Articles containing the keyword 'optimization'

Process-based tree growth models are recognized to be flexible tools which are valuable for investigating tree growth in relation to changing environment or silvicultural treatments. In the context of forestry, we address two key modelling problems: allocation of growth which determines total wood production, and distribution of wood along the stem which determines stem form and wood quality. Growth allocation and distribution are the outcome of carbon translocation, which may be described by the Munch theory. We propose a simpler gradient process to describe the carbon distribution in the phloem of conifers. This model is a reformulation of a carbon diffusion-like process proposed by Thornley in 1972. By taking into account the continuity of the cambium along the stem, we obtain a one-dimensional reaction-diffusion model which describes both growth allocation between foliage, stem and roots, and growth distribution along the stem. Distribution of wood along the stem is then regarded as an allocation process at a smaller scale. A preliminary sensitivity analysis is presented. The model predicts a strong relationship between morphology and foliage-root allocation. It also suggests how empirical data, such as stem analysis, could be used to calibrate and validate allocation rules in process-based growth models.

• Deleuze, E-mail: cd@mm.unknown
• Houllier, E-mail: fh@mm.unknown

An alternative approach to formulating a forestry goal programming problem is presented. First, single objective optima levels are solved. The Analytical Hierarchy Process is applied in the estimation of a priori weights of deviations from the goal target levels. The ratios of the weights can be interpreted as relative importance of the goals, respectively. The sum of the weighted deviations from all single optima levels associated with the management goals is minimized. Instead of absolute deviations, relative ones are used. A case study problem of forest management planning with several objectives, measured in different units, is analysed.

The PDF includes an abstract in Finnish.

• Kangas, E-mail: jk@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

The paper presents a simple model of long-term forest management planning in tree plantations. The model is particularly suitable for developing countries where the research resources are limited. The management plan is prepared in two steps. First, one or several treatment schedules are simulated for each calculation unit (age class, compartment, etc.) over the selected planning period. Second, an optimal combination treatment schedules according to the selected objectives and constraints is searched by mathematical programming. The simulation of growth is based on the prediction of the diameter distribution at the desired time point. All stand characteristics are derived from this distribution. The models needed in the yield simulation can be estimated from temporary sample plots. A case study management plan for 13,000 ha of Pinus kesiya (Royle ex Gordon) plantations in Zambia is presented to demonstrate the system.

The PDF includes an abstract in Finnish.

• Pukkala, E-mail: tp@mm.unknown
• Mubita, E-mail: om@mm.unknown
• Saramäki, E-mail: js@mm.unknown

The study presents methods that incorporate the amenity of a forest area into the management planning. The management plan is based on treatment schedules simulated for each compartment over the 20-year planning period. The best combination of treatment schedules is selected by multi-objective optimization. The amenity is divided into two parts: (1) within-stand amenity and (2) the amenity of landscape when viewed afar (distant scene). The within-stand amenity is expressed in terms of adjective sum which is estimated from stand characteristics. The adjective sum of the whole area in a selected year can be taken as an objective or constraining variable of optimization. The assessment of the distant scene is based on computer illustrations which show the predicted temporal change of landscape according to a particular management plan.

The PDF includes a summary in Finnish.

• Pukkala, E-mail: tp@mm.unknown

The paper examines the needs, premises and criteria for effective public participation in tactical forest planning. A method for participatory forest planning utilizing the techniques of preference analysis, professional expertise and heuristic optimization is introduced. The techniques do not cover the whole process of participatory planning, but are applied as a tool constituting the numerical core for decision support. The complexity of multi-resource management is addressed by hierarchical decision analysis which assesses the public values, preferences and decision criteria toward the planning situation. An optimal management plan is sought using heuristic optimization. The plan can further be improved through mutual negotiations, if necessary. The use of the approach is demonstrated with an illustrative example. Its merits and challenges for participatory forest planning and decision making are discussed and a model for applying it in general forest planning context is depicted. By using the approach, valuable information can be obtained about public preferences and the effects of taking them into consideration on the choice of the combination of standwise treatment proposals for a forest area. Participatory forest planning calculations, carried out by the approach presented in the paper, can be utilized in conflict management and in developing compromises between competing interests.

• Kangas, E-mail: jk@mm.unknown
• Loikkanen, E-mail: tl@mm.unknown
• Pukkala, E-mail: tp@mm.unknown
• Pykäläinen, E-mail: jp@mm.unknown

A nonlinear programming algorithm was combined with two individual-tree growth simulators consisting of distance-independent diameter and height growth models and mortality models. Management questions that can be addressed by the optimization model include the timing, intensity and type of thinning, rotation age, and initial density. The results were calculated for Norway spruce (Picea abies (L.) H. Karst.) stands on Oxalis-Myrtillus site in Southern Finland, where the stand density after clearing of a seedling stand is about 2,000 trees/ha.

