Stability and Regularization of Vector Problems of Integer Linear Programming

In this article we consider the problem of finding the Pareto set, and also the problem of lexicographic optimization. We study several types of stability, understood as preservation of certain properties of the efficient solution set under "small" changes of input data. The borders of such changes are ascertained. Necessary and sufficient conditions of stability are specified. A regularizing operator is proposed for transferring a probably unstable problem to a series of stable ones.

[1]  Yury Nikulin,et al.  Numerical measure of strong stability and strong quasistability in the vector problem of integer linear programming , 1999, Comput. Sci. J. Moldova.

[2]  SotskoP,et al.  Some concepts of stability analysis in combinatorial optimization , 2003 .

[3]  V. Emelichev,et al.  Sensivity analysis of efficient solutions of the vector problem of minimisation of linear forms on a set of permutations , 2000 .

[4]  Horst W. Hamacher,et al.  Algorithms for flows with parametric capacities , 1989, ZOR Methods Model. Oper. Res..

[5]  Guenther Ruhe,et al.  Parametric maximal flows in generalized networks – complexity and algorithms , 1988 .

[6]  S. Smale,et al.  Global analysis and economics V: Pareto theory with constraints , 1974 .

[7]  On a quantitative measure of stability for a vector problem in integer programming , 1998 .

[8]  On the radii of steadiness, quasi-steadiness, and stability of a vector trajectory problem on lexicographic optimization , 1998 .

[9]  V. Tanaev,et al.  Stability Radius of an Optimal Schedule: A Survey and Recent Developments , 1998 .

[10]  Vladimir A. Emelichev,et al.  Stability of a majority efficient solution of a vector linear trajectorial problem , 1999, Comput. Sci. J. Moldova.

[11]  V. A. Emelichev,et al.  Stability radius of an efficient solution to a vector quadratic problem of boolean programming , 2001 .

[12]  V.A. EMELICHEV,et al.  On the radius of stability of a vector problem of linear Boolean programming , 2000 .