Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

TitleStability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions
Publication TypeJournal Article
Year of Publication2020
AuthorsLebedeva, ТТ, Semenova, NV, Sergienko, TI
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2020.10.015
Issue10
SectionInformation Science and Cybernetics
Pagination15-21
Date Published10/2020
LanguageUkrainian
Abstract

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

Keywordsmixed integer optimization problem, Pareto-optimal solutions, perturbations of initial data, stability, vector criterion
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