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Stability and Regularization of Vector Problems of Integer Linear Programming

by Berdysheva, R.A., Emelichev, V.A., Girlich, E., Krichko, V.N., Nikulin, Yu. V., Podkopaev, D.P., Yanushkevich, O.A..

Series: 1999-29, Preprints

90C27 Combinatorial optimization
90C29 Multi-objective and goal programming

In this paper we study various types of stability of vector ILP-problems. The problem of
finding the Pareto set and the problem of lexicographic optimization are considered.
Borders of change of input data preserving certain properties of efficient solution sets are
obtained. Necessary and sufficient conditions of stability are specified. Regularizing
operators are proposed for transferring a probably unstable vector ILP-problem to a
series of stable ones, which are equivalent to the initial problem.

multiobjective discrete linear optimization, stability, regularization