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Articles by Pete Bettinger

Category: Research article

article id 7803, category Research article
Lingbo Dong, Pete Bettinger, Huiyan Qin, Zhaogang Liu. (2018). Reflections on the number of independent solutions for forest spatial harvest scheduling problems: a case of simulated annealing. Silva Fennica vol. 52 no. 1 article id 7803. https://doi.org/10.14214/sf.7803
Highlights: No one particular neighborhood search technique of simulated annealing was found to be universally acceptable; The optimal number of independent solutions necessary for addressing the area restriction harvest scheduling model was described with a negative logarithmic function that was related with the problem size. However, optimal number of independent solutions necessary was not sensitive to the problem size for non-spatial and unit restriction harvest scheduling model problems, which should be somewhat above 250 independent runs; The types of adjacency constraints have moderate effects on the number of independent solutions, but these effects are not significant.

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 ORCID ID:E-mail: farrell0503@126.com
  • Bettinger, Warnell School of Forestry and Natural Resources, University of Georgia, Athens 30602, GA, USA ORCID ID:E-mail: pbettinger@warnell.uga.edu
  • Qin, College of Economic and Management, Northeast Forestry University, Harbin 150040, China ORCID ID:E-mail: huiyanqin@hotmail.com
  • Liu, College of Forestry, Northeast Forestry University, Harbin 150040, China ORCID ID:E-mail: lzg19700602@163.com (email)
article id 1683, category Research article
Karol Przeździecki, Jarosław Zawadzki, Chris Cieszewski, Pete Bettinger. (2017). Estimation of soil moisture across broad landscapes of Georgia and South Carolina using the triangle method applied to MODIS satellite imagery. Silva Fennica vol. 51 no. 4 article id 1683. https://doi.org/10.14214/sf.1683
Highlights: Temperature vegetation dryness indices were calculated from MODIS satellite imagery to estimate subsurface soil moisture at different depths using the triangle method; Observations were carried out over the vast areas of Georgia and South Carolina, USA, covered with diverse land uses that, included dense forests and agricultural areas; The triangle method may be useful in forestry management applications where the productivity potential of a region and the hydrologic role of forests in that region are of concern.

We describe here a study based on analysis of vegetation indices and land surface temperatures, which provides relevant information for estimating soil moisture at regional scales. Through an analysis of MODIS satellite imagery and in situ moisture data, the triangle method was used to develop a conceptual land surface temperature−vegetation index model, and spatial temperature-vegetation dryness index (TVDI) values to describe soil moisture relationships for a broad landscape. This study was situated mainly within two states of the southern United States (Georgia and South Carolina). The total study area was about 30 million hectares. The analyses were conducted using information gathered from the 2009 growing season (from the end of March to September). The results of the study showed that soil moisture content was inversely proportional to TVDI, and that TVDI based on the normalized difference vegetation index (NDVI) had a slightly higher correlation with soil moisture than TVDI based on the enhanced vegetation index (EVI).

  • Przeździecki, Warsaw University of Technology, Faculty of Building Services, Hydro and Environmental Engineering, 00-653, Nowowiejska 20, Warszawa, Poland ORCID ID: http://orcid.org/0000-0002-2275-5223 E-mail: karol_przezdziecki@is.pw.edu.pl (email)
  • Zawadzki, Warsaw University of Technology, Faculty of Building Services, Hydro and Environmental Engineering, 00-653, Nowowiejska 20, Warszawa, Poland ORCID ID: http://orcid.org/0000-0003-2842-0018 E-mail: j.j.zawadzki@gmail.com
  • Cieszewski, University of Georgia, Warnell School of Forestry and Natural Resources, 180 E Green St, Athens, GA 30602, USA ORCID ID: http://orcid.org/0000-0003-2842-4406 E-mail: thebiomat@gmail.com
  • Bettinger, University of Georgia, Warnell School of Forestry and Natural Resources, 180 E Green St, Athens, GA 30602, USA ORCID ID: http://orcid.org/0000-0002-5454-3970 E-mail: pbettinger@warnell.uga.edu
article id 1622, category Research article
Lingbo Dong, Pete Bettinger, Zhaogang Liu, Huiyan Qin, Yinghui Zhao. (2016). Evaluating the neighborhood, hybrid and reversion search techniques of a simulated annealing algorithm in solving forest spatial harvest scheduling problems. Silva Fennica vol. 50 no. 4 article id 1622. https://doi.org/10.14214/sf.1622
Highlights: The performances of neighborhood, hybrid and reversion search strategies of simulated annealing were evaluated when implemented with a forest spatial harvest scheduling problem; The performances of alternative search strategies of simulated annealing were all systematic and clear better than the conventional strategy; The reversion techniques were significant superior to the other search strategies in solving forest spatial harvest scheduling problems.

