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Articles by Jianping Zhu

Category: Research article

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:

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