Examining the potential of particle swarm optimization for spatial forest planning and developing a solution quality index for heuristic techniques
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Both mathematical and heuristic methods have advanced rapidly in spatial forest planning over the past 20 years. In this research, we conduct a world-wide literature review and extensive analysis of the status and trends over the past two decades in spatial forest planning. The literature review results suggest that methods used in forest planning have shifted somewhat from exact analytical solution techniques to heuristic techniques. Limitations in mixed integer programming, heuristic parameter selection processes, modification and enhancements to heuristics, and measurements of heuristic solution quality are some of the gaps we have identified. Particle swarm optimization is a promising new population-based heuristic that might be useful for spatial forest planning. In my implementation of PSO to a southern U.S. forest planning problem, the algorithm gradually converged upon a final solution with some appropriate modifications, and a reasonable objective function value was reached. However, only 86% of the global optimal value could be reached, suggesting that PSO, acting alone, is not too useful for realistic forest planning problems. With regard to heuristics, most researchers and practitioners use various traditional statistics to assess the solution quality. In this research, we try to assess methods whereby one can develop a relationship to assess the quality of a new heuristic (when applied to a similar planning problem) without having to locate the exact, global optimum solution to the problem. A minor goal is to propose a method one can pursue to estimate heuristic performance in the absence of an exact solution to a problem. Three different statistical methods were applied to develop a measure of heuristic quality in spatial forest planning. My recommendation is to use a non-linear regression approach to estimate heuristic solution quality in the absence of a known optimal solution, because these models fit the experimental data well, and the relationships among variables are better represented. When used alone, PSO performed rather weakly in solving a typical southern forest planning problem. When testing new heuristics, researchers generally initiate new searches with randomly-defined initial solutions to ensure independence of data (final solutions). In my final chapter, I assess whether PSO, when initiated with a high-quality set of initial solutions (particles), can fine-tune and improve the overall quality of a resulting forest plan. Results indicate that PSO can improve upon the higher quality initial solutions generated by another heuristic. This work provided three advances to the forestry sciences: a published literature review illustrating the trends and gaps in spatial forest planning, an application of heuristics to forest planning problems, and the assessment methods for heuristic solution quality.