The optimum thinning programs were characterized by late first thinnings (at dominant height of 15–17 m) and relatively high growing stock levels. It was optimal to thin from above, unless mean annual increment was maximized instead of an economic objective. In most cases, the optimum number of thinnings was two or three. Compared to a no-thinning alternative, thinnings increased revenues by 15 –45% depending on the objective of stand management. Optimum rotation was strongly dependent on the interest rate.

Hooke and Jeeves’ direct search method was used for determining optimum solutions. The performance of the optimization algorithm was examined in terms of the number of functional evaluations and the equivalence of the objective function values of repeated optimizations.

The PDF includes a summary in Finnish.

• Valsta, E-mail: lv@mm.unknown

• López, Inland Norway University of Applied Sciences, Faculty of Applied Ecology, Agricultural Sciences and Biotechnology, P.O. Box 2400, Koppang, Norway https://orcid.org/0009-0006-6860-3408 E-mail: lucas.lopez@inn.no
• Sjølie, Inland Norway University of Applied Sciences, Faculty of Applied Ecology, Agricultural Sciences and Biotechnology, P.O. Box 2400, Koppang, Norway https://orcid.org/0000-0001-8099-3521 E-mail: hanne.sjolie@inn.no
• Nabhani, Inland Norway University of Applied Sciences, Faculty of Applied Ecology, Agricultural Sciences and Biotechnology, P.O. Box 2400, Koppang, Norway E-mail: abbas.nabhani@inn.no
• Aguilar, Swedish University of Agricultural Sciences, Department of Forest Economics, SE-901 83 Umeå, Sweden E-mail: francisco.aguilar@slu.se

• Eyvindson, Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Campus Ås, Norway; Natural Resource Institute Finland (Luke), Bioeconomy and Environment, Laatokartanonkaari 9, 00790 Helsinki, Finland https://orcid.org/0000-0003-0647-1594 E-mail: kyle.eyvindson@nmbu.no
• Kangas, Natural Resources Institute Finland (Luke), Bioeconomy and Environment, Yliopistokatu 6, 80100 Joensuu, Finland https://orcid.org/0000-0002-8637-5668 E-mail: annika.kangas@luke.fi
• Nahorna, Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Campus Ås, Norway https://orcid.org/0000-0002-5497-0315 E-mail: olha.nahorna@nmbu.no
• Hunault-Fontbonne, Faculty of Environmental Sciences and Natural Resource Management, Norwegian University of Life Sciences, Campus Ås, Norway https://orcid.org/0009-0004-1864-5162 E-mail: juliette.hunault@nmbu.no
• Potterf, Ecosystem Dynamics and Forest Management Group, Technical University of Munich, Hans Carl-von-Carlowitz-Platz 2, 85354 Freising, Germany https://orcid.org/0000-0001-6763-1948 E-mail: maria.potterf@tum.de

A major after-use option for former peat harvesting areas has been afforestation. The profitability of afforestation with Scots pine trees (Pinus sylvestris L.) was studied in two 31–32-year old experiments in southern and northern Finland. The stands were established by seeding and planting, and various fertilization treatments and drainage intensities were tested. The financial performance for each plot was assessed in three steps. First, the costs occurred during the measurement time were summed up according to their present value. Then, for the rest of the rotation (i.e., from the age of 31/32 onwards) the stand management was optimized in order to maximize the net present value (MaxNPV). Finally, bare land values (BLVs) were calculated by summing up the present value of costs and the MaxNPV and converting the sum of the series into infinity. The afforestation method did not affect the mean annual increment (MAI; 9.2–9.5 m³ ha^–1 a^–1) in the southern experiment. In the northern experiment the afforestation method, ditch spacing and fertilization had significant effects on the MAI of the stands. The average MAI of the planted pines was 8.9 m³ ha^–1 a^–1, and for seeded pines it was 7.5 m³ ha^–1 a^–1. The BLV at an interest rate of 3% was positive for all stands in both regions. In the northern region afforestation method, ditch spacing and fertilization also had a significant effect on the BLV. When the interest rate was 5%, almost two thirds of the stands had a negative BLV in both regions.

