Перегляд за автором "Chorna, O."

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  • Немає доступних мініатюр
    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.
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    Публікація
    Elements transpositions and their impact on the cyclic structure of permutations
    (LUBLIN--RZESZOW, 2015) Grebennik, I. V.; Chorna, O.
    The objective of this paper is the investigation of the cyclic structure and permutation properties based on neighbor elements transposition properties and the properties of the permutation polyhedron. In this paper we consider special type of transpositions of elements in a permutation. A feature of these transpositions is that they corresponding to the adjacency criterion in a permutation polyhedron. We will investigate permutation properties with the help of the permutation polyhedron by using the immersing in the Euclidian space. Six permutation types are considered in correspondence with the location of arbitrary components. We consider the impact of the corresponding components on the cyclic structure of permutations depending on the type of a permutation.
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    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.
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    Публікація
    Visualizing Feasible Regions for Optimization Problems on High-Dimensional Permutations using Dimensionality Reduction Methods
    (2023) Grebennik, I; Chorna, O.; Urniaieva, I
    This paper presents an investigation on the usage of modern dimensionality reduction methods for classic combinatorial optimization problems. We propose the use of t-Distributed Stochastic Neighbor Embedding (t-SNE) method to visualize feasible regions on high-dimensional permutations, aiming to avoid the consequences of combinatorial explosion. The results of the study indicate that the proposed approach can provide valuable insights and improve the understanding of the solution space of high-dimensional permutations for the application of local search approaches.