The Emergence and Formation  of the Theory of Optimal Set Partitioning  for Sets of the n Dimensional Euclidean Space. Theory and Application

Elena M. Kiseleva

doi:10.1615/JAutomatInfScien.v50.i9.10

Journal of Automation and Information Sciences

Éditeur en chef: Arkadiy A. Chikriy (open in a new tab)

Éditeur associés: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

Publication de 12 numéros par an

ISSN Imprimer: 1064-2315

ISSN En ligne: 2163-9337

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The Emergence and Formation of the Theory of Optimal Set Partitioning for Sets of the n Dimensional Euclidean Space. Theory and Application

Volume 50, Numéro 9, 2018, pp. 1-24

DOI: 10.1615/JAutomatInfScien.v50.i9.10

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Elena M. Kiseleva
Oles Honchar Dnipro National University, Dnepr

RÉSUMÉ

The history of emergence and formation, the structure and main results of the theory of optimal set partitioning which was developed during the previous fifty years by the author and her students are presented. The examples of OSP application to the variety of essentially different theoretical optimization problems that can be interpreted mathematically as continuous optimal set partitioning problems are described. The real-world applications of the theory are illustrated by the example of solving the generalized location–allocation problem. The future directions of the optimal set partitioning theory are discussed.

MOTS CLÉS: optimal set partitioning, generalized location–allocation problem, theoretical optimization problems, sets of Euclidean space

CITÉ PAR

Komyak Valentina, Sobol Oleksandr, Kartashov Oleksii, Yakovleva Iryna, Komyak Vladimir, Danilin Alexander, Lyashevskaya Olena, Computer simulation of the partitioning by mutually orthogonal lines, 2019 IEEE 15th International Conference on the Experience of Designing and Application of CAD Systems (CADSM), 2019. Crossref
Kiseleva Å. Ì., Prytomanova O. M., Us S. A., Solving a Two-Stage Continuous-Discrete Problem of Optimal Partition–Allocation with a Given Position of the Centers of Subsets, Cybernetics and Systems Analysis, 56, 1, 2020. Crossref
Kiseleva Olena, Prytomanova Olga, Serhieiev Oleksii, An Algorithm for Solving the Optimal Set Partitioning Problem with Constraints on the Centers Location, 2020 IEEE 2nd International Conference on System Analysis & Intelligent Computing (SAIC), 2020. Crossref
Kiseleva Elena, Prytomanova Olga, Padalko Vadim, An Algorithm for Constructing Additive and Multiplicative Voronoi Diagrams Under Uncertainty, in Lecture Notes in Computational Intelligence and Decision Making, 1246, 2021. Crossref
Hart Liudmyla, Combined Approach to Solving the Neumann Problem for a Parametric Quasilinear Elliptic Equation, in Advances in Computer Science for Engineering and Manufacturing, 463, 2022. Crossref
Kiseleva Elena, Prytomanova Olga, Hart Liudmyla, Blyuss Oleg, Application of the Theory of Optimal Set Partitioning for Constructing Fuzzy Voronoi Diagrams, in System Analysis & Intelligent Computing, 1022, 2022. Crossref

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