• Aro, Natural Resources Institute Finland (Luke), Bioeconomy and environment, Itäinen Pitkäkatu 4A, FI-20520 Turku, Finland E-mail: lasse.aro@luke.fi
• Ahtikoski, Natural Resources Institute Finland (Luke), Natural resources, Paavo Havaksentie 3, FI-90570 Oulu, Finland https://orcid.org/0000-0003-1658-3813 E-mail: anssi.ahtikoski@luke.fi
• Hytönen, Natural Resources Institute Finland (Luke), Natural resources, Teknologiakatu 7, FI-67100 Kokkola, Finland http://orcid.org/0000-0001-8475-3568 E-mail: jyrki.hytonen@luke.fi

Korean pine (Pinus koraiensis Siebold & Zucc.) is economically the most important tree species in northeast China. Korean pine plantations are established and managed for the production of timber and seeds. Despite the importance of the species, few models have been developed for the comparison of alternative management schedules. Model development is affected by the fact that permanent sample plots and thinning experiments have not been designed and managed for modeling purposes. The permanent sample plots include few non-thinned plots, and weak trees are removed in thinning treatments, leading to low mortality rate. Moreover, the measurement interval is irregular. This study used optimization-based modeling approach in tree-level diameter increment and survival modeling to deal with the above problems. Models for self-thinning limit were developed to alleviate the problem of underestimated mortality arising from the features of the data. In addition, improved site index and individual-tree height models were developed. The model of Lundqvist and Korf was used as the site index model and the model proposed by Schumacher as the height model. Quantile regression was used to model the maximum stand basal area and maximum number of trees as a function of mean tree diameter and site index. Tree diameter, stand basal area, basal area in larger trees and site index were used as the predictors of diameter increment and tree survival. The models developed in this study constitute a model set that is suitable for simulation and optimization studies. The models produced simulation results that correspond to measured stand development.

• Jin, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China http://orcid.org/0000-0003-2971-2709 E-mail: xingji_jin@163.com
• Pukkala, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China; University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi
• Li, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China http://orcid.org/0000-0002-4058-769X E-mail: fengrili@126.com
• Dong, Key Laboratory of Sustainable Forest Ecosystem Management - Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, Heilongjiang, People’s Republic of China http://orcid.org/0000-0002-3985-9475 E-mail: ldonglihu2006@163.com

This study examined a theoretical model for stand structures from the volumes of pulpwood and saw logs of clear-cut stands. The average stem size was used to estimate the number of cut trees. The distribution was solved using nonlinear derivative-free optimization. The truncated 2-parameter Weibull distribution was used to describe the stand structure of the commercial stems. This method was first tested with harvester data collected from seven clear-cut stands in southern Finland. Validation included reliability in the stand characteristics and goodness-of-fit of the species-specific distributions. The distributions provided unbiased estimates for the saw log volume, while the bias in the estimated pulpwood volume was 2%. The standard stand characteristics from the Weibull distributions corresponded notably well with the harvester data. A Kolmogorov-Smirnov (KS) test rejected two distributions out of 21 cases, when the accurate input variables were available for the theoretical model. The results of the study suggest that the presented method is a relevant option for predicting the stand structure. In practice, the reliability of the presented method was dependent on the quality of the information available from the stand prior to cutting. With a timber trade data set, the solution for the distribution for a clear-cut section was found. The goodness-of-fit was dependent on the accuracy of the visually assessed timber trade variables. Especially the average stem size proved difficult to assess due to high number of understorey pulpwood stems. Due to overestimated average stem sizes, the solved number of harvested trees was underestimated. Less than 50% of the distributions predicted for clear-cut sections passed the KS test.

• Siipilehto, Natural Resources Institute Finland (Luke), Latokartanonkaari 9, P.O. Box 2, FI-00790 Helsinki, Finland E-mail: jouni.siipilehto@luke.fi
• Rajala, Metsä Group, Revontulenpuisto 2, P.O. Box 10, 02020 METSÄ, FI-02100 Espoo, Finland E-mail: miika.rajala@metsagroup.com

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

• Zamora-Cristales, Department of Forest Engineering, Resources, and Management, College of Forestry, Oregon State University, 280 Peavy Hall, Corvallis, OR 97331, USA E-mail: rene.zamora@oregonstate.edu
• Boston, Department of Forest Engineering, Resources, and Management, College of Forestry, Oregon State University, 280 Peavy Hall, Corvallis, OR 97331, USA E-mail: kevin.boston@oregonstate.edu
• Sessions, Department of Forest Engineering, Resources, and Management, College of Forestry, Oregon State University, 280 Peavy Hall, Corvallis, OR 97331, USA E-mail: john.sessions@oregonstate.edu
• Murphy, Waiariki Institute of Technology, Rotorua, New Zealand E-mail: glen.murphy@waiariki.ac.nz

