An application of a reduced cost approach to spatial forest planning

Abstract

The task of forest planning is to find the best combination of treatment schedules for forest stands. With many stands and several alternatives per stand the number of possible combinations becomes very large and standard heuristics for combinatorial optimization such as simulated annealing (SA), tabu search, and genetic algorithm become slow. One way to deal with the problem of large decision space is to decompose the forest-level problem into stand-level subproblems. We developed a spatial application of the decomposing technique proposed by Hoganson and Rose. This method maximizes the reduced cost (RC) of each stand. The dual prices of forest-level constraints appear in the RC function and they tie the stand-level problems together. In our spatial application of the RC method we used a multiobjective stand-level objective function. The function included spatial objective variables, the values of which depended on adjacent stands. The dual prices of nonspatial forest-level constraints were gradually adjusted by using a variant of the subgradient method, until the set of stand-level solutions fulfilled the forest-level constraints. The method was compared with a cellular automaton and the SA heuristic in a spatial problem in two different forests. The results suggest that the spatial application of the RC method is competitive with heuristics currently used in forest planning. It was slightly superior to SA in terms of the objective function value of SA. The method is easy to use because it has few parameters. © 2009 by the Society of American Foresters.