Articles containing the keyword 'combinatorial optimization'

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.

• Dong, College of Forestry, Northeast Forestry University, Harbin 150040, China E-mail: farrell0503@126.com
• Bettinger, Warnell School of Forestry and Natural Resources, University of Georgia, Athens 30602, GA, USA E-mail: pbettinger@warnell.uga.edu
• Qin, College of Economic and Management, Northeast Forestry University, Harbin 150040, China E-mail: huiyanqin@hotmail.com
• Liu, College of Forestry, Northeast Forestry University, Harbin 150040, China E-mail: lzg19700602@163.com

Heuristic techniques have been increasingly used to address the complex forest planning problems over the last few decades. However, heuristics only can provide acceptable solutions to difficult problems, rather than guarantee that the optimal solution will be located. The strategies of neighborhood, hybrid and reversion search processes have been proved to be effective in improving the quality of heuristic results, as suggested recently in the literature. The overall aims of this paper were therefore to systematically evaluate the performances of these enhanced techniques when implemented with a simulated annealing algorithm. Five enhanced techniques were developed using different strategies for generating candidate solutions. These were then compared to the conventional search strategy that employed 1-opt moves (Strategy 1) alone. The five search strategies are classified into three categories: i) neighborhood search techniques that only used the change version of 2-opt moves (Strategy 2); ii) self-hybrid search techniques that oscillate between 1-opt moves and the change version of 2-opt moves (Strategy 3), or the exchange version of 2-opt moves (Strategy 4); iii) reversion search techniques that utilize 1-opt moves and the change version of 2-opt moves (Strategy 5) or the exchange version of 2-opt moves (Strategy 6). We found that the performances of all the enhanced search techniques of simulated annealing were systematic and often clear better than conventional search strategy, however the required computational time was significantly increased. For a minimization planning problem, Strategy 6 produced the lowest mean objective function values, which were less than 1% of the means developed using conventional search strategy. Although Strategy 6 performed very well, the other search strategies should not be neglected because they also have the potential to produce high-quality solutions.

• Dong, Department of Forest Management, College of Forestry, Northeast Forestry University, Harbin 150040, China E-mail: farrell0503@126.com
• Bettinger, Warnell School of Forestry and Natural Resources, University of Georgia, Athens 30602, GA, USA E-mail: pbettinger@warnell.uga.edu
• Liu, Department of Forest Management, College of Forestry, Northeast Forestry University, Harbin 150040, China E-mail: lzg19700602@163.com
• Qin, Department of Forestry Economic, College of Economic & Management, Northeast Forestry University, Harbin 150040, China E-mail: huiyanqin@hotmail.com
• Zhao, Department of Forest Management, College of Forestry, Northeast Forestry University, Harbin 150040, China E-mail: zyinghui0925@126.com