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 ORCID ID:E-mail: farrell0503@126.com
  • Bettinger, Warnell School of Forestry and Natural Resources, University of Georgia, Athens 30602, GA, USA ORCID ID:E-mail: pbettinger@warnell.uga.edu
  • Liu, Department of Forest Management, College of Forestry, Northeast Forestry University, Harbin 150040, China ORCID ID:E-mail: lzg19700602@163.com (email)
  • Qin, Department of Forestry Economic, College of Economic & Management, Northeast Forestry University, Harbin 150040, China ORCID ID:E-mail: huiyanqin@hotmail.com
  • Zhao, Department of Forest Management, College of Forestry, Northeast Forestry University, Harbin 150040, China ORCID ID:E-mail: zyinghui0925@126.com
article id 1232, category Research article
Pete Bettinger, Mehmet Demirci, Kevin Boston. (2015). Search reversion within s-metaheuristics: impacts illustrated with a forest planning problem. Silva Fennica vol. 49 no. 2 article id 1232. https://doi.org/10.14214/sf.1232
Highlights: The interruption of the sequence of events used to explore a solution space and develop a forest plan, and the re-initiation of the search process from a high-quality, known starting point (reversion) seems necessary for some s-metaheuristics; When using a s-metaheuristic, higher quality forest plans may be developed when the reversion interval is around six iterations of the model.
The use of a reversion technique during the search process of s-metaheuristics has received little attention with respect to forest management and planning problems. Reversion involves the interruption of the sequence of events that are used to explore the solution space and the re-initiation of the search process from a high-quality, known starting point. We explored four reversion rates when applied to three different types of s-metaheuristics that have previously shown promise for the forest planning problem explored, threshold accepting, tabu search, and the raindrop method. For two of the s-metaheuristics, we also explored three types of decision choices, a change to the harvest timing of a single management unit (1-opt move), the swapping of two management unit’s harvest timing (2-opt moves), and the swapping of three management unit’s harvest timing (3-opt moves). One hundred independent forest plans were developed for each of the metaheuristic / reversion rate combinations, all beginning with randomly-generated feasible starting solutions. We found that (a) reversion does improve the quality of the solutions generated, and (b) the rate of reversion is an important factor that can affect solution quality.
  • Bettinger, School of Forestry and Natural Resources, 180 E. Green Street, University of Georgia, Athens, Georgia, USA 30602 ORCID ID:E-mail: pbettinger@warnell.uga.edu (email)
  • Demirci, General Directorate of Forestry, Ministry of Forest and Water Affairs, Republic of Turkey ORCID ID:E-mail: mehmetdemirci@yahoo.com
  • Boston, Department of Forest Engineering, Resources and Management, College of Forestry, Oregon State University, USA ORCID ID:E-mail: Kevin.Boston@oregonstate.edu
article id 276, category Research article
Jianping Zhu, Pete Bettinger, Rongxia Li. (2007). Additional insight into the performance of a new heuristic for solving spatially constrained forest planning problems. Silva Fennica vol. 41 no. 4 article id 276. https://doi.org/10.14214/sf.276
The raindrop method of searching a solution space for feasible and efficient forest management plans has been demonstrated as being useful under a limited set of circumstances, mainly where adjacency restrictions are accommodated using the unit restriction model. We expanded on this work and applied the model (in a modified form) to a problem that had both wood flow and area restriction adjacency constraints, then tested the problem formulation on six hypothetical forests of different sizes and age class distributions. Threshold accepting and tabu search were both applied to the problems as well. The modified raindrop method’s performance was best when applied to forests with normal age class distributions. 