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)

Arias-Rodil, Manuel; Pukkala, Timo; González-González, José Mario; Barrio-Anta, Marcos; Diéguez-Aranda, Ulises

doi:10.1139/cjfr-2015-0044

Cited by 22 publications

(13 citation statements)

References 43 publications

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“…For stand-level optimization, there are various different algorithms to choose from [35,36], e.g., the derivative-free direct search method such as the Hooke and Jeeves method, differential evolution, particle swarm optimization [37], hybrid optimization strategies which combine separate algorithms (e.g., [16]) or depth-first search algorithms which apply a search tree consisting of a backtracking mechanism [37]. In this study, we applied a new algorithm which has recently been introduced to forest applications: sequential quadratic programming (SQP) [38].…”

Section: Discussionmentioning

confidence: 99%

Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (Pinus Sylvestris L.) Stand in Finland

Pyy

Ahtikoski

Laitinen

et al. 2017

Forests

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Abstract:In general, matrix models are commonly applied to predict tree growth for size-structured tree populations, whereas empirical-statistical models are designed to predict tree growth based on a vast amount of field observations. From the theoretical point of view, matrix models can be considered to be more generic since their dependency on ad hoc growth conditions is far less prevalent than that of empirical-statistical models. On the other hand, the main pitfall of matrix models is their inability to include variation among the individuals within a size class, occasionally resulting in less accurate predictions of tree growth compared to empirical-statistical models. Thus, the relevant question is whether a matrix model can capture essential tree-growth dynamics/characteristics so that the model produces accurate stand projections which can further be applied in practical decision-making. Such a dynamic characteristic in our model is the basal area of trees, which causes nonlinearity in time. Therefore, our matrix model is a nonlinear model. The empirical data for models was based on 20 sample plots representing 8360 tree records. Further, according to the model, stand projections were produced for three Scots pine (Pinus sylvestris L.) sapling stands (age of 25 years, stand density fluctuating from 850 to 1400 stems ha −1 ). Then, (even-aged) stand management was optimized by applying sequential quadratic programming (SQP) among those growth predictions. The objective function of the optimization task was to maximize the net present value (NPV) of the ongoing rotation. The stands were located in Northern Ostrobothnia, Finland, on nutrient-poor soil type. The results indicated that initial stand density had an effect on optimal solutions-optimal stand management varied with respect to thinnings (timing and intensity) as well as to optimal rotation. Further, an increasing discount rate shortened considerably the optimal rotation period, and relaxing the minimum thinning removal to 30 m 3 ha −1 resulted in an increase both in number of thinnings and in the maximum net present value.

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Section: Discussionmentioning

confidence: 99%

Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (Pinus Sylvestris L.) Stand in Finland

Pyy

Ahtikoski

Laitinen

et al. 2017

Forests

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“…Although the election of a proper method for stand-level optimization is problem-dependent (Pukkala 2009;AriasRodil et al 2015), the Hooke and Jeeves' method has always shown competitive performance when compared with other stand-level optimization methods, e.g., population-based methods and ''depth-search first'' method (Pukkala 2009;García-Gonzalo et al 2014;Arias-Rodil et al 2015). In our case, where a stochastic model was in the optimal schedules for Stands 1 and 2 with different cone prices (0, 0.1, 0.3 and 0.5 € ha -1 ) when discount rate is 3 % Eur J Forest Res used, results from Fig.…”

Section: Discussionmentioning

confidence: 99%

Optimal management of Pinus pinea stands when cone and timber production are considered

Pasalodos-Tato¹,

Pukkala

Calama³

et al. 2016

Eur J Forest Res

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Pinus pinea is one of the most important tree species in the Mediterranean region due to the economic value of its edible seeds called ''piñones''. Timber also represents an important source of income from this species. Generally, P. pinea stands have been managed to maximize either timber or seed production, optimization of the joint production of both products being rare. The difficulty in optimizing seed or joint production is the highly stochastic masting habit of P. pinea. The aim of the present study was to find the optimal management of P. pinea stands from the economic point of view when both seed and timber production are considered. A growth and yield model was employed to simulate the dynamics of P. pinea stands of the northern Iberian Peninsula. The novelty of the study is the implementation of a cone yield model that is able to predict expected cone harvests and seed yields when masting is stochastic. The model was linked with an optimization algorithm to obtain optimal schedules for two different stands. The results showed that seed production of P. pinea in the northern plateau of the Iberian Peninsula may increase the soil expectation value by more than 300 % in dense stands and 200 % in sparse stands. When seed yields were considered, rotation lengths were longer and thinnings were delayed. The results were highly sensitive to cone prices and discount rates.

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“…Due to the huge number of alternatives, optimization was used to find the best possible values for the parameters of the CA. The method used was particle swarm optimization (Pukkala 2009;Arias-Rodil et al 2015), which has been found to work well when the number of simultaneously optimized variables is high (Jin et al 2018). A description of the particle swarm optimization algorithm used in this study is presented in Appendix 1 in ESM.…”

Section: Optimizationmentioning

confidence: 99%

Optimized cellular automaton for stand delineation

Pukkala

2018

J. For. Res.

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Forest inventories based on remote sensing often interpret stand characteristics for small raster cells instead of traditional stand compartments. This is the case for instance in the Lidar-based and multi-source forest inventories of Finland where the interpretation units are 16 m 9 16 m grid cells. Using these cells as simulation units in forest planning would lead to very large planning problems. This difficulty could be alleviated by aggregating the grid cells into larger homogeneous segments before planning calculations. This study developed a cellular automaton (CA) for aggregating grid cells into larger calculation units, which in this study were called stands. The criteria used in stand delineation were the shape and size of the stands, and homogeneity of stand attributes within the stand. The stand attributes were: main site type (upland or peatland forest), site fertility, mean tree diameter, mean tree height and stand basal area. In the CA, each cell was joined to one of its adjacent stands for several iterations, until the cells formed a compact layout of homogeneous stands. The CA had several parameters. Due to high number possible parameter combinations, particle swarm optimization was used to find the optimal set of parameter values. Parameter optimization aimed at minimizing within-stand variation and maximizing between-stand variation in stand attributes. When the CA was optimized without any restrictions for its parameters, the resulting stand delineation consisted of small and irregular stands. A clean layout of larger and compact stands was obtained when the CA parameters were optimized with constrained parameter values and so that the layout was penalized as a function of the number of small stands (\ 0.1 ha). However, there was within-stand variation in fertility class due to small-scale variation in the data. The stands delineated by the CA explained 66-87% of variation in stand basal area, mean tree height and mean diameter, and 41-92% of variation in the fertility class of the site. It was concluded that the CA developed in this study is a flexible new tool, which could be immediately used in forest planning.

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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)

Cited by 22 publications

References 43 publications

Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (Pinus Sylvestris L.) Stand in Finland

Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (Pinus Sylvestris L.) Stand in Finland

Optimal management of Pinus pinea stands when cone and timber production are considered

Optimized cellular automaton for stand delineation

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