Application of interval mathematical models of optimization placement problems of geometric objects

Authors

DOI:

https://doi.org/10.15587/1729-4061.2015.36753

Keywords:

geometric design, interval geometry, interval mathematical model, optimization

Abstract

At present, the methods of mathematical modeling of real objects and processes play an important role in developing systems, aimed at processing geometric information. Such systems are based on mathematical models of real world objects, optimization methods and theory of building intelligent systems. The research is focused on the applied aspects of interval mathematical modeling in a geometric design.

The classification of implementations of the interval mathematical model of the basic interval optimization placement problem, many implementations of which covers a broad class of scientific and applied placement problems, according to the type of classification of mathematical programming problems was performed.

Various types of interval mappings of interval mathematical models in Euclidean space for the transition from the optimization problem in interval space to an equivalent optimization problem in Euclidean space were constructed.

The method for solving the interval optimization problem in  as the two-criteria optimization problem in Euclidean space  was further developed.

New science-based developments in the theory of geometric design and interval geometry provide a solution to the important applied problem of accounting errors in modeling and solving optimization problems of geometric design.

The proposed tools for mathematical modeling and solving interval optimization placement problems were used in developing computer programs: "PackingofIntervalParallelepipeds", "PackingofIntervalPolygons", "Simulation of alloy properties".

Author Biography

Людмила Григорівна Євсеєва, Poltava interregional higher vocational school, st. Bіryuzova 64 a, Poltava, Ukraine, 36009

Candidate of Physical and Mathematical Sciences, Associate Professor

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Published

2015-02-27

How to Cite

Євсеєва, Л. Г. (2015). Application of interval mathematical models of optimization placement problems of geometric objects. Eastern-European Journal of Enterprise Technologies, 1(4(73), 18–26. https://doi.org/10.15587/1729-4061.2015.36753

Issue

Vol. 1 No. 4(73) (2015): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2015 Людмила Григорівна Євсеєва

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