• Rathke, University of Natural Resources and Life Sciences, Institute of Production and Logistics, Feistmantelstraße 4, 1180 Vienna, Austria E-mail: joern.rathke@boku.ac.at
• Huka, University of Natural Resources and Life Sciences, Institute of Production and Logistics, Feistmantelstraße 4, 1180 Vienna, Austria E-mail: maria.huka@boku.ac.at
• Gronalt, University of Natural Resources and Life Sciences, Institute of Production and Logistics, Feistmantelstraße 4, 1180 Vienna, Austria E-mail: manfred.gronalt@boku.ac.at

• Öhman, SLU, Department of Forest Resource Management, SE-901 83 Umeå, Sweden E-mail: karin.ohman@srh.slu.se
• Eriksson, SLU, Department of Forest Resource Management, SE-901 83 Umeå, Sweden E-mail: loe@nn.se

• Pasalodos-Tato, INIA, Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria. Madrid, Spain E-mail: pasalodos.maria@inia.es
• Pukkala, University of East Finland, Joensuu, Finland E-mail: tp@nn.fi
• Rigueiro-Rodríguez, University of Santiago de Compostela, Lugo, Spain E-mail: arr@nn.es
• Fernández-Nunez, University of Santiago de Compostela, Lugo, Spain E-mail: efn@nn.es
• Mosquera-Losada, University of Santiago de Compostela, Lugo, Spain E-mail: mrml@nn.es

• Qi, Ecole Centrale Paris, Laboratory of Applied Mathematics, Grande Voie des Vignes, 92295 Chatenay-Malabry, France; Institute of Automation, Chinese Academy of Sciences, LIAMA/NLPR, P.O.Box 2728, Beijing, China E-mail: qiruitree@gmail.com
• Letort, Ecole Centrale Paris, Laboratory of Applied Mathematics, Grande Voie des Vignes, 92295 Chatenay-Malabry, France E-mail: vl@nn.fr
• Kang, Institute of Automation, Chinese Academy of Sciences, LIAMA/NLPR, P.O.Box 2728, Beijing, China E-mail: mk@nn.cn
• Cournède, Ecole Centrale Paris, Laboratory of Applied Mathematics, Grande Voie des Vignes, 92295 Chatenay-Malabry, France; INRIA saclay Ile-de-France, EPI Digiplant, Parc Orsay Université, 91893 Orsay cedex, France E-mail: phc@nn.fr
• Reffye, INRIA saclay Ile-de-France, EPI Digiplant, Parc Orsay Université, 91893 Orsay cedex, France; CIRAD, UMR AMAP, Montpellier, F-34000 France E-mail: pdr@nn.fr
• Fourcaud, CIRAD, UMR AMAP, Montpellier, F-34000 France E-mail: tf@nn.fr

• Pukkala, University of Joensuu, Faculty of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@joensuu.fi

• Kanzian, University of Applied Life Sciences Vienna, Institute of Forest Engineering, Peter Jordan Strasse 82, A-1190 Vienna, Austria E-mail: christian.kanzian@boku.ac.at
• Holzleitner, University of Applied Life Sciences Vienna, Institute of Forest Engineering, Peter Jordan Strasse 82, A-1190 Vienna, Austria E-mail: fh@nn.at
• Stampfer, University of Applied Life Sciences Vienna, Institute of Forest Engineering, Peter Jordan Strasse 82, A-1190 Vienna, Austria E-mail: ks@nn.at
• Ashton, Southern Regional Extension Forestry, Forestry Bldg. 4-420, University of Georgia, Athens, GA 30602, USA E-mail: sa@nn.us

• Zeng, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: hongcheng.zeng@joensuu.fi
• Pukkala, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: tp@nn.fi
• Peltola, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: hp@nn.fi
• Kellomäki, University of Joensuu, Faculty of Forest Sciences, P. O. Box 111, FI-80101 Joensuu, Finland E-mail: sk@nn.fi

• Backéus, SLU, Dept. of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden E-mail: sofia.backeus@resgeom.slu.se
• Wikström, SLU, Dept. of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden E-mail: pw@nn.se
• Lämås, SLU, Dept. of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden E-mail: tl@nn.se

• Rantala, Finnish Forest Research Institute, Suonenjoki Research Station, Juntintie 154, FI-77600 Suonenjoki, Finland E-mail: juho.rantala@metla.fi

• Aalto, Finnish Meteorological Institute, Air Quality Research, Sahaajankatu 20 E, FIN-00810 Helsinki, Finland E-mail: tuula.aalto@fmi.fi
• Hari, University of Helsinki, Dept. of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland E-mail: ph@nn.fi
• Vesala, University of Helsinki, Dept. of Physics, P.O. Box 64, FIN-00014 University of Helsinki, Finland E-mail: tv@nn.fi

• Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: jyrki.kangas@metla.fi
• Leskinen, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: pl@nn.fi
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: tp@nn.fi

• Pykäläinen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: jouni.pykalainen@joensuu.fi