On one type of stability for multiobjective integer linear programming problem with parameterized optimality

• Main Authors: Vladimir A. Emelichev, Yury Nikulin
• Format: Article
• Language: English
• Published: Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2020-12-01
• Series: Computer Science Journal of Moldova
• Subjects: multiobjective problem; integer programming; pareto set; a set of extreme solutions; stability radius; h{\"o}lder's norms
• Online Access: http://www.math.md/files/csjm/v28-n3/v28-n3-(pp249-268).pdf

A multiobjective problem of integer linear programming with parametric optimality is addressed. The parameterization is introduced by dividing a set of objectives into a family of disjoint subsets, within each Pareto optimality is used to establish dominance between alternatives. The introduction of this principle allows us to connect such classical optimality sets as extreme and Pareto. The admissible perturbation in such problem is formed by a set of additive matrices, with arbitrary H\"{o}lder's norms specified in the solution and criterion spaces. The lower and upper bounds for the radius of strong stability are obtained with some important corollaries concerning previously known results.