A Comparison of the Pattern Search Algorithm and the Modified PATH Algorithm for Optimizing an Individual Tree Model

Abstract

A new stand-level dynamic programming algorithm was developed for determining the optimal residual diameter distribution for multiple stand entries. The proposed algorithm consists of the PATH algorithm and the concept of region-limiting strategies and iterated dynamic programming. Employing the proposed algorithm, a dynamic programming model was constructed with the Stand Prognosis Model, a single-tree/distance-independent growth model for forest types in the northern Rocky Mountains. Convergence, accuracy, and efficiency of the algorithm are discussed in comparison with a nonlinear programming algorithm, the Hooke and Jeeves method. For problems with three or more thinnings, the proposed algorithm yielded superior solutions with less computation time than did the Hooke and Jeeves method. For one and two thinning problems, the Hooke and Jeeves method provided better solutions. The advantage of the proposed algorithm stems from the ability of dynamic programming approaches to avoid including multiple partial local optima in the solution, and a clearer relationship to established principles of concave optimization. For. Sci. 36(2):394-412.