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 <р < ∞ 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∞

Substantiating optimum parameters and efficiency of rotary brush cutters

The problem of untimely forest thinning is quite common in today's society. It leads to the emergence of the underbrush, which negatively impacts the growth and development of young trees. Therefore, this work aims to estimate the feasibility of applying a new rotary brush cutter model to eliminate excessive vegetation. The dependence of the tractor's speed when removing underbrush with different diameters of tree trunks was established by performing mathematical modeling to optimize the brush cutter parameters. Three types of flexible inertia cutting devices were investigated: flat knives, sprocket chains, and knife chains. Knife chains are the most optimal choice as they cut plants most efficiently (94.61% and 92.5% for two-year and three-year underbrush, respectively). They also show the lowest energy consumption for underbrush with a trunk between 1 and 2.4 cm in diameter. Further experiments are required to determine if the developed mathematical model can be used for more neglected forestry stands. © 2022 Institut za Istrazivanja. All rights reserved

Solving the problem of trucking optimization by automating the management process

This article discusses the solution to the optimization problem associated with trucking by automating the management process, namely the creation of software. The authorsconsiderthe main problem, because of which there is a need to automate processes. The introduction of software into the organization will help to maximize freight profit and fully automate the components that make up the process of transportation. Characteristicsof the software and the depiction of interface are presented