Кафедра системотехніки (СТ)
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Перегляд Кафедра системотехніки (СТ) за автором "Grebennik, I."
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Публікація Distribution of Permutations with Different Cyclic Structure in Mathematical Models of Transportation Problems(2022) Grebennik, I.; Chorna, O.; Urniaieva, I.The paper is devoted to the investigation of problems of the class Pick-up and Delivery routing problems (PDP). This class is characterized by the multidimensionality of the input data, the requirement for decision-making in conditions of uncertainty and the requirement for rapid generation of solutions. Therefore, heuristic algorithms have proven to be good for solving PDP problems. Among the heuristic algorithms used to solve such problems is a wide class of Large-scale neighborhood algorithms, in which algorithms based on the use of cyclic transfer theory deserve special attention. If the collection and delivery of goods from many senders to many recipients is served by several trucks - the question arises of the distribution of points to visit between vehicles. One approach to solving the problem of splitting multiple shipping points into non-intersecting clusters is an approach that uses heuristic start splitting and then improves it by moving some shipping points between clusters using cyclic transfers. The study of the properties of cyclic permutations and the study of the cyclic structure of arbitrary elements of the permutations set is a promising direction for increasing of efficiency of the cyclic transfer approach to solve PDP problems. This paper is devoted to the study of the distribution of permutations with different cyclic structure in the set of permutations for increasing the efficiency of solving PDP problems. Experiments were conducted to study the distribution of permutations with different cyclic structure among sample populations with different qualitative characteristics. On the basis of the analysis and results of experiments the conclusions concerning features of distribution of permutations with various cyclic structure are made. Taking into account these features allows you to increase the efficiency of the cyclic transfer method in solving transport routing problems.Публікація Mathematical Model of Containers Placement in Rail Terminal Operations Problem(2019) Grebennik, I.; Dupas, R.; Urniaieva, I.; Kalaida, N.; Ivanov, V.In the paper the increasing of efficiency for rail terminal operations is analyzed. The problem of optimization the placement of containers on railway platforms and in the storage area at railway transshipment yard is formulated. A combinatorial optimization model of the problem is constructed, its properties are discussed, an example is considered.Публікація Muticriteria Balance Layout Problem of 3d-Objects(Sofia, Bulgaria, 2017) Grebennik, I.; Romanova, T.; Kovalenko, A.; Urniaieva, I.; Shekhovtsov, S.The paper studies the optimal layout problem of 3D-objects in a container with circular racks. The problem takes into account placement constraints (non-overlapping, containment, distance constraints), as well as, behaviour characteristics of the mechanical system (equilibrium, moments of inertia and stability characteristics). We construct a mathematical model of the problem in the form of multicriteria optimisation problem and call the problem the Multicriteria Balance Layout Problem (MBLP). We also consider several realisations of MBLP problem that depend on forms of objective functions and behaviour constraints. В статье рассматривается оптимальная задача размещения 3D-объектов в контейнере с круглыми стойками. В этой задаче учитываются ограничения размещения (неперекрывающиеся, сдерживающие, дистанционные ограничения), а также характеристики поведения механической системы (равновесие, моменты инерции и характеристики устойчивости). Мы строим математическую модель задачи в виде многокритериальной задачи оптимизации и называем проблему проблемой многокритериальной балансной компоновки (ПМБК). Мы также рассмотрим несколько реализаций проблемы ПМБК, которые зависят от форм объективных функций и ограничений поведения.Публікація Optimization of linear functions on a cyclic permutation Based on the random search(2016) Grebennik, I.; Baranov, A.; Chorna, O.; Gorbacheva, E.For creating adequate mathematical models of combinatorial problems of constructing optimal cyclic routes, mathematical modeling and solving a number of planning and control tasks solutions of optimization problems on the set of cyclic permutations are required. Review of the publications on combinatorial optimization demonstrates that the optimization problem on the cyclic permutations have not been studied sufficiently. This paper is devoted to solving optimization problem of a linear function with linear constraints on the set of cyclic permutations. For solving problems of this class using of known methods, taking into account the properties of a combinatorial set of cyclic permutations, is proposed. For this purpose we propose a method based on the ideology of random search. Heuristic method based on the strategy of the branch and bound algorithm is proposed to solve auxiliary optimization problem of a linear function without constraints on the set of cyclic permutations. Since application of the branch and bound algorithm immediately leads to an exponential growth of the complexity with increasing the dimension of the problem a number of modifications are suggested. Modifications allow reducing computational expenses for solving higher dimension problems. The effectiveness of the proposed improvements is demonstrated by computational experiments.Публікація Random Generation Of Combinatorial Sets With Special Properties(Polish Academy of Sciences Branch in Lublin, University of Engineering and Economics in Rzeszów, Lviv Polytechnic National University, 2016) Grebennik, I.; Lytvynenko, O.General approach for solving the problem of random generation of compositional k images of combinatorial sets (k-sets) has been proposed. K-sets are powerful apparatus that can be applied for solving many scientific and applied problems. Though many literature is dedicated to the problem of generating combinatorial configurations, existing studies deals mostly with simple combinatorial configurations like combinations, permutations etc. The algorithms of generation both basic combinatorial sets and k-sets have been described. Algorithm for random generation of basic sets allows generating various combinatorial sets, and laws of constructing basic combinatorial sets can be pre-set. If identification of the laws fails, the algorithm allows using other algorithms to generate basic sets. Complexity of described algorithms has been evaluated. The complexity of the algorithm of generation k-sets is determined by the complexity of generation of basic sets, as well as the complexity of operations of nsubstitution and a number of levels of a certain k-set. The described approach to the random generation is very flexible since it allows obtaining various results by varying algorithm parameters. In its turn, it allows adjusting the number of elements for both basic sets and k-sets. The developed software allows solving the described problems of random generation of k -sets and basic combinatorial sets.Публікація Three-dimensional one-to-one pickup and delivery routing problem with loading constraints(2016) Grebennik, I.; Lytvynenko, O.; Baranov, O.; Dupas, R.We propose mathematical model and solving strategy for PDP with 3D loading constraints in terms of combinatorial configuration instead of traditional approach that uses boolean variables. We solve traditional one-to-one Pickup and Delivery Problem in combination with problem of packing delivered items into vehicles by means of proposed combinatorial generation algorithm.Публікація Train arrangement in scheduling for rail-rail transshipment yard(UNWE, 2017) Grebennik, I.; Dupas, R.; Lytvynenko, O.; Urniaieva, I.Article considers problem of scheduling freight trains in rail-rail transshipment yards. Besides scheduling the service slots of trains, article additionally solves the problem of train arrangement, i.e. assigning each train to a railway track. Mathematical model and solving method for described problem are given. The key feature of given mathematical model is that is uses combinatorial objects (tuples of permutations) instead of traditional Boolean variables. Solution method is based on generation of combinatorial sets as well, which is quite unusual approach comparing with existing solution methods for described problem.