Stoyan Y.G., Yakovlev S.V.
Theory and methods of Euclidian combinatorial optimization: current state and prospects

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 reviewed. 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. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: combinatorial configuration, Euclidean combinatorial set, Euclidean models, optimization, Optimization, Combinatorial optimization problems, Continuous functionals, Current status, Discrete optimization problems, Euclidean, Euclidean spaces, Theory and methods, Combinatorial optimization

Cite:
Stoyan Y.G., Yakovlev S.V. (2020). Theory and methods of Euclidian combinatorial optimization: current state and prospects. Cybernetics and Systems Analysis, 56 (3), 30–46. doi: https://doi.org/10.1007/s10559-020-00253-6 http://jnas.nbuv.gov.ua/article/UJRN-0001121517 [In Russian].