1-opt tabu search worked best on forests with young age class distributions. Threshold accepting and the raindrop method both performed well on forests with older age class distributions. On average, the raindrop method produced higher quality solutions for most of the problems, and in all but one case where it did not, the solutions generated were not significantly different than the heuristic that located a better solution. The advantage of the raindrop method is that it uses only two parameters and does not require extensive parameterization. The disadvantage is the amount of time it needs to solve problems with area restriction adjacency constraints. We suggest that it may be advantageous to use this heuristic on problems with relatively simple spatial forest planning constraints, and problems that do not involve young initial age class distributions. However, generalization of the performance of the raindrop method to other forest planning problems is problematic, and will require examination by those interested in pursuing this planning methodology. Given that our tests of the raindrop method are limited to a small set of URM and ARM formulations, one should view the combined set of work as additional insight into the potential performance of the method on problems of current interest to the forest planning community.
  • Zhu, Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA 30602, USA ORCID ID:E-mail:
  • Bettinger, Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA 30602, USA ORCID ID:E-mail: pbettinger@warnell.uga.edu (email)
  • Li, Warnell School of Forestry and Natural Resources, University of Georgia, Athens, GA 30602, USA ORCID ID:E-mail:
article id 477, category Research article
Pete Bettinger, Jianping Zhu. (2006). A new heuristic method for solving spatially constrained forest planning problems based on mitigation of infeasibilities radiating outward from a forced choice. Silva Fennica vol. 40 no. 2 article id 477. https://doi.org/10.14214/sf.477
A new heuristic method to mitigate infeasibilities when a choice is forced into a solution was developed to solve spatially constrained forest planning problems. One unique aspect of the heuristic is the introduction of unchosen decision choices into a solution regardless of the resulting infeasibilities, which are then mitigated by selecting next-best choices for those spatial units that are affected, but in a radiating manner away from the initial choice. As subsequent changes are made to correct the affected spatial units, more infeasibilities may occur, and these are corrected as well in an outward manner from the initial choice. A single iteration of the model may involve a number of changes to the status of the decision variables, making this an n-opt heuristic process. The second unique aspect of the search process is the periodic reversion of the search to a saved (in computer memory) best solution. Tests have shown that the reversion is needed to ensure better solutions are located. This new heuristic produced solutions to spatial problems that are of equal or comparable in quality to traditional integer programming solutions, and solutions that are better than those produced by two other basic heuristics. Three small hypothetical forest examples illustrate the performance of the heuristic against standard versions of threshold accepting and tabu search. In each of the three examples, the variation in solutions generated from random starting points is smaller with the new heuristic, and the difference in solution values between the new heuristic and the other two heuristics is significant (p<0.05) when using an analysis of variance. However, what remains to be seen is whether the new method can be applied successfully to the broader range of operations research problems in forestry and other fields.
  • Bettinger, Warnell School of Forest Resources, University of Georgia, Athens, GA 30602, USA ORCID ID:E-mail: pbettinger@forestry.uga.edu (email)
  • Zhu, Warnell School of Forest Resources, University of Georgia, Athens, GA 30602, USA ORCID ID:E-mail:
article id 545, category Research article
Pete Bettinger, David Graetz, Kevin Boston, John Sessions, Woodam Chung. (2002). Eight heuristic planning techniques applied to three increasingly difficult wildlife planning problems. Silva Fennica vol. 36 no. 2 article id 545. https://doi.org/10.14214/sf.545
