ОПТИМІЗАЦІЯ РОЗБИТТЯ ОБЛАСТІ НА ПІДОБЛАСТІ ЗА ЗАДАНИМИ ОБМЕЖЕННЯМИ У ПРОСТОРІ

• Дата: 2020
• Автори: Komyak, V.M., Sоbоl, A.N., Danilin, A.N., Komyak, V.V., Kyazimov, K.T.
• Формат: Стаття
• Мова: English
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Теми: геометричний об'єкт; геометрична інформація; розбиття; трасування; конфігураційний простір; узагальнені змінні; математична модель; оптимізація
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/443
• Назва журналу: Problems of Control and Informatics

The tasks of geometric design (packaging, layout, covering, partitioning) consist in optimizing the display of geometric information about objects in accordance with a given quality criterion and limitations. Geometrical information about a geometrical object consists of three components: spatial shape, metric shape parameters that determine their sizes and spatial placement parameters. The configuration space of geometric objects is based on the formalization of the concept of geometric information. The mapping of multiple objects into their configuration space according to a given set of constraints defines the spatial configuration of geometric objects. The article introduces the concept of the spatial configuration of partitioning an area into subareas, with the help of which a new model of its partitioning into two types of subareas is constructed, each of which is divided into subareas according to different quality criteria and restrictions. As an example, the problem of partitioning a threedimensional area (building) into two types of subareas has been solved, the first is subareas for functional purpose (premises) with maximization of their volumes, taking into account design standards. The second is subareas that determine a rational network of routes, according to a given criterion, an example of which is the time of complete evacuation of people from a building with restrictions on both the flow parameters of the people and the metric characteristics of the routes, taking into account design standards. Petri nets are used to calculate the time of movement of homogeneous flows of people, and individual-and-flow movement are used for heterogeneous flows of people with normalized density. Consideration of metric characteristics and placement parameters of objects as generalized independent variables will allow us to propose new mathematical models and optimization methods for synthesizing spatial configurations in the future and can be used, for example, when partitioning vehicle compartments during cargo transportation and storage, in pattern recognition systems, robotics, etc.