Optimizing any-aged management of mixed-species stands. I. Performance of a coordinate-search process

Abstract

Optimal any-aged management problems for mixed-species stands have been solved for the first time. Problem formulation calls for periodic planting and harvesting controls to be applied without constraints on the stand age or size structure over time; classical definitions of both even- and uneven-aged management are, thus, subsets of this general any-aged management definition. The solution technique is a derivative-free, coordinate-search process called the method of Hooke and Jeeves. The optimizer incorporates without modification the Stand Prognosis Model, a single-tree simulator that is used extensively in the western United States. This paper focuses on sensitivity analysis and performance of the optimizer on problems with both short and long time horizons and with different definitions of the harvest controls. Superior harvest regimes are found by defining harvest controls with relatively wide diameter-class boundaries and with broad species groups. In all cases examined, there is variability in present value and harvest pattern associated with the choice of the starting point for the optimizer. The cause of these multiple optima is a nonconvex and discontinuous response surface produced by the single-tree simulator. This points out the need to examine the results from several random starts before making conclusions about optimal timber harvesting.

Optimising the management of Scots pine (Pinus sylvestris L.) stands in Spain based on individual-tree models

“…This algorithm has been commonly used for optimising the management of both even-aged stands [14,16,21,26,27,30] and uneven-aged stands [3,11,21]. The direct search method algorithm operates using two search modes: exploratory search and pattern search.…”

“…Determination of the optimum combination of many variables needs a set of models and a simulator able to predict the stand development under any set of management parameters. Seeking for the best set of management parameters can be automated by using optimisation [1,5,9,11,14,17,27,31].…”

Stand-Level Forest Management Planning Approaches

“…This technique is very popular because it is easy to use and can perform well with discreteness of growth models on the expected concavity of the response surface. The Hooke and Jeeves method is described as a Bdirect search method^, which involves a sequential examination of the changes that occur when a problem is solved and the results are compared to the Bbest^solution among the derived [25][26][27][28][29][30][31][32][33]. Generally, the Hooke-Jeeves algorithm consists of two major phases: an Bexploratory search^around the base point and a Bpattern search^in a direction selected for optimization (minimization or maximization) [16].…”

Proceedings of the 1991 Symposium on Systems Analysis in Forest Resources

“…A recent development in deterministic stand level optimization studies is the use of nonlinear programming and the stand management control variables (Roise 1986b, Bare and Qalach 1987, Haight and Monserud 1990a, Haight and Monserud 1990b, Valsta 1990, Yoshimoto, et al 1990). This nonlinear programming problem can be stated as where g(u) is the objective function generated by the stand simulator, u is the vector of control variables, xo is some initial condition for the stand simulator, and C is the set of feasible solutions.…”