A Mathematical Model of Tree Selection in a Homogeneous Plantation during Improvement Thinning. С. 38-50

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630*24

DOI:

10.37482/0536-1036-2025-2-38-50

Abstract

Currently, the qualitative composition of merchantable forests of maturity age and approaching it is often unsatisfactory. This is largely due to the lack of improvement thinning or its improper carrying out. The productivity of logging operations during improvement thinning is low, and the resulting timber in most cases turns out to be unclaimed. Mechanization of improvement thinning is inconvenient from a production point of view and economically unprofitable. At the same time, in the Russian Federation there are examples of the implementation of advanced foreign practices of improvement thinning by machine using a harvester and a forwarder. The use of this method allows for a multiple increase in productivity. The unit costs (rub/m3) in this case are higher than the costs of clear cutting of mature and overmature plantations, but often lower than when felling forests. It is possible to further increase the efficiency of machine logging complexes during improvement thinning operations by automating the selection of trees for logging. The basis for such selection should be the main objective of this type of logging – obtaining the most optimal size and quality characteristics of plantations by the age of their maturity. This becomes possible when taking into account the competition of woody plants in the plantation before and after improvement thinning. The article introduces a mathematical formulation of the problem of assigning trees for logging in a homogeneous plantation. It is shown that the number of possible solutions is growing exponentially. An algorithm based on the greedy method is implemented, and an experimental comparison of this method with a random result, as well as with the removal of a tree with the closest neighbour among all trees, is performed. Testing the algorithm on experimental data has shown that it is more effective than the other two.

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. Grigorev³*, Doctor of Engineering, Prof.; ResearcherID: S-7085-2016, ORCID: https://orcid.org/0000-0002-5574-1725
Anna M. Voronova¹, Candidate of Engineering, Assoc. Prof.; ORCID: https://orcid.org/0009-0004-9567-6421
Ilya S. Dolzhikov⁴, Candidate of Engineering; ORCID: https://orcid.org/0000-0002-2738-0483
Varvara P. Druzyanova⁵, Doctor of Engineering, Prof.; ResearcherID: AAG-2463-2019, ORCID: https://orcid.org/0000-0001-5409-3837

Affiliation

¹Petrozavodsk State University, prosp. Lenina, 33, Petrozavodsk, 185910, Russian Federation;
²Saint Petersburg State Forest Technical University named after S.M. Kirov, Institutskii per.,
³Arctic State Agrotechnological University, sh. Sergelyakhskoe, 3rd km, 3, Yakutsk, 677007,
⁴Saint Petersburg State University of Architecture and Civil Engineering, ul. 2ya
⁵North-Eastern Federal University named after M.K. Ammosov, ul. Belinskogo, 58, Yakutsk,
677000, Russian Federation; druzvar@mail.ru

Keywords

improvement thinning, selection of trees for logging, mathematical modeling, greedy algorithm, complete weighted graph, optimization criteria

For citation

Rego G.E., Grigoreva O.I., Grigorev I.V., Voronova A.M., Dolzhikov I.S., Druzyanova V.P. A Mathematical Model of Tree Selection in a Homogeneous Plantation during Improvement Thinning. Lesnoy Zhurnal = Russian Forestry Journal, 2025, no. 2, pp. 38–50. (In Russ.). https://doi.org/10.37482/0536-1036-2025-2-38-50

