Tatsuhito Ueki

Identification of effective implementations of simulated annealing for optimizing thinning schedules for single forest stands

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.

An Evaluation of the Use of Simulated Annealing to Optimize Thinning Rates for Single Even-Aged Stands

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.