Modeling and Simulation of Coverage Problem in Geometric Design Systems

Yakovlev, Sergiy; Kartashov, Oleksii; Komyak, Valentina; Shekhovtsov, Sergiy; Sobol, Oleksandr; Yakovleva, Iryna

doi:10.1109/cadsm.2019.8779303

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…For the analytical description of these limitations, the phi-function apparatus has been advanced, in particular, quasi-phi functions, which showed its effectiveness and adequacy in solving multi-numerical applied optimization problems for the arrangement of three-dimensional bodies and two-dimensional objects (cutting, packing, and coverage) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Discussion Of Results From the Implementation Of The Constructed Mathematical Models And Their Practical Usementioning

confidence: 99%

“…That makes it possible to describe the optimization tasks of geometric design (cutting, packing, covering, and partitioning) in the form of nonlinear programming tasks and has a wide range of applications. Thus, the theory of optimization geometric design [3] is intended to solve a series of applied optimization problems of packing [14], parsing [15], coverage [16], traced coverage [17]. These tasks relate to devising energy-and resource-saving technologies in priority sectors of the national economy in the automation and modeling of the processes of arrangement of objects of different physical nature.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Building a model and an algorithm for modeling the movement of people carrying goods when they are evacuated from premises

Pankratov

Komyak

Kyazimov

et al. 2021

EEJET

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Evacuation is often the only way to save a person who is in a life-threatening situation. At present, evacuation software is used to simulate the movement of human flows, which does not always reflect the real processes of their movement. Therefore, it is a relevant task to build models for modeling the movement of human flows for different types of emergencies, different categories of human movement, and various spatial forms of their representation. Such a task arises when evacuating people from premises for various functional purposes. During evacuation, people often carry some goods. When people move carrying some goods, their horizontal projection takes a more complex shape than an ellipse or circle considered in earlier studies. Moreover, in practice, there is often a task to model the movement of people taking into consideration the maximum permissible distances between them. This paper reports the new quasi-phi functions of interaction between the ellipse and rectangle accounting for the maximum allowable distances between them. The proposed mathematical apparatus has made it possible to formalize the interaction between objects, thereby enabling the construction of a well-substantiated mathematical model, as well as the methods and algorithms for modeling the movement of people carrying some goods. The possibility to simulate the movement of people with certain objects has shown taking into consideration the maximum permissible distances between them. A test example of the movement of people along four corridors was simulated, in each of which there were 28 people subsequently merging into one flow. Given the uniform distribution of three types of cargo: «backpacks», «suitcases», and «bags on wheels», the movement slowed down by about 4 %. When half of the evacuees had «bags on wheels» that can move away from people at arm’s length, the slowdown was about 6 %.

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Section: Discussion Of Results From the Implementation Of The Constructed Mathematical Models And Their Practical Usementioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Building a model and an algorithm for modeling the movement of people carrying goods when they are evacuated from premises

Pankratov

Komyak

Kyazimov

et al. 2021

EEJET

Self Cite

View full text Add to dashboard Cite

show abstract

“…The two-stage scheme presented in Section 2 can be applied for the general optimized multi-spherical covering. An extension of the covering approach to the case of more complex objects [33][34][35][36] is an interesting direction for the future research. Some results on this topic are on the way.…”

Section: Discussionmentioning

confidence: 99%

An Optimized Covering Spheroids by Spheres

et al. 2020

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Covering spheroids (ellipsoids of revolution) by different spheres is studied. The research is motivated by packing non-spherical particles arising in natural sciences, e.g., in powder technologies. The concept of an ε -cover is introduced as an outer multi-spherical approximation of the spheroid with the proximity ε . A fast heuristic algorithm is proposed to construct an optimized ε -cover giving a reasonable balance between the value of the proximity parameter ε and the number of spheres used. Computational results are provided to demonstrate the efficiency of the approach.

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“…Currently, there is a rapidly growing interest in the effective solution of the problems of optimum coverage of areas with circles known as the problems of circular coverage (see, e.g., [1,2]). One of the interesting application of coverage problems in the geometric design systems is considered in [3,4].…”

Section: Introductionmentioning

confidence: 99%

Covering an Arbitrary Shaped Domain by Identical Circles

Pankratov¹,

Romanova²,

Antoshkin³

et al. 2019

Proceedings of the 21st International Workshop on Computer Science and Information Technologies (CSIT 2019)

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The problem of covering a bounded disconnected arbitrary shaped area (domain) by identical circles is considered. To describe analytically the coverage conditions we use special continuous and everywhere defined functions for modelling relations between circles and the border of the area. A new function for modelling the relations between three circles when covering the interior part of the domain is defined. An integrated mathematical model of the coverage problem is provided in the form of a nonlinear programming problem. A new strategy for solving the problem is proposed. To demonstrate the efficiency of the developed algorithm an example of solving the problem for optimizing the length of the network connecting centers of the circles is presented.

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Modeling and Simulation of Coverage Problem in Geometric Design Systems

Cited by 5 publications

References 11 publications

Building a model and an algorithm for modeling the movement of people carrying goods when they are evacuated from premises

Building a model and an algorithm for modeling the movement of people carrying goods when they are evacuated from premises

An Optimized Covering Spheroids by Spheres

Covering an Arbitrary Shaped Domain by Identical Circles

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