Abstract
The conditions of stability against input data perturbations in vector-valued criterion for multi-objective optimization problem with continuous partial criterion functions and feasible set of arbitrary structure are established. The sufficient and necessary conditions of three types of stability for the problem of finding Pareto optimal solutions are proved.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
L. N. Kozeratskaya, T. T. Lebedeva, and T. I. Sergienko, “Mixed integer vector optimization. Stability issues,” Cybern. Syst. Analysis, Vol. 27, No. 1, 76–80 (1991).
L. N. Kozeratskaya, “Vector optimization problems: Stability in the decision space and in the space of alternatives,” Cybern. Syst. Analysis, Vol. 30, No. 6, 891–899 (1994).
I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability Analysis and Parametric Analysis of Discrete Optimization Problems [in Russian], Naukova Dumka, Kyiv (1995).
T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Stability of vector problems of integer optimization: Relationship with the stability of sets of optimal and nonoptimal solutions,” Cybern. Syst. Analysis, Vol. 41, No. 4, 551–558 (2005).
T. T. Lebedeva and T. I. Sergienko, “Stability of a vector integer quadratic programming problem with respect to vector criterion and constraints,” Cybern. Syst. Analysis, Vol. 42, No. 5, 667–674 (2006).
T. T. Lebedeva and T. I. Sergienko, “Different types of stability of vector integer optimization problem: General approach,” Cybern. Syst. Analysis, Vol. 44, No. 3, 429–433 (2008).
T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Qualitative characteristics of the stability vector discrete optimization problems with different optimality principles,” Cybern. Syst. Analysis, Vol. 50, No. 2, 228–233 (2014).
I. V. Sergienko, T. T. Lebedeva, and N. V. Semenova, “Existence of solutions in vector optimization problems,” Cybern. Syst. Analysis, Vol. 36, No. 6, 823–828 (2000).
T. I. Sergienko, “Conditions of Pareto optimization problems solvability. Stable and unstable solvability,” in: S. Butenko, P. Pardalos, and V. Shylo (eds.), Optimization Methods and Applications, Vol. 130, Springer Optimization and Its Applications, Springer, Cham (2017), pp. 457–464.
V. A. Emelichev and K. G. Kuzmin, “Stability radius of a vector integer linear programming problem: Case of a regular norm in the space of criteria,” Cybern. Syst. Analysis, Vol. 46, No. 1, 72–79 (2010).
V. A. Emelichev, V. M. Kotov, K. G. Kuzmin, T. T. Lebedeva, N.V. Semenova, and T.I. Sergienko, “Stability and effective algorithms for solving multiobjective discrete optimization problems with incomplete information,” J. Autom. Inform. Sci., Vol. 46, No. 2, 27–41 (2014).
V. Emelichev and Yu. Nikulin, “On the quasistability radius for a multicriteria integer linear programming problem of finding extremum solutions,” Cybern. Syst. Analysis, Vol. 55, No. 6, 949–957 (2019).
V. V. Podinovskii and V. D. Nogin, Pareto Optimal Solutions to Multi-objective Problems [in Russian], Nauka, Moscow (1982).
I. I. Lyashko, V. F. Emel’yanov, and O. K. Boyarchuk, Mathematical Analysis, Pt. 1 [in Ukrainian], Vyshcha Shkola, Kyiv (1992).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2020, pp. 107–114.
Rights and permissions
About this article
Cite this article
Lebedeva, T.T., Semenova, N.V. & Sergienko, T.I. Multi-Objective Optimization Problem: Stability against Perturbations of Input Data in Vector-Valued Criterion. Cybern Syst Anal 56, 953–958 (2020). https://doi.org/10.1007/s10559-020-00315-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-020-00315-9