Integer programming problems with a vector criterion: Parametric analysis and investigation of stability

Integer programming problems with a vector criterion: Parametric analysis and investigation of stability

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Article ID: iaor19921508
Country: United States
Volume: 40
Start Page Number: 98
End Page Number: 100
Publication Date: Jun 1990
Journal: Soviet Mathematics Doklady
Authors: , ,
Keywords: programming: parametric
Abstract:

Maximize the vector criterion (1) equ1, which is defined on the set (2) equ2, where equ3, equ4, equ5, D is a bounded subset of equ6, equ7,equ8 and equ9. The authors also use the following conventional expression for problem (1), (2): equ10, where equ11. As is known, a point equ12 is said to be effective (or Pareto-optimal) if equ13, equ14; it is said to be weakly effective (semi-effective, optimal in the Slater sense) if equ15equ16, and strictly effective if equ17. The set of all effective points is denoted by equ18, the set of weakly effective points by P(C, X), and the set of strictly effective points by S(C, X). Obviously, equ19. A vector maximization problem usually consists of finding effective points in the set of admissible solutions. Parametric analysis of mathematical programming problems is performed on the basis of models and methods of parameteric programming, the subject of which is optimization problems whose coefficients (all of them or individual ones) are functions of one or more parameters. They propose carrying out a parametric analysis of problem (1), (2) on the basis of the following multicriterial parameter model: equ20, where C(t)=equ21, equ22, equ23, equ24, equ25, equ26, and equ27,equ28 and equ29 are real-valued polynomial functions of the parameter equ30.

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