•We explored effective simulated annealing implementations for thinning scheduling.•32 implementations were adapted for four benchmark yield models.•The implementations’ performance were evaluated ...with 625 different parameter sets.•An energy function was devised to limit the range of temperature parameters.•The best implementation for daily usage by foresters was identified.
We explored the most effective implementation of simulated annealing (SA) to optimize thinning schedules for single even-aged stands, with respect to the reliability of optimality. To enable foresters to use this implementation in a variety of situations, four yield models were set as benchmarks. We defined 32 implementations, each a different combination of variable control methods, proposal densities, cooling functions, and controlling the width of the proposal density. We tested these implementations using 625 SA parameter sets, resulting from the combination of five values each for initial and final temperature, the number of temperature levels, and proposal density width. We defined an energy function that enables us to predict potentially appropriate ranges of temperature parameters that relate to minimum acceptance rate. We ran each implementation 40 times for each yield model with each parameter set. To evaluate the reliability of SA under optimal parameters, we compared the objective values for the 40 runs using the best parameter set between implementations. To evaluate robustness under suboptimal parameter settings, we compared the variation in the mean objective values for all parameter sets between implementations. The variable control method significantly affected the reliability of SA under optimal parameters. Use of the Cauchy distribution for proposal density improved robustness under suboptimal parameter settings. The widths of proposal densities were better controlled when not taking temperature into account. The effect of cooling-function choice was relatively non-significant. We identified the implementation that appears best for both evaluations, and discussed the adjustment of its parameters.
While optimal forest harvesting regulations (regional forest regeneration schedules) have been established using the linear programming technique, its modeling restriction is still a challenge in ...practice. In this study, we developed an alternative framework for establishing an optimal forest harvesting regulation using the continuous approximation technique. The regulation problem was reformulated as a problem to find optimal smooth control of regeneration area, thereby overcoming the difficulties in finding the global optimum for the optimization models that include nonlinear or more complex models. A seven-dimensional optimization model was developed involving efficient assurance of the convergence to a stable forest state and prohibition of clearcutting in immature stands. Using this model, we established optimal forest harvesting regulations in Nagano Prefecture, Japan. Simulated annealing was utilized to explore optimal solutions. Analyses based on extreme value theory and comparison with solutions produced by grid search indicated that the best solutions may be sufficiently close to global optima. The best solutions suggested controlling timber supply to keep prices high in the early years, due to the supply-demand log price model and the use of net present value as the objective function. Because of the low profitability of the region, the solution suggested delaying the achievement of the target state as far as possible.
Damage to the understory of shelterwood systems during generational succession is an issue that has been debated for a long time. In this study, we analyzed the spatial relationship between damaged ...understory trees and harvested trees during the final cutting in a shelterwood forest stand dominated by Chamaecyparis obtusa (cypress) in central Japan. We surveyed the positions of all cypress trees and observed the final cutting operation. By measuring the felling direction, the physical contact between the harvested trees and understory trees was reproduced using the Geographic Information System (GIS). Logistic regression was performed using the extracted frequencies of physical contact as explanatory variables and variables important for reproducing the spatial pattern of the damaged understory were selected. The model selection indicated that the damage to the understory could be explained by the contact between the understory trees and the crowns and trunks of felled trees. The understory height was relatively ineffective in explaining the spatial damage pattern. The model could reproduce the spatial distribution of damage rates more realistically than conventional models which depend on the distance from stumps or roads. It was quantitatively revealed that controlling the felling direction was an important factor in mitigating understory damage.
The yield percentage by tree species was estimated and the effect on the amount of wood biomass resources available was examined. In order to estimate the yield percentage of larch, cypress, cedar, ...and red pine by species, the results of logging operations in Nagano Prefecture were used to determine the amount of timber cut and sold, and to estimate the yield of lumber produced. As a result, the yield percentage of all tree species in clear-cutting was lower than the conventional value, and in thinning, it was higher than the conventional value for all tree species except red pine. In addition, by yarding system, the value for vehicle-based yarding was higher than that for overhead wire-based yarding. Using these results, we estimated the amount of wood biomass resources available when the yield percentage was taken into account for each tree species and when the percentage was assumed to be constant as in the conventional method. The results showed that the availability of larch, cypress, and cedar increased, while that of red pine decreased, compared to the estimation by the conventional method. The results suggest that it is important to accurately estimate the yield percentage.
We evaluated the potential of simulated annealing as a reliable method for optimizing thinning rates for single even-aged stands. Four types of yield models were used as benchmark models to examine ...the algorithm’s versatility. Thinning rate, which was constrained to 0–50% every 5 years at stand ages of 10–45 years, was optimized to maximize the net present value for one fixed rotation term (50 years). The best parameters for the simulated annealing were chosen from 113 patterns, using the mean of the net present value from 39 runs to ensure the best performance. We compared the solutions with those from coarse full enumeration to evaluate the method’s reliability and with 39 runs of random search to evaluate its efficiency. In contrast to random search, the best run of simulated annealing for each of the four yield models resulted in a better solution than coarse full enumeration. However, variations in the objective function for two yield models obtained with simulated annealing were significantly larger than those of random search. In conclusion, simulated annealing with optimized parameters is more efficient for optimizing thinning rates than random search. However, it is necessary to execute multiple runs to obtain reliable solutions.
•An analytical framework is proposed to determine subsidising policy for forestry.•Subsidised forest stands are selected so that the governmental expense is minimised.•Subsidy rates for all stands ...are also minimised under the optimal rotation ages.•The framework helps in determining policy with simple optimisations.•It provides efficient subsidised stand selection reflecting practical constraints.
There are regions where forestry is required for wood production but the profitability is so low that many forest stands cannot be managed without subsidisation. Hence, the policymakers should design an efficient subsidising system involving the selection of subsidised forest stands. In this paper, we present an analytical framework for the proposition through the construction of a normal forest (a forest state such that the age distribution of stands is uniform) that consists of only stands that need to be subsidised for regeneration. The normal forest is constructed so that it supplies the required annual wood yield with minimum governmental expense for the subsidy. The rotation age of the normal forest is set to an optimal rotation age based on the soil expectation value of the stands under the minimum subsidy rates. The normal forest can be derived without numerical integration when the dominant tree height distribution follows a generalised gamma distribution. We present an application of the framework for four tree species in the Nagano Prefecture, Japan. The result of the application shows that the framework enables us to select the subsidised stands for efficient governmental funding, implying the practical conditions of the stands and requirements of wood demands, by using optimisation functions in a commercial spreadsheet program.
We investigated whether collisions of harvested trees with understory might explain the presence of damaged understory spanning an entire forest compartment. Specifying understory damage caused by ...harvesting operations is necessary to compare the economic advantages of any residual understory against the high expenses of shelterwood harvesting. Existing models for explaining understory damage were unclear and unable to quantify the amount of residual understory. Therefore, we used collisions between felled trees and the understory as explanatory variables and discovered that the collisions may be spatial indicators; however, we have not yet evaluated whether these indicators are applicable across large areas. In this paper, we looked at another final cutting and used the collisions to estimate the damage to the understory again. Results showed that the coordinates of collisions may spatially describe the state of the understory after final cutting, even at an entire forest compartment. This practice suggests that we can intentionally mitigate damage to the understory by avoiding physical impacts to the understory during final cutting. We expect to compare the silvicultural benefits of residual understory and harvesting costs spatially.
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