|Lebedeva, ТТ |
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
|Dopov. Nac. akad. nauk Ukr. 2020, 10:15-21|
|Section: Information Science and Cybernetics|
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.
|Keywords: mixed integer optimization problem, Pareto-optimal solutions, perturbations of initial data, stability, vector criterion|
1. Podinovsky, V. V. & Nogin, V. D. (1982). Pareto optimal solutions in multicriteria problems. Moscow: Nauka (in Russian).
2. Kozeratskaya, L. N., Lebedeva, T. T. & Sergienko, I. V. (1991). Mixed integer vector optimization problem: stability questions. Cybernetics, 27, No. 1, pp. 76-80.
3. Lyashko, I. I., Emelyanov, V. F. & Boyarcyuk, O. K. (1992). Mathematical analysis. Part. 1. Kyiv: Visha shcola. (in Ukrainian).
4. Lebedeva, T. T., Semenova, N. V. & Sergienko, T. I. (2014). Qualitative characteristics of the stability vector discrete optimization problems with different optimality principles. Cybernetics and Systems Analysis, 50, No. 2, pp. 228-233.
5. Lebedeva, T. T., Semenova, N. V. & Sergienko, T. I. (2005). Stability of vector problems of integer optimization: relationship with the stability of sets of optimal and nonoptimal solutions. Cybernetics and Systems Analysis, 41, No. 4, pp. 551-558.