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Articles containing the keyword 'simulated annealing'.

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 1326, category Research article
Joanna Bachmatiuk, Jordi Garcia-Gonzalo, Jose Guilherme Borges. (2015). Analysis of the performance of different implementations of a heuristic method to optimize forest harvest scheduling. Silva Fennica vol. 49 no. 4 article id 1326. https://doi.org/10.14214/sf.1326
Highlights: The number of treatment schedules available for each stand has an impact on the optimal configuration of opt-moves (i.e. number stands where the treatment schedule is changed in an iteration); Considering a large number of treatment schedules per stand, the one-opt move implementation is preferred, yet when considering a low number of decision choices the two-opt moves option performs better.

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.

  • Bachmatiuk, Centro de Estudos Florestais, Instituto Superior de Agronomia, Universidade de Lisboa, Lisboa, Portugal ORCID ID:E-mail: jbachmatiuk@isa.ulisboa.pt (email)
  • Garcia-Gonzalo, Centro de Estudos Florestais, Instituto Superior de Agronomia, Universidade de Lisboa, Lisboa, Portugal ORCID ID:E-mail: jordigarcia@isa.ulisboa.pt
  • Borges, Centro de Estudos Florestais, Instituto Superior de Agronomia, Universidade de Lisboa, Lisboa, Portugal ORCID ID:E-mail: joseborges@isa.ulisboa.pt
article id 956, category Research article
Michał Zasada. (2013). Evaluation of the double normal distribution for tree diameter distribution modeling. Silva Fennica vol. 47 no. 2 article id 956. https://doi.org/10.14214/sf.956
The double normal distribution consists of two normal distributions truncated at their means and then combined in such a way, that points of truncation now become the overall distribution mode. So far, parameters of the double normal distribution have been estimated exclusively using the method of moments. This study evaluates the maximum likelihood method for the estimation of the double normal distribution parameters in Scots pine stands in Poland, and compares it to the results of the method of moments and the two-parameter Weibull distribution fitted using the maximum likelihood method and the method of moments. Presented results show that it is not recommended to use the maximum likelihood method of parameter fitting with Nelder-Mead and quasi-Newton optimization algorithms for the double normal distribution for small samples. However, it can be used for large samples, giving the fit comparable to the two-parameter Weibull distribution and providing parameters having sound practical and biological meaning. In the case of smaller samples for the double normal distribution it is recommended to apply the maximum likelihood method with the alternative simulated annealing optimization algorithm, use the method of moments or substitute the described distribution with more the flexible and robust Weibull distribution. For the smaller samples, the method of moments was superior to the maximum likelihood method.
  • Zasada, Warsaw University of Life Sciences, Faculty of Forestry, Laboratory of Dendrometry and Forest Productivity, Nowoursynowska 159, 02-776 Warsaw, Poland ORCID ID:E-mail: michal.zasada@wl.sggw.pl (email)
article id 299, category Research article
Hongcheng Zeng, Timo Pukkala, Heli Peltola, Seppo Kellomäki. (2007). Application of ant colony optimization for the risk management of wind damage in forest planning. Silva Fennica vol. 41 no. 2 article id 299. https://doi.org/10.14214/sf.299
Ant colony optimization (ACO) is still quite a new technique and seldom used in the field of forest planning compared to other heuristics such as simulated annealing and genetic algorithms. This work was aimed at evaluating the suitability of ACO for optimizing the clear-cut patterns of a forest landscape when aiming at simultaneously minimizing the risk of wind damage and maintaining sustainable and even flow of periodical harvests. For this purpose, the ACO was first revised and the algorithm was coded using the Visual Basic Application of the ArcGIS software. Thereafter, the performance of the modified ACO was demonstrated in a forest located in central Finland using a 30-year planning period. Its performance was compared to simulated annealing and a genetic algorithm. The revised ACO performed logically since the objective function value was improving and the algorithm was converging during the optimization process. The solutions maintained a quite even periodical harvesting timber while minimizing the risk of wind damage. Implementing the solution would result in smooth landscape in terms of stand height after the 30-year planning period. The algorithm is quite sensitive to the parameters controlling pheromone updating and schedule selecting. It is comparable in solution quality to simulated annealing and genetic algorithms.
  • Zeng, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: hongcheng.zeng@joensuu.fi (email)
  • Pukkala, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Peltola, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Kellomäki, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail:
article id 357, category Research article
Elizabeth Dodson Coulter, John Sessions, Michael G. Wing. (2006). Scheduling forest road maintenance using the analytic hierarchy process and heuristics. Silva Fennica vol. 40 no. 1 article id 357. https://doi.org/10.14214/sf.357
The management of low-volume roads has transitioned from focusing on maintenance designed to protect a capital investment in road infrastructure to also include environmental effects. In this study, two models using mathematical programming are applied to schedule forest road maintenance and upgrade activities involving non-monetary benefits. Model I uses a linear objective function formulation that maximizes benefit subject to budgetary constraints. Model II uses a non-linear objective function to maximize the sum of benefits divided by the sum of all costs in a period. Because of the non-linearity of the constraints and the requirements that the decision variables be binary, the solutions to both problem formulations are found using two heuristics, simulated annealing and threshold accepting. Simulated annealing was found to produce superior solutions as compared to threshold accepting. The potential benefit for completing a given road maintenance or upgrade project is determined using the Analytic Hierarchy Process (AHP), a multi-criterion decision analysis technique. This measure of benefit is combined with the economic cost of completing a given project to schedule maintenance and upgrade activities for 225 km (140 miles) of road in forested road systems within western Oregon. This combination of heuristics, cost-benefit analysis, environmental impacts, and expert judgment produces a road management schedule that better fits the current road management paradigm.