References

1. Bogachev P.V., Grigoreva O.I. Control of the Quality and Efficiency of Logging According to the Standards of the Intensive Forestry Model in the Tikhvin Forestry of the Leningrad Region. Aktual’nye problemy lesnogo khozyajstva i derevopererabotki: Materials of the All-Russian Scientific and Practical Conference. Ed. by Yu.M. Kazakov et al. Kazan, Kazan National Research Technological University, 2023, pp. 16–19. (In Russ.).
2. Bogachev P.V., Grigoreva O.I., Grigorev G.A. Using Absolute Density as a Criterion for the quality of Improvement Thinning. Povyshenie effektivnosti lesnogo kompleksa: Materials of the 9th All-Russian National Scientific and Practical Conference with International Participation. Petrozavodsk, Petrozavodsk State University, 2023, pp. 40–41. (In Russ.).
3. Buzykin A.I. Sustainability of Forest Cenoses in Connection with Their Spatial Structure and Biodiversity: Research Effort: Grant no. 01-04-48176. The Russian Foundation for Basic Research, 2001. (In Russ.).
4. Grigoreva O.I., Panarin A.O. Promising Ways to Improve the Efficiency of Improvement Thinning in Young Stands. Aktual’nye problemy lesnogo khozyajstva i derevopererabotki: Materials of the All-Russian Scientific and Practical Conference. Ed. by Yu.M. Kazakov et al. Kazan, Kazan National Research Technological University, 2023, pp. 70–73. (In Russ.).
5. Grigoreva O.I., Panarin A.O. Improving the Efficiency of Forest Management. Povyshenie effektivnosti lesnogo kompleksa: Materials of the 9th All-Russian National Scientific and Practical Conference with International Participation. Petrozavodsk, Petrozavodsk State University, 2023, pp. 61–62. (In Russ.).
6. Karpechko A.Yu. Features of Root Formation in Spruce and Mixed Stands after Improvement Thinning in South Karelia. Aktual’nye problemy lesnogo kompleksa, 2007, no. 17, pp. 160–163. (In Russ.).
7. Korotyuk O.M. The Importance and Problems of Improvement Thinning. Trudy Bratskogo gosudarstvennogo universiteta. Seriya: Estestvennye i inzhenernye nauki – razvitiyu regionov Sibiri = Proceedings of the Bratsk State University. Series: Natural and Engineering Sciences for the Development of Siberian Regions, 2009, vol. 1, pp. 142–147. (In Russ.).
8. Kuz’michev V.V. Patterns of Stand Growth. Novosibirsk, Nauka Publ., 1977. 150 p. (In Russ.).
9. Maslakov E.L. Formation of Pine Young Stands. Moscow, Lesnaya promyshlennost’ Publ., 1984. 168 p. (In Russ.).
10. Mikhailova L.M., Kunitskaya O.A., Motovilov A.I. Prospects for Machine Systems Based on Low-Mechanization Tools for Small-Volume Logging and Forestry Operations. Strategiya i perspektivy razvitiya agrotekhnologij i lesnogo kompleksa Yakutii do 2050 goda: Collection of Scientific Articles Based on the Materials of the All-Russian Scientific and Practical Conference with International Participation Dedicated to the 100th Anniversary of the Formation of the Yakut ASSR and the 85th Anniversary of the First President of the Republic of Sakha (Yakutia) M. E. Nikolaev (Nikolaev Readings), 2022, pp. 735–742. (In Russ.).
11. Mikhailova N.V., Mikhailov A.V. Three-Dimensional Simplified Model of Light Competition of Trees in a Forest. Matematicheskoe modelirovanie v ekologii: Materials of the National Conference with International Participation. Pushchino, Institute of Physicochemical and Biological Problems in Soilscience of the Russian Academy of Sciences, 2009, pp. 178–179. (In Russ.).
12. Morkovina S.S. Financial Support for the Digital Transformation of Forestry in the Russian Federation. Aktual’nye voprosy teorii i praktiki finansovo-khozyajstvennoj deyatel’nosti: Collection of Materials of the 2nd All-Russian (National) Scientific and Practical Conference. Voronezh, Nauchnaya kniga Publ., 2020, pp. 109–112. (In Russ.).
13. Morkovina S.S., Panyavina E.A., Avdeeva I.A. Study of the System of Rationing in Forestry of Russia. Lesotekhnicheskij zhurnal = Forestry Engineering Journal, 2019, vol. 9, no. 1 (33), pp. 176–187. (In Russ.). https://doi.org/10.12737/article_5c9201723dbb21.63764253
14. Morkovina S.S., Topcheev A.N. Digitalization in the Forestry Sector: Prospects and Potential. Sovremennye tendentsii razvitiya menedzhmenta i gosudarstvennogo upravleniya: Materials of the Interregional Correspondence Scientific and Practical Conference: in 2 vol. Ed. by A.V. Polyanin. Oryol, Central Russian Institute of Management – Branch of The Russian Presidential Academy of National Economy and Public Administration, 2019, pp. 125–127. (In Russ.).
