A mathematical model for optimizing the design of a forest highway network using remote sensing data

Effective design of forest road networks is crucial for optimizing logging costs, forest management, and sustainable access to resources. Traditional approaches often suffer from high costs, labor intensity, and limited accuracy of initial data, especially in complex terrain and dense forests. This article presents a mathematical model for computer-aided design and optimization of forest road routes. The project area is discretized as a weighted graph, with nodes representing points on the digital terrain model (DEM) and arcs representing potential road segments. The model aims to minimize total construction cost, considering segment length, terrain, longitudinal slope (affecting earthwork volumes) via a special appreciation coefficient, and the need for culverts at watercourse crossings. Special attention is given to integrating highly detailed terrain data obtained through airborne laser scanning (LiDAR), including unmanned aerial vehicles (UAVs). LiDAR enables high-precision DEMs that penetrate the forest canopy, which is essential for accurate terrain modeling, identifying optimal corridors, obstacles (e.g., waterlogged or landslide-prone areas), and optimizing earthwork volumes. The article details the mathematical formulation as a shortest path problem on a graph, with a cost-minimizing objective function and constraints. Methods for extracting initial data from LiDAR point clouds are discussed: DEM creation, elevation extraction, slope calculation, and hydrographic network analysis using GIS. The developed model, utilizing optimal path algorithms (Dijkstra, A*), provides an objective, efficient, and economically justified choice of forest road routes, enhancing design quality. The authors also discuss prospects for further model development, including integrating soil type data.

1. Abdelwahab M.A.Kh. Substantiation of methodology for designing earthwork production during the construction of timber transport roads: author’s abstract. Diss. … Cand. Tech. Sci. St. Petersburg, 2020. 20 p. (In Russ.)

2. Akay A. E. Minimizing total costs of forest roads with computer-aided design model. Sadhana, 2006, vol. 31, iss. 5, pp. 621–633.

3. Hatta Antah F., Khoiry M.A., Abdul Maulud K.N., Abdullah A. Perceived Usefulness of Airborne LiDAR Technology in Road Design and Management: A Review. Sustainability, 2021, vol. 13, art. no. 11773.

4. Heinimann H.R. Forest Road Network and Transportation Engineering – State and Perspectives. Croatian journal of forest engineering, 2017, vol. 38, iss. 2, p. 155–173.

5. Hrůza P., Mikita T., Tyagur N., Krejza Z., Cibulka M., Procházková A., Patočka Z. Detecting Forest Road Wearing Course Damage Using Different Methods of Remote Sensing. Remote Sensing, 2018, vol. 10, iss. 4, art. no. 492.

6. İnan M., Öztürk T. A simple approach on forest roads drainage structures planning using GIS: A case study of Şile-Turkey. Anatolian Journal of Forest Research, 2022, vol. 8, iss. 2, pp. 104–110.

7. Jaafari A., Pazhouhan I., Bettinger P. Machine Learning Modeling of Forest Road Construction Costs. Forests, 2021, vol. 12, iss. 9, art. no. 1169.

8. Kardoš M., Sačkov I., Tomaštík J., Basista I., Borowski Ł., Ferenčík M. Elevation Accuracy of Forest Road Maps Derived from Aerial Imaging, Airborne Laser Scanning and Mobile Laser Scanning Data. Forests, 2024, vol. 15, iss. 5, art. no. 840.

9. Katarov V.K., Rozhin D.V., Syunyov V.S. Optimal Design of Forest Road Networks: From Methods to Solutions. Resources and Technology, 2023, vol. 20, no. 3, pp. 32–47. (In Russ.)

10. Krogstad F., Schiess P. The allure and pitfalls of using LiDAR topography in harvest and road design. Joint Conference of IUFRO 3.06 Forest Operations under Mountainous Conditions and the 12th International Mountain Logging Conference. 2004, 10 p.

11. Layton D.A., LeDoux C.B., Hassler C.C. Cost Estimators for Construction of Forest Roads in Central Appalachians. USDA Forest Service, NE-RP-665, 1992. 4 p.

12. Matinnia B., Parsakhoo A., Mohamadi J., Shataee Jouibary S. Study of the LiDAR accuracy in mapping forest road alignments and estimating the earthwork volume. Journal of Forest Science, 2018, vol. 64, iss. 11, pp. 469–477.

13. Pyatin D.S. Improving Methods for Solving the Problem of Automated Planning of Forest Road Networks. Engineering Bulletin of the Don, 2020, no. 4 (64), art. no. 6428. (In Russ.)

14. Shin J. Road-network location heuristics for the tactical harvest scheduling model: master's thesis. Lakehead University, 2022. 53 p.

15. Watanabe M., Saito M., Toda K., Shirasawa H. Rain-Driven Failure Risk on Forest Roads around Catchment Landforms in Mountainous Areas of Japan. Forests, 2023, vol. 14, iss. 3, art. no. 537.