Applying simulated annealing using different methods for the neighborhood search in forest planning problems

Adjacency constraints along with even flow harvest constraints are important in long term forest planning. Simulated annealing (SA) is previously successfully applied when addressing such constraints. The objective of this paper was to assess the performance of SA under three new methods of introducing biased probabilities in the management unit (MU) selection and compare them to the conventional method that assumes uniform probabilities. The new methods were implemented as a search vector approach based on the number of treatment schedules describing sequences of silvicultural treatments over time and standard deviation of net present value within MUs (Methods 2 and 3, respectively), and by combining the two approaches (Method 4). We constructed three hundred hypothetical forests (datasets) for three different landscapes characterized by different initial age class distributions (young, normal and old). Each dataset encompassed 1600 management units. The evaluation of the methods was done by means of objective function values, first feasible iteration and time consumption. Introducing a bias in the MU selection improves solutions compared to the conventional method (Method 1). However, an increase of computational time is in general needed for the new methods. Method 4 is the best alternative because, for large parts of the datasets, produced the best average and maximum objective function values and had lower time consumption than Methods 2 and 3. Although Method 4 performed very well, Methods 2 and 3 should not be neglected because for a considerable number of datasets the maximum objective function values were obtained by these methods.