Registration Number
0223U001875,
0122U200404
, R & D reports
Title
Develop mathematical models and methods for solving optimization problems, computational mathematics and recognition to build supercomputer technologies.
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Head
Sergienko Ivan V., Доктор фізико-математичних наук
Registration Date
04-02-2023
Organization
V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine
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A theoretical study of the efficience of combinations (portfolios and teams) of algorithms was conducted. It is found that the team approach provides a super-linear acceleration of the search for high-quality solutions, and the portfolio of algorithms approaches a linear speed-up factor. Conditions for the existence and stability of solutions of vector optimization problems with continuous criteria functions and an feasible set of arbitrary structure under perturbances of vector criterion input data are established. This opens wide prospects for the regularization of these incorrectly formulated problems and the construction of effective methods for their solution. Mathematical models of parameter identification for problems of mass transfer substances in the form of a different-scale differential mathematical problem in a nanoporous medium were studied. Generalized problems and corresponding conjugate problems are constructed. On the basis of the theory of optimal control of the state of multi-component distributed systems, explicit expressions of the gradients of non-linear functionals are obtained for the identification of some parameters of the presented initial-boundary problems by gradient methods. A methodology for search diversification in ant colony optimization algorithms has been developed, which allows expanding the scope of search in these algorithms, creating conditions for finding improved solutions by avoiding premature convergence. This strategy can be used in any modification of ant algorithms, making it a universal means of improving the efficiency of algorithms of this family. New methods of machine learning for decision-making problems based on dynamic fuzzy knowledge representation networks have been developed. Modifications of Bayesian procedures for recognizing inflammatory processes in brain gliomas based on erythrocyte sedimentation rate indicators have been developed. A database of amino acid sequences of proteins, values of torsion angle
Product Description
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Vareniuk Nataliia A.
Gulyanitskyi Leonid F.
Gupal Anatoliy M.
Semenova Nataliia V.
Shylo Volodymyr P.
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2023-02-04
