Pichugina O.S., Yakovlev S.V.
Continuous representations and functional extensions in combinatorial optimization

The concepts of functional representation of a set of points of the Euclidean arithmetic space and an extension of functions from the set onto its superset are introduced. Functional representations of sets are related to their extensions. Strict functional representations of the Boolean set, general permutation, and polypermutation sets are derived. The advantages of applying strict representations of Euclidean combinatorial sets to construct functional extensions from them and to solve combinatorial problems are presented. © 2016, Springer Science+Business Media New York.

Keywords: Boolean set, combinatorial optimization, continuous functional representation of a set, Euclidean combinatorial set, extension of functions, general set of permutations, Computer science, Cybernetics, Boolean set, Combinatorial problem, Continuous functionals, Euclidean, Functional extension, Functional representation, general set of permutations, Combinatorial optimization

Cite:
Pichugina O.S., Yakovlev S.V. (2016). Continuous representations and functional extensions in combinatorial optimization. Cybernetics and Systems Analysis, 52 (6), 102-113. doi: https://doi.org/10.1007/s10559-016-9894-2 http://jnas.nbuv.gov.ua/article/UJRN-0000582980 [In Russian].