Stability, pseudostability and quasistability of vector trajectorial lexicographic optimization problem

Lower bounds of stability, pseudostability and quasistability radii of lexicographic set in vector combinatorial problem on systems of subsets of finite set with partial criteria of more general kinds have been found. Many specialists are engaged in study of stability of discrete optimization problems to perturbations of their parameters (see [1-3]). Need for investigation of stability of optimization problems is connected with inaccuracy of the input data, inadequacy of mathematical models to real processes, mistakes of computations and other factors. The stability of single-criterion trajectorial discrete optimization problems have been investigated in detail. Many well-known optimization problems on graphs, Boolean programming problems, and also scheduling problems, can be described as the special cases [3-9]. Analyzing stability of such problems the authors paid the main attention to the calculation of the stability radius. This notion for a single-criterion trajectorial problem was introduced by V.K.Leontiev [4]. Necessary and sufficient conditions of three types of stability (in our terms stability, quasistability and pseudostability) of Pareto set in vector integer programming problems were obtained in [10-13]. The papers [14-17] is devoted to stability of trajectorial problems with partial criteria of the three most widespread types: MINSUM, c ©1998 by R.Berdysheva, V.Emelichev, E.Girlich ∗This work was partially supported by Fundamental Reseaches Foundation of Belarus, International Soros Program and DAAD (Germany).