As both spatial and temporal characteristics of desired future conditions are becoming important measures of forest plan success, forest plans and forest planning goals are becoming complex. Heuristic techniques are becoming popular for developing alternative forest plans that include spatial constraints. Eight types of heuristic planning techniques were applied to three increasingly difficult forest planning problems where the objective function sought to maximize the amount of land in certain types of wildlife habitat. The goal of this research was to understand the relative challenges and opportunities each technique presents when more complex difficult goals are desired. The eight heuristic techniques were random search, simulated annealing, great deluge, threshold accepting, tabu search with 1-opt moves, tabu search with 1-opt and 2-opt moves, genetic algorithm, and a hybrid tabu search / genetic algorithm search process. While our results should not be viewed as universal truths, we determined that for the problems we examined, there were three classes of techniques: very good (simulated annealing, threshold accepting, great deluge, tabu search with 1-opt and 2-opt moves, and tabu search / genetic algorithm), adequate (tabu search with 1-opt moves, genetic algorithm), and less than adequate (random search). The relative advantages in terms of solution time and complexity of programming code are discussed and should provide planners and researchers a guide to help match the appropriate technique to their planning problem. The hypothetical landscape model used to evaluate the techniques can also be used by others to further compare their techniques to the ones described here.
  • Bettinger, Department of Forest Resources, Oregon State University, Corvallis, OR 97331 ORCID ID:E-mail: pete.bettinger@orst.edu (email)
  • Graetz, Department of Forest Resources, Oregon State University, Corvallis, OR 97331 ORCID ID:E-mail:
  • Boston, Carter Holt Harvey Forest Fibre Solutions, Tokoroa, New Zealand ORCID ID:E-mail:
  • Sessions, Department of Forest Engineering, Oregon State University, Corvallis, OR 97331 ORCID ID:E-mail:
  • Chung, Department of Forest Engineering, Oregon State University, Corvallis, OR 97331 ORCID ID:E-mail:
article id 578, category Research article
Kevin Boston, Pete Bettinger. (2001). Development of spatially feasible forest plans: a comparison of two modeling approaches. Silva Fennica vol. 35 no. 4 article id 578. https://doi.org/10.14214/sf.578
Spatial goals are becoming more frequent aspects of forest management plans as regulatory and organizational policies change in response to fisheries and wildlife concerns. The combination of green-up constraints (harvesting restrictions that prevent the cutting of adjacent units for a specified period of time) and habitat requirements for red-cockaded woodpeckers (RCW) in the southeastern U.S. suggests that spatially feasible forest plans be developed to guide management activities. We examined two modeling approaches aimed at developing management plans that had both harvest volume goals, RCW habitat, and green-up constraints. The first was a two-stage method that in one stage used linear programming to assign volume goals, and in a second stage used a tabu search – genetic algorithm heuristic technique to minimize the deviations from the volume goals while maximizing the present net revenue and addressing the RCW and green-up constraints. The second approach was a one-stage procedure where the entire management plan was developed with the tabu search – genetic algorithm heuristic technique, thus it did not use the guidance for timber volume levels provided by the LP solution. The goal was to test two modeling approaches to solving a realistic spatial harvest scheduling problem. One is where to volume goals are calculated prior to developing the spatially feasible forest plan, while the other approach simultaneously addresses the volume goals while developing the spatially feasible forest plan. The resulting forest plan from the two-stage approach was superior to that produced from the one-stage approach in terms of net present value. The main point from this analysis is that heuristic techniques may benefit from guidance provided by relaxed LP solutions in their effort to develop efficient forest management plans, particularly when both commodity production and complex spatial wildlife habitat goals are considered. Differences in the production of forest products were apparent between the two modeling approaches, which could have a significant effect on the selection of wood processing equipment and facilities.
  • Boston, Forest Fibre Solutions, Carter Holt Harvey, Tokoroa, New Zealand ORCID ID:E-mail: kevin.boston@chh.co.nz (email)
  • Bettinger, Department of Forest Resources, Oregon State University, Corvallis, OR 97331 ORCID ID:E-mail:

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