The paper considers the problem of optimizing the placement of sensors in hybrid positioning systems operating in dynamic production environments. Modern industrial facilities are characterized by a variable structure, the presence of mobile elements, complex topology, and equipment installation restrictions, which necessitates effective approaches to the design of positioning systems. The aim of the study is to develop a method and algorithm for placing sensors (anchors) at industrial facilities, taking into account the criticality of certain areas of the site, which makes it possible to ensure the required positioning accuracy at minimal equipment costs. A methodology for creating hybrid positioning systems based on zoning the space of an industrial facility and using fragmentary structures is proposed. To ensure the necessary accuracy and reliability, taking into account spatial and economic criteria, a metaheuristic evolutionary algorithm is used, which makes it possible to obtain a suboptimal solution. The algorithm is implemented using a greedy strategy and further adaptation of the population based on mutations and selection. The method allows to take into account the site configuration, technical limitations of positioning technologies' radii of action, and requirements for coverage density. Methods of discretizing the site into polygons that can be defined by geometric shapes are considered. The novelty of the study is the development of a method for placing sensors (anchors) at industrial facilities, taking into account the criticality of individual areas of the industrial site, which makes it possible to create hybrid systems and integrate different technologies. The practical value lies in the development of an algorithm for optimizing the placement of sensors for the design of positioning systems on dynamic objects with a complex structure, in particular, in construction, logistics, and industry. Further research involves expanding the possibilities of using the method by taking into account the scaling of objects, comparing different metaheuristic optimization strategies.
[1] Moreno-Salinas D., Pascoal A.M., Aranda J. Optimal Sensor Placement for Multiple Target Positioning with Range-Only Measurements in Two-Dimensional Scenarios // Sensors. — 2013. — Vol. 13, No. 8. — P. 10674–10710. [Електронний ресурс]. Режим доступу: https://doi.org/10.3390/s130810674
[2] Wang Y., Ma S., Li X. Spatial Positioning Method Based on Range-Only Measurement of Multi-Station Radar // Heliyon. — 2023. — Vol. 9, Issue 12. — Article e21193. [Електронний ресурс]. Режим доступу: https://doi.org/10.1016/j.heliyon.2023.e21193
[3] Crespillo M., González-García C., Elosegui P., de Vicente P. Sensor Placement in an Irregular 3D Surface for Improving Localization Accuracy // Sensors. — 2023. — Vol. 23, No. 14. — Article 6316. [Електронний ресурс]. Режим доступу: https://doi.org/10.3390/s23146316
[4] Moreno-Salinas D., Aranda J., Pascoal A.M. Genetic Algorithm to Solve Optimal Sensor Placement for Underwater Vehicle Localization // Sensors. — 2022. — Vol. 22, No. 20. — Article 7655. [Електронний ресурс]. Режим доступу: https://doi.org/10.3390/s22207655
[5] Shahmansoori A., Chorti A., Poor H.V. Stealthy Optimal Range-Sensor Placement for Target Localization // arXiv preprint. — 2023. [Електронний ресурс]. Режим доступу: https://arxiv.org/abs/2412.04316
[6] Goldberg D. E. Genetic Algorithms in Search, Optimization, and Machine Learning. — Addison-Wesley, 1989. — 412 p.
[7] Deb K. Multi-objective Optimization Using Evolutionary Algorithms. — Wiley, 2001. — 528 p.
[8] I. V. Kozin, Fragment structures and evolutionary algorithms, in: O. Kiselyova (Ed.), Problems of applied mathematics and mathematical modeling: Collection of scientific works, Oles Honchar Dnipropetrovsk National University, 2008, pp. 138–146. ISSN 2074-5893.
[9] I. V. Kozin, N. K. Maksyshko, V. A. Perepelitsa, Fragmentary structures in discrete optimization problems 53 (2017) 931–936. doi:10.1007/s10559-017-9995-6.
[10] I. V. Kozin, S. I. Polyuga, On properties of fragmentary structures (2012) 99–106. URL: https: //web.znu.edu.ua/herald//issues/2012/mat-1-2012/099-106.pdf