A new mixed-integer programming model for spatial forest planning

The unit restriction model and the area restriction model are the two main approaches to dealing with adjacency in forest harvest planning. In this paper, we present a new mixed-integer programming (MIP) formulation that can be classified as both a unit restriction approach and an area restriction approach. We need to generate a feasible cluster to formulate the model. However, unlike other approaches, there is no need to generate specific model constraints representing computationally burdensome clusters for large cases. We describe and analyze our approach by comparing it with the most efficient approaches presented in the literature. Comparisons are made from modeling and computational points of view. Results showed that the proposed model was competitive with regard to modeling complexity and size of formulation. Furthermore, it is easy to implement in standard modeling software.

Selection and Penalty Strategies for Genetic Algorithms Designed to Solve Spatial Forest Planning Problems

Genetic algorithms (GAs) have demonstrated success in solving spatial forest planning problems. We present an adaptive GA that incorporates population-level statistics to dynamically update penalty functions, a process analogous to strategic oscillation from the tabu search literature. We also explore performance of various selection strategies. The GA identified feasible solutions within 96%, 98%, and 93% of a nonspatial relaxed upper bound calculated for landscapes of 100, 500, and 1000 units, respectively. The problem solved includes forest structure constraints limiting harvest opening sizes and requiring minimally sized patches of mature forest. Results suggest that the dynamic penalty strategy is superior to the more standard static penalty implementation. Results also suggest that tournament selection can be superior to the more standard implementation of proportional selection for smaller problems, but becomes susceptible to premature convergence as problem size increases. It is therefore important to balance selection pressure with appropriate disruption. We conclude that integrating intelligent search strategies into the context of genetic algorithms can yield improvements and should be investigated for future use in spatial planning with ecological goals.

The use of cellular automaton approach in forest planning

This study presents an optimization method based on cellular automaton (CA) for solving spatial forest planning problems. The CA maximizes stand-level and neighbourhood objectives locally, i.e., separately for different stands or raster cells. Global objectives are dealt with by adding a global part to the objective function and gradually increasing its weight until the global targets are met to a required degree. The method was tested in an area that consisted of 2500 (50 × 50) hexagons 1 ha in size. The CA was used with both parallel and sequential state-updating rules. The method was compared with linear programming (LP) in four nonspatial forest planning problems where net present value (NPV) was maximized subject to harvest constraints. The CA solutions were within 99.6% of the LP solutions in three problems and 97.9% in the fourth problem. The CA was compared with simulated annealing (SA) in three spatial problems where a multiobjective utility function was maximized subject to periodical harvest and ending volume constraints. The nonspatial goal was the NPV and the spatial goals were old forest and cutting area aggregation as well as dispersion of regeneration cuttings. The CA produced higher objective function values than SA in all problems. Especially, the spatial objective variables were better in the CA solutions, whereas differences in NPV were small. There were no major differences in the performance of the parallel and sequential cell state-updating modes of the CA.