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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Druckformat: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v52.i2.20
pages 13-26

Optimization of Partitioning the Domain into Subdomains According to Given Limitation of Space

Valentina M. Komyak
National University of Civil Defense of Ukraine, Kharkov
Alexander N. Sobol
National University of Civil Defense of Ukraine, Kiev
Alexander N. Danilin
National University of Civil Defense of Ukraine, Kharkov
Vladimir V. Komyak
National University of Civil Defense of Ukraine, Kharkov
Kyazim Takhir ogly Kyazimov
Academy of Ministry of Emergency Situations of Azerbaijan, Baku (Azerbaijan)


The tasks of geometric design (packaging, layout, coating, partitioning) consists in optimizing the display of geometric information about objects in accordance with a given quality criterion and limitations. The geometric information about a geometric object consists of three components: spatial form, metric form 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 many objects onto their configuration space according to a given set of restrictions defines the spatial configuration of geometric objects. The article introduces the concept of the spatial configuration of partitioning a domain into subdomains via which a new model of its partitioning into two types of subdomains is constructed, each of which is divided into subdomains according to different quality criteria and limitations. As an example, the problem of partitioning a three-dimensional domain (building) into two types of subdomains has been solved, the former is the subdomains for the functional purpose (premises) with maximization of their volumes taking into account design standards. The latter is the subdomains 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 constraints on both the flow parameters of the people and the metric characteristics of the routes in view of the design standards. Petri nets are used to calculate the time of movement of homogeneous flows of people, and their sequential individual and flow movement is used for the heterogeneous flows of people. 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 vehicles compartments during cargo transportation and storage in pattern recognition systems, robotics, etc.


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