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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.85
Yu.G. Stoyan1, S.V. Yakovlev2


1 A. Pidgorny Institute of Mechanical Engineering Problems
of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine

2 N.Ye. Zhukovskiy National Aerospace University
“Kharkiv Aviation Institute,” Kharkiv, Ukraine

svsyak7@gmail.com

THEORY AND METHODS OF EUCLIDIAN COMBINATORIAL OPTIMIZATION:
CURRENT STATE AND PROSPECTS

Abstract. Euclidean combinatorial optimization problems are considered as discrete optimization problems on a set of combinatorial configurations mapped into an arithmetic Euclidean space. Modern methods of Euclidean combinatorial optimization are overviewed. The properties of the corresponding images of combinatorial sets are described. A theory of continuous functional representations and convex extensions is proposed for solving this class of problems. Areas of practical application and promising research areas are indicated.

Keywords: combinatorial configuration, Euclidean combinatorial set, Euclidean models, optimization.



FULL TEXT

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