15. Morkovina S.S., Shanin I.I. Application of Digital Technologies in the Forestry Complex. Vyzovy tsifrovoj ekonomiki: razvitie komfornoj gorodskoj sredy: Proceedings of the 3rd All-Russian Scientific and Practical Conference with International Participation, 2020, pp. 553–555. (In Russ.).
16. Rubtsov M.V. Structural Transformation of Monodominant Forest Stand Communities in Age Dynamics: Research Effort: Grant no. 96-04-49836. The Russian Foundation for Basic Research, 1996. (In Russ.).
17. Sekretenko O.P., Grabarnik P.Y. Analysis of Tree Stand Horizontal Structure Using Random Point Field Methods. Sibirskij lesnoj zhurnal = Siberian Journal of Forest Science, 2015, no. 3, pp. 32–44. (In Russ.).
18. Sennov S.N. Dynamics of Spruce Stands of Different Origins. Lesovedenie = Russian Journal of Forest Science, 1992, no. 1, p. 3. (In Russ.).
19. Sennov S.N. The Results of an Experimental Study of Competition in Stands. Izvestia Sankt-Peterburgskoj lesotehnicheskoj akademii, 1993, no. 11, p. 160. (In Russ.).
20. Sennov S.N. The Results of an Experimental Study of Tree Relationships in Mixed Plantations. Izvestia Sankt-Peterburgskoj lesotehnicheskoj akademii, 2003, no. 170, pp. 21–31. (In Russ.).
21. Sennov S.N., Melnikov E.S. Peculiarities of Interspecific Relationships Between Trees. Izvestia Sankt-Peterburgskoj lesotehnicheskoj akademii, 1996, no. 4, p. 39. (In Russ.).
22. Terskov I.A., Terskova M.I. On the Regularities of the Thinning Process of Light-Limited Stands. Mathematical Analysis of the Components of Forest Biogeocenoses. Novosibirsk, Nauka Publ., 1979, pp. 25–44. (In Russ.).
23. Trushevskij P.V., Kunitskaya O.A. The Influence of Technology and the System of Forestry Machines on the Concentration of Logging Residues. Aktual’nye problemy lesnogo khozyajstva i derevopererabotki: Materials of the All-Russian Scientific and Practical Conference. Ed. by Yu.M. Kazakov et al. Kazan, Kazan National Research Technological University, 2023, pp. 110–113. (In Russ.).
24. Trushevskij P.V., Kunitskaya O.A. Modern Systems of Machines for Clearing Cutting Areas from Logging Residues. Aktual’nye problemy lesnogo khozyajstva i derevopererabotki: Materials of the All-Russian Scientific and Practical Conference. Ed. by Yu.M. Kazakov et al. Kazan, Kazan National Research Technological University, 2023, pp. 121–126. (In Russ.).
25. Berglin E., Brodal G.S. A Simple Greedy Algorithm for Dynamic Graph Orientation. Algorithmica, 2020, vol. 82, pp. 245–259. https://doi.org/10.1007/s00453-018-0528-0
26. Hertz E., Kunickaya O., Runova E., Tikhonov E., Timokhov R., Mikhaylenko E., Chemshikova Ju., Perfiliev P. Forest Preservation Techniques in the Urals. International Journal of Environmental Studies, 2023, vol. 80, iss. 4, pp. 1055–1064. https://doi.org/10.1080/00207233.2022.2096959
27. Karp R.M. Reducibility Among Combinatorial Problems. 50 Years of Integer Programming 1958–2008. Berlin, Heidelber, Springer, 2010, pp. 219–241. https://doi.org/10.1007/978-3-540-68279-0_8
28. Morkovina S.S., Kunickaya O., Dolmatova L., Markov O., Nguyen V.L., Baranova T., Shadrina S., Grin’ko O. Comparative Analysis of Economic Aspects of Growing Seedlings with Closed and Open Root Systems: The Experience of Russia. Asian Journal of Water, Environment and Pollution, 2021, vol. 18, iss. 2, pp. 19–26. https://doi.org/10.3233/AJW210015
29. Rego G.E., Grigoreva O.I., Voronov R.V. Algorithms for Calculating Schemes of Transport Routes in a Felling Area. IOP Conference Series: Earth and Environmental Science, 2021, vol. 806, art. no. 012025. https://doi.org/10.1088/1755-1315/806/1/012025
30. Ryabukhin P., Kunickaya O., Burgonutdinov A., Makuev V., Sivtseva T., Zadrauskaite N., Hertz E., Markov O. Improving the Efficiency of Forest Companies by Optimizing the Key Indicators of Sustainable Forest Management: a Case Study of the Far East. Forest Science and Technology, 2022, vol. 18, iss. 4, pp. 190–200. https://doi.org/10.1080/21580103.2022.2128900
31. Ryan C.T., Smith R.L. A Greedy Algorithm for Finding Maximum Spanning Trees in Infinite Graphs. Operations Research Letters, 2022, vol. 50, iss. 6, pp. 655–659. https://doi.org/10.1016/j.orl.2022.10.004