A Mathematical Model for Tree Selection That Accounts for a Specified Absolute Stand Density During Improvement Thinning Operations. P. 82–94

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https://doi.org/10.37482/0536-1036-2026-3-82-94

Abstract

There is a concept in forestry known as “absolute stand density” – the sum of the cross-sectional areas of all trees in the stand at a height of 1.3 meters, converted to 1 hectare. Currently, LIDAR tree survey mapping technology for forest areas is becoming increasingly widespread. It provides data on tree coordinates and diameters, as well as other information. This data enables the calculation of stand density. Designing a reduction in the absolute stand density during improvement thinning operations in a uniform stand needs to make an optimal selection of trees to be harvested in order to achieve the target density while ensuring the maximum possible growing space for the remaining trees. This paper presents a problem of selecting trees for improvement thinning operations, which aims to maintain a specified stand density while ensuring an even spatial distribution of the remaining trees. The research aims at developing a mathematical model for the optimal selection of trees for harvesting as a decision support system to improve the efficiency of improvement thinning operations. We propose a genetic algorithm to solve this problem. The genetic algorithm uses the results of tree survey LiDAR scanning of the stand. In the algorithm, each tree is encoded as a binary vector, and the target function combines the maximization of total pairwise distances with penalties for violating constraints on the planned stand density and the minimum distance between trees left for further growth. When planning to reduce the absolute completeness of the plantation, during logging of forest maintenance, in a homogeneous plantation, it is necessary to make the optimal choice of trees assigned to logging in order to achieve the planned completeness, and at the same time provide the maximum possible living space for the trees left for rearing. The article presents the formulation of the problem of selecting trees for logging, assuming the preservation of a given proportion of the completeness of plantings while ensuring a uniform spatial distribution of the remaining trees. The aim of the work is to develop a mathematical model of optimal tree selection as a decision support system to improve the efficiency of logging due to the optimal choice of trees to be removed. To solve the problem, a genetic algorithm is proposed that assumes the results of a sub-tree LIDAR survey of the plantation, in which each tree is encoded by a binary vector, and the objective function combines maximizing the total pairwise distances and penalties for violating restrictions on the planned completeness of the plantation and the minimum distance between trees left to grow. The theoretical justification for the complexity of the problem is discussed, and it is shown that, in the general case, it is NP-hard. The proposed approach has been successfully tested on real-world tree survey LiDAR data, confirming its effectiveness and practical applicability in forestry.

Funding: The research was carried out within the framework of the scientific school “Innovative Solutions in Logging Industry and Forest Management” and funded by the Russian Science Foundation Grant No. 23-16-00092, https://rscf.ru/project/23-16-00092/

Authors

Grigorij E. Rego¹, Candidate of Engineering; ResearcherID: AFX-5848-2022, ORCID: https://orcid.org/0000-0002-2235-8113
Olga I. Grigoreva², Candidate of Agriculture, Assoc. Prof.; ResearcherID: AAC-9570-2020, ORCID: https://orcid.org/0000-0001-5937-0813
Igor V. Grigorev^3*, Doctor of Engineering, Prof.; ResearcherID: S-7085-2016, ORCID: https://orcid.org/0000-0002-5574-1725
Varvara P. Druzyanova⁴, Doctor of Engineering, Prof.; ResearcherID: AAG-2463-2019, ORCID: https://orcid.org/0000-0001-5409-3837
Elena Yu. Matvienko⁵, Candidate of Agriculture, Assoc. Prof.;
ORCID: https://orcid.org/0000-0002-6767-315X

Affiliation

¹Petrozavodsk State University, prosp. Lenina, 33, Petrozavodsk, Russia, 185910; regogr@yandex.ru
²Saint Petersburg State Forest Technical University, Institutskiy per., 5, Saint Petersburg, Russia, 194021; grigoreva_o@list.ru
³Arctic State Agrotechnological University, sh. Sergelyakhskoye, 3-y km, 3, Yakutsk, Russia, 677007; silver73@inbox.ru*
⁴North-Eastern Federal University in Yakutsk, ul. Belinskogo, 58, Yakutsk, Russia, 677000; druzvar@mail.ru
⁵Novocherkassk Engineering and Reclamation Institute named after A.K. Kortunov, ul. Pushkinskaya, 111, Novocherkassk, Rostov Region, Russia, 346428; zhikalena11@mail.ru

Keywords

genetic algorithm, absolute stand density, reduction in absolute stand density, target absolute stand density, evenness of tree distribution, combinatorial optimization, metaheuristics, LiDAR stand surveying, improvement thinning, retention of trees

For citation

Rego G.E., Grigorieva O.I., Grigoriev I.V., Druzyanova V.P., Matvienko E.Yu. A Mathematical Model for Tree Selection That Accounts for a Specified Absolute Stand Density During Improvement Thinning Operations. Lesnoy Zhurnal = Russian Forestry Journal, 2026, no. 3, pp. 82–94. (In Russ.). https://doi.org/10.37482/0536-1036-2026-3-82-94

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