Use of depth-first search and direct search methods to optimize even-aged stand management: a case study involving maritime pine in Asturias (northwest Spain)

Abstract

Maritime pine (Pinus pinaster Ait.) is one of the most important timber species in Asturias and more generally in northwest Spain. A dynamic growth model has recently been developed for this species and region, allowing computation of the merchantable volume by two alternative methods: a disaggregation system and a stand volume ratio function. The model enables optimization of the management schedule for the species by modifying the rotation age and the number, intensity, and timing of thinning operations. The two methods of volume estimation were compared in optimization by using the depth-first search (DFS) method, and both were found to provide similar results. Because the stand volume ratio function is computationally much more efficient, it was used in the next step, in which five direct search methods were tested: Hooke and Jeeves method (HJ); differential evolution (DE); particle swarm optimization (PS); evolution strategy (ES); Nelder and Mead method (NM); the last four are population-based methods. The HJ and DE methods yielded the highest values of the objective function, slightly outperforming the results of DFS in most cases, which proved to be about 100 times slower than HJ and 30 times slower than DE. DE was more stable than HJ (standard deviation was €30.6·ha−1 for HJ and €8.8·ha−1 for DE) and was therefore used for subsequent evaluation of the effects of site quality, stem density, and discount rate on the optimal management schedule. Rotation age and timing of thinnings both decreased as site quality and discount rate increased. The optimal management schedules often included three heavy thinning operations. The pseudo-code of the optimization methods tested is provided in an Appendix.