  • Coulter, College of Forestry and Conservation, University of Montana, 32 Campus Drive, Missoula, MT 59812, USA ORCID ID:E-mail: elizabeth.coulter@cfc.umt.edu (email)
  • Sessions, Department of Forest Engineering, College of Forestry, Oregon State University, 204 Peavy Hall, Corvallis, OR 97331-5706, USA ORCID ID:E-mail:
  • Wing, Department of Forest Engineering, College of Forestry, Oregon State University, 204 Peavy Hall, Corvallis, OR 97331-5706, USA ORCID ID:E-mail:
article id 396, category Research article
Timo Pukkala, Mikko Kurttila. (2005). Examining the performance of six heuristic optimisation techniques in different forest planning problems. Silva Fennica vol. 39 no. 1 article id 396. https://doi.org/10.14214/sf.396
The existence of multiple decision-makers and goals, spatial and non-linear forest management objectives and the combinatorial nature of forest planning problems are reasons that support the use of heuristic optimisation algorithms in forest planning instead of the more traditional LP methods. A heuristic is a search algorithm that does not necessarily find the global optimum but it can produce relatively good solutions within reasonable time. The performance of different heuristics may vary depending on the complexity of the planning problem. This study tested six heuristic optimisation techniques in five different, increasingly difficult planning problems. The heuristics were evaluated with respect to the objective function value that the techniques were able to find, and the time they consumed in the optimisation process. The tested optimisation techniques were 1) random ascent (RA), 2) Hero sequential ascent technique (Hero), 3) simulated annealing (SA), 4) a hybrid of SA and Hero (SA+Hero), 5) tabu search (TS) and 6) genetic algorithm (GA). The results, calculated as averages of 100 repeated optimisations, were very similar for all heuristics with respect to the objective function value but the time consumption of the heuristics varied considerably. During the time the slowest techniques (SA or GA) required for convergence, the optimisation could have been repeated about 200 times with the fastest technique (Hero). The SA+Hero and SA techniques found the best solutions for non-spatial planning problems, while GA was the best in the most difficult problems. The results suggest that, especially in spatial planning problems, it is a benefit if the method performs more complicated moves than selecting one of the neighbouring solutions. It may also be beneficial to combine two or more heuristic techniques.
  • Pukkala, University of Joensuu, Faculty of Forestry, P.O. BOX 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: timo.pukkala@forest.joensuu.fi (email)
  • Kurttila, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail:
article id 419, category Research article
Tero Heinonen, Timo Pukkala. (2004). A comparison of one- and two-compartment neighbourhoods in heuristic search with spatial forest management goals. Silva Fennica vol. 38 no. 3 article id 419. https://doi.org/10.14214/sf.419
This study presents a comparison of the performance of four heuristic techniques with one- and two-compartment neighbourhoods in harvest scheduling problems including a spatial objective variable. The tested heuristics were random ascent, Hero, simulated annealing and tabu search. All methods seek better solutions by inspecting the neighbourhood solutions, which are combinations that can be obtained by changing the treatment schedule in one (one-compartment neighbourhood) or two (two-compartment neighbourhood) compartments. The methods and neighbourhoods were examined in one artificial and four real landscapes ranging from 700 to 981 ha in size. The landscapes had 608 to 900 stand compartments, and the examined planning problems had 2986 to 4773 binary decision variables. The objective function was a multi-objective utility function. The spatial objective variable was the percentage of compartment boundary that joins two compartments, both of which are to be cut during the same 20-year period. The non-spatial objectives were net incomes of three consecutive 20-year management periods and the remaining growing stock volume at the end of the third 20-year period. In another problem formulation, the total harvest of the first 20-year period was used as an objective variable together with the spatial objective. The results showed that a two-compartment neighbourhood was systematically and often clearly better than a one-compartment neighbourhood. The improvements were greatest with the simplest heuristics, random ascent and Hero. Of the four heuristics, tabu search and simulated annealing proved to be the best methods, but with a two-compartment neighbourhood the differences between methods were negligible.
  • Heinonen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail:
  • Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: timo.pukkala@joensuu.fi (email)
article id 605, category Research article
Paul C. Van Deusen. (2001). Scheduling spatial arrangement and harvest simultaneously. Silva Fennica vol. 35 no. 1 article id 605. https://doi.org/10.14214/sf.605
A method based on the Metropolis algorithm is developed for creating desirable spatial configurations on the landscape while simultaneously dealing with other objectives commonly associated with harvest scheduling. Spatial configurations are loosely specified and stochastically attained, which contrasts with other adjacency constraints based on specific block size limits. This method makes it possible to improve habitat and connectivity, and to create buffer zones as part of the scheduling process. It also works with a mapped set of polygons/forest stands and does not require a gridded system.
  • Van Deusen, NCASIS, Northeast Regional Center, 600 Suffolk Street, Fifth Floor, Lowell, MA 01854, USA ORCID ID:E-mail: pvandeusen@ncasi.org (email)
article id 657, category Research article
Paul C. Van Deusen. (1999). Multiple solution harvest scheduling. Silva Fennica vol. 33 no. 3 article id 657. https://doi.org/10.14214/sf.657
Application of the Metropolis algorithm for forest harvest scheduling is extended by automating the relative weighting of objective function components. Previous applications of the Metropolis algorithm require the user to specify these weights, which demands substantial trial and error in practice. This modification allows for general incorporation of objective function components that are either periodic or spatial in nature. A generic set of objective function components is developed to facilitate harvest scheduling for a wide range of problems. The resulting algorithm generates multiple feasible solutions rather than a single optimal solution.
  • Van Deusen, Principal Research Scientist, NCASI, Northeast Regional Center, Tufts University, 1 Anderson Hall, Medford, Massachusetts 02155, USA ORCID ID:E-mail: pvandeus@tufts.edu (email)

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