forest plans; however, the models designed usually lack the spatial detail and associated constraints (e.g., harvest adjacency) necessary for contemporary tactical forest planning processes. To accommodate spatial constraints, a linear problem is often transformed into a mixed-integer linear programming model because integer variables are needed to represent harvest decisions. Heuristic methods have been suggested for use in developing forest plans that have complex spatial relationships. In this study, two heuristic methods (threshold accepting and tabu search) were initiated with a relaxed linear programming solution to compare against cases in which they were initiated with random, feasible solutions (the norm). Western and southern United States forests were used as study areas, and each problem included final harvest adjacency constraints. Although seeding heuristic search processes with high-quality feasible starting points that are informed by a relaxed linear programming solution may seem to be an advantageous strategy, our research results are not overwhelmingly in favor of this. In at least one case, statistical analyses suggested that the random seed strategy produced results that were not significantly different than the high-quality seed strategy. Management and Policy Implications For those who are considering the use of heuristic methods for the development of spatial forest plans, seeding heuristic search processes with high-quality feasible starting points may seem to be an advantageous strategy. However, our research regarding two different forest case studies provided results that are not overwhelmingly in favor of this choice of strategy. Some seeding strategies provided higher quality forest plans than the typical random, feasible seeds used in research efforts. However, in one case that we studied, statistical analyses could not affirm that the random seed strategy produced significantly different results than seeding strategies that used high-quality feasible starting points derived from a relaxed linear programming solution.