Author:
Lebedeva Т.Т., ,Semenova N.V.,Sergienko T.I., ,
Abstract
The article is devoted to the study of the influence of uncertainty in initial data on the solutions of optimiza-tion multicriterial problems. In the optimization problems, including problems with vector criterion, small per-turbations in initial data can result in solutions strongly different from the true ones. The results of the con-ducted researches allow us to extend the known class of vector optimization problems, stable with respect to in-put data perturbations in vector criterion. We are talking about stability in the sense of Hausdorff lower semicontinuity for point-set mapping that characterizes the dependence of the set of optimal solutions on the input data of the vector optimization problem. The conditions of stability against input data perturbations in vector criterion for the problem of finding Pareto optimal solutions with continuous partial criterion func-tions and feasible set of arbitrary structure are obtained by studying the sets of points that are stable belonging and stable not belonging to the Pareto set.
Publisher
National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka)
Reference14 articles.
1. 1. Kozeratskaya, L.N., Lebedeva, T.T. & Sergienko, T.I. (1991). Mixed integer vector optimization: stability issues. Cybernetics and Systems Analysis. 27, No. 1, pp. 76-80.
2. Vector optimization problems: stability in the decision space and in the space of alternatives;Kozeratskaya;Cybernetics and Systems Analysis 30 No 6,1994
3. 3. Sergienko, I.V., Kozeratskaya, L.N. & Lebedeva, T.T. (1995). Study of the stability and the parametric analysis of discrete optimization problems. Kyiv: Naukova Dumka.
4. Stability of vector problems of integer optimization: Relationship with the stability of sets of optimal and nonoptimal solutions;Lebedeva;Cybernetics and Systems Analysis 41 No 4,2005
5. Set of strictly efficient points of mixed integer vector optimization problem as a measure of problem's stability;Kozeratskaya;Cybernetics and Systems Analysis 33 No 6,1997
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献