Several kinds of Stability of efficient Solutions in Vector Trajectorial discrete Optimization Problem

This work was partially supported by DAAD, Fundamental Researches Foundation of Belarus and International Soros Science Education Program We consider a vector discrete optimization problem on a system of non- empty subsets (trajectories) of a finite set. The vector criterion of the pro- blem consists partial criterias of the kinds MINSUM, MINMAX and MIN- MIN. The stability of eficient (Pareto optimal, Slater optimal and Smale op- timal) trajectories to perturbations of vector criterion parameters has been investigated. Suficient and necessary conditions of eficient trajectories local stability have been obtained. Lower evaluations of eficient trajectories sta- bility radii, and formulas in several cases, have been found for the case when l(inf) -norm is defined in the space of vector criterion parameters

Tests of efficiency for a discrete multicriteria optimization problem

Not available

Strong stability for multiobjective investment problem with perturbed minimax risks of different types and parameterized optimality

A multicriteria investment Boolean problem of minimizing lost profits with parameterized efficiency and different types of risks is formulated. The lower and upper bounds on the radius of the strong stability of efficient portfolios are obtained. Several earlier known results regarding strong stability of Pareto efficient and extreme portfolios are confirmed.</p

Several kinds of Stability of efficient Solutions in Vector Trajectorial discrete Optimization Problem

This work was partially supported by DAAD, Fundamental Researches Foundation of Belarus and International Soros Science Education Program We consider a vector discrete optimization problem on a system of non- empty subsets (trajectories) of a finite set. The vector criterion of the pro- blem consists partial criterias of the kinds MINSUM, MINMAX and MIN- MIN. The stability of eficient (Pareto optimal, Slater optimal and Smale op- timal) trajectories to perturbations of vector criterion parameters has been investigated. Suficient and necessary conditions of eficient trajectories local stability have been obtained. Lower evaluations of eficient trajectories sta- bility radii, and formulas in several cases, have been found for the case when l(inf) -norm is defined in the space of vector criterion parameters

Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem

We consider a multiple criterion Boolean programming problem with MINMAX partial criteria. The extreme level of independent perturbations of partial criteria parameters such that efficient (Pareto optimal) solution preserves optimality was obtained

Мера устойчивости многокритериальной задачи целочисленного линейного программирования с параметрическим принципом оптимальности

In this paper, we consider a multicriteria integer linear programming problem with a parametric principle of optimality. Parameterization is realized by dividing the set of criteria into several disjoint groups (subsets) of criteria ordered by importance, with Pareto dominance within each group. The introduced parametric principle of optimality made it possible to connect such classical principles of optimality as lexicographic and Pareto ones. For the stability radius, which is the limiting level of perturbations of the parameters of the problem, not causing the appearance of new optimal solutions, the upper and lower estimations are obtained in the case of arbitrary Hölder’s norms in the criterion space and solution space. Some previously known results on the stability of the Boolean linear programming problem are formulated as corollaries.Рассматривается многокритериальная задача целочисленного линейного программирования с параметрическим принципом оптимальности. Параметризация реализована путем разбиения множества критериев на несколько упорядоченных по важности непересекающихся групп (подмножеств) критериев с доминированием по Парето в пределах каждой группы. Введенный параметрический принцип оптимальности позволил связать такие классические принципы оптимальности, как лексикографический и паретовский. Для радиуса устойчивости, который является предельным уровнем возмущений параметров задачи, не приводящих к появлению новых оптимальных решений, получены верхняя и нижняя оценки в случае произвольных норм Гёльдера в критериальном пространстве и пространстве решений. Некоторые ранее известные результаты по устойчивости булевой задачи линейного программирования сформулированы в качестве следствий.

УСТОЙЧИВОСТЬ ИНВЕСТИЦИОННОЙ ЗАДАЧИ МАРКОВИЦА С КРИТЕРИЯМИ КРАЙНЕГО ОПТИМИЗМА

The multicriteria investment boolean Markowitz problem with extreme optimism criteria is considered. Upper and lower bounds of the radius of the stability of this problem are given in the case of the arbitrary Holder metric lp, 1 &lt;р &lt; ∞ in the portfolio space and the Chebyshev metric lx in the space of financial market states and in the space of investment project profitability.Получены нижняя и верхняя оценки радиуса устойчивости многокритериальной инвестиционной буле¬вой задачи Марковица с критериями крайнего оптимизма в случае, когда в пространстве портфелей задана произвольная метрика Гёльдера l p,1 ≤ p ≤  ∞, а в критериальном пространстве доходности инвестиционного проекта и пространстве состояний финансового рынка - чебышевская метрика l∞