Tabu Search Experience in Forest Management and Planning

Abstract

Tabu search was initially developed by Glover (1989, 1990), and has been applied to a number of forest management and planning problems (Murray & Church 1995; Bettinger et al. 1997, 1998, 2002; Boston & Bettinger 1999; Brumelle et al. 1998). In general, when using tabu search to address forest management and planning problems, a number of forest plans are deterministically developed and assessed, each subsequent plan being slightly different than its predecessor, and thus each is considered an iteration of the modeling process. A large number of iterations are usually required to ensure that the search process has explored the solution space sufficiently. In most cases in forest planning, tabu search is used as a 1-opt search process, where a feasible forest plan is modified by changing the status (harvest timing, prescription, etc.) of a single forest management unit, thus creating a new plan. However, as we will see, other intensification and diversification processes have been used to expand the capabilities of the search process. A tabu search process begins with an initial, randomly defined, feasible solution (forest plan) (Figure 1). A simple Monte Carlo (i.e., random) process is generally used to select timber stands and management prescriptions, and constraints are assessed with programming logic to ensure that each choice results in a feasible solution. Feasibility is not difficult to obtain in the initial solution, as most choices are made by avoiding the violation of constraints. However, the initial solution is generally of low quality. This process is consistent with much of the work related to the use of heuristics in forestry (e.g., Bettinger et al. 1998). With each iteration (k) of the tabu search algorithm, a new feasible solution (x k) is created from a transformation of the previous feasible solution (x k-1) by a move (δ). A δ is a transition from one feasible solution to another feasible solution. The δ may represent the change that results in the best possible improvement in solution x k-1, or that results in the least deterioration in the value of x k-1 (Voβ 1993). With this search technique, a δ can consist of assigning a different prescription to a timber stand (1-opt δ) or swapping the prescriptions assigned to two different timber stands (2-opt δ). A candidate δ cannot consist of the assignment of more than one prescription to a timber stand. Each feasible δ requires that it does not result in a violation of the constraints. In all cases, a tabu tenure is assigned to each δ and aspiration criteria are employed. Most forest planning applications of tabu search involve the scheduling of harvests to timber stands. However, the allocation of timber stands and cutting patterns to logging systems has been