Table 1. The general description of simulated annealing (SA) algorithm. |

1: Set SA parameters: start temperature ( 2: Generate an initial feasible solution by assigning a random prescription to each management unit (MU). Set this solution as the current ( 3: Compute the objective function value of 4: Generate a candidate solution ( 5: Check the conformity of the new candidate solution ( 6: Evaluate the feasibility of candidate solution 7: Compute the objective function value of 8: If the objective function value of 9: Let 10: Evaluate the acceptability of the candidate solution 11: If the non-improving solution is rejected, then directly go to step 12. Otherwise, let 12. 12: If 13: If |

Table 2. The statistical results of 1000 independent objective function values (10^{6} m^{3}) of the three planning problems for each hypothetical forest dataset when using three different neighborhood search techniques of simulated annealing (SA). The largest minimum objective function value for each planning scenario is highlighted in italic, the maximum objective function value is highlighted in boldface, the maximum mean objective function value is highlighted with a shadow, and the smallest standard deviation (SD) value is highlighted with underline. Method 1 represents the standard version of SA using 1-opt moves, Method 2 represents the exchange version of SA using 2-opt moves, and Method 3 represents the change version of SA using 2-opt moves. NON represents the non-spatial planning problems, URM represents the unit restriction model, ARM represents the area restriction model. | ||||||||||||||

Forest | Model | Method 1 | Method 2 | Method 3 | ||||||||||

Min. | Max. | Mean | SD | Min. | Max. | Mean | SD | Min. | Max. | Mean | SD | |||

400 | NON | 0.558 | 0.623 | 0.572 | 0.013 | 0.561 | 0.634 | 0.574 | 0.013 | 0.560 | 0.638 | 0.575 | 0.014 | |

ARM | 0.553 | 0.622 | 0.567 | 0.013 | 0.555 | 0.630 | 0.568 | 0.012 | 0.556 | 0.637 | 0.568 | 0.013 | ||

URM | 0.457 | 0.598 | 0.486 | 0.023 | 0.460 | 0.598 | 0.488 | 0.023 | 0.463 | 0.612 | 0.489 | 0.024 | ||

1600 | NON | 2.217 | 2.602 | 2.267 | 0.083 | 2.222 | 2.616 | 2.266 | 0.074 | 2.224 | 2.635 | 2.267 | 0.072 | |

ARM | 2.127 | 2.577 | 2.201 | 0.080 | 2.136 | 2.587 | 2.197 | 0.064 | 2.137 | 2.607 | 2.202 | 0.066 | ||

URM | 1.714 | 2.420 | 1.847 | 0.084 | 1.706 | 2.441 | 1.848 | 0.081 | 1.720 | 2.448 | 1.855 | 0.083 | ||

3600 | NON | 4.887 | 5.744 | 5.041 | 0.260 | 4.894 | 5.752 | 5.005 | 0.208 | 4.892 | 5.800 | 4.980 | 0.168 | |

ARM | 4.741 | 5.683 | 4.910 | 0.218 | 4.757 | 5.673 | 4.872 | 0.139 | 4.766 | 5.727 | 4.897 | 0.180 | ||

URM | 3.859 | 4.692 | 4.288 | 0.174 | 3.814 | 4.687 | 4.280 | 0.182 | 3.866 | 5.338 | 4.285 | 0.181 | ||

6400 | NON | 8.790 | 10.237 | 9.102 | 0.508 | 8.794 | 10.482 | 9.042 | 0.488 | 8.809 | 10.499 | 9.025 | 0.457 | |

ARM | 8.258 | 10.086 | 8.778 | 0.579 | 8.306 | 10.303 | 8.603 | 0.440 | 8.331 | 10.304 | 8.617 | 0.437 | ||

URM | 6.860 | 8.183 | 7.631 | 0.298 | 6.862 | 8.172 | 7.660 | 0.299 | 6.897 | 8.154 | 7.647 | 0.283 | ||

10000 | NON | 13.675 | 15.620 | 14.319 | 0.795 | 13.695 | 16.212 | 14.141 | 0.832 | 13.719 | 16.274 | 14.178 | 0.863 | |

ARM | 12.782 | 15.475 | 13.946 | 1.010 | 12.913 | 15.983 | 13.490 | 0.856 | 12.893 | 15.885 | 13.555 | 0.870 | ||

URM | 10.705 | 12.711 | 12.007 | 0.439 | 10.873 | 12.724 | 12.028 | 0.433 | 10.887 | 12.690 | 12.050 | 0.418 |