On quasistability of a vector combinatorial problem with Σ-MINMAX and Σ-MINMIN partial criteria

نویسندگان

  • Vladimir A. Emelichev
  • Kirill G. Kuzmin
  • Andrey M. Leonovich
چکیده

We consider one type of stability (quasistability) of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem) with non-linear partial criteria is in focus. Two necessary and sufficient conditions for stability of this problem are proved. Mathematics Subject Classification 2000: 90C10, 90C05, 90C29, 90C31.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Stability and accuracy functions in multicriteria combinatorial optimization problem with Σ-MINMAX and Σ-MINMIN partial criteria

Abstract: We consider a vector generic combinatorial optimization problem in which initial coefficients of objective functions are subject to perturbations. For Pareto and lexicographic principles of efficiency we introduce appropriate measures of quality of a given feasible solution from the point of view of its stability. These measures correspond to so-called stability and accuracy functions...

متن کامل

On quasistability radius of a vector trajectorial problem with a principle of optimality generalizing Pareto and lexicographic principles

A multicriterion linear combinatorial problem with a parametric principle of optimality is considered. This principle is defined by a partitioning of partial criteria onto Pareto preference relation groups within each group and the lexicographic preference relation between them. Quasistability of the problem is investigated. This type of stability is a discrete analog of Hausdorff lower semi-co...

متن کامل

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 optim...

متن کامل

Numerical measure of strong stability and strong quasistability in the vector problem of integer linear programming

In this paper we consider a vector integer programming problem with the linear partial criteria. Numerical evaluations of two types of stability of the Pareto set have been found. Usually the stability (quasistability) of a vector optimization problem (see [1-10]) is understood as the property of nonappearance of new optimal solutions (preservation of initial) under small perturbations of the p...

متن کامل

Measure of stability of a Pareto optimal solution to a vector integer programming problem with fixed surcharges in the l1 and l∞ metrics

In this paper we consider a vector integer programming problem with Pareto principle of optimality for the case where partial criteria belong to the class of separable piecewise linear functions. The limit level of the initial data’s perturbations in the space of vector criteria parameters with norms l1 and l∞, preserved Pareto optimality of the solutions is investigated. Formulas of the quasis...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • The Computer Science Journal of Moldova

دوره 12  شماره 

صفحات  -

تاریخ انتشار 2004