Current issue: 55(2)
Under compilation: 55(3)
To assess the quality of results obtained from heuristics through statistical procedures, a number of independently generated solutions to the same problem are required, however the knowledge of how many solutions are necessary for this purpose using a specific heuristic is still not clear. Therefore, the overall aims of this paper are to quantitatively evaluate the effects of the number of independent solutions generated on the forest planning objectives and on the performance of different neighborhood search techniques of simulated annealing (SA) in three increasing difficult forest spatial harvest scheduling problems, namely non-spatial model, area restriction model (ARM) and unit restriction model (URM). The tested neighborhood search techniques included the standard version of SA using the conventional 1-opt moves, SA using the combined strategy that oscillates between the conventional 1-opt moves and the exchange version of 2-opt moves, and SA using the change version of 2-opt moves. The obtained results indicated that the number of independent solutions generated had clear effects on the conclusions of the performances of different neighborhood search techniques of SA, which indicated that no one particular neighborhood search technique of SA was universally acceptable. The optimal number of independent solutions generated for all alternative neighborhood search techniques of SA for ARM problems could be estimated using a negative logarithmic function based on the problem size, however the relationships were not sensitive (i.e., 0.13 < p < 0.78) to the problem size for non-spatial and URM harvest scheduling problems, which should be somewhat above 250 independent runs. The types of adjacency constraints did moderately affect the number of independent solutions necessary, but not significantly. Therefore, determining an optimal number of independent solutions generated is a necessary process prior to employing heuristics in forest management planning practices.
Finding an optimal solution of forest management scheduling problems with even flow constraints while addressing spatial concerns is not an easy task. Solving these combinatorial problems exactly with mixed-integer programming (MIP) methods may be infeasible or else involve excessive computational costs. This has prompted the use of heuristics. In this paper we analyze the performance of different implementations of the Simulated Annealing (SA) heuristic algorithm for solving three typical harvest scheduling problems. Typically SA consists of searching a better solution by changing one decision choice in each iteration. In forest planning this means that one treatment schedule in a single stand is changed in each iteration (i.e. one-opt move). We present a comparison of the performance of the typical implementation of SA with the new implementation where up to three decision choices are changed simultaneously in each iteration (i.e. treatment schedules are changed in more than one stand). This may allow avoiding local optimal. In addition, the impact of SA - parameters (i.e. cooling schedule and initial temperature) are tested. We compare our heuristic results with a MIP formulation. The study case is tested in a real forest with 1000 stands and a total of 213116 decision choices. The study shows that when the combinatorial problem is very large, changing simultaneously the treatment schedule in more than one stand does not improve the performance of SA. Contrarily, if we reduce the size of the problem (i.e. reduce considerably the number of alternatives per stand) the two-opt moves approach performs better.