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    Wyświetlanie 1-3 z 3
    Tytuł:
    Random generation of combinatorial sets with special properties
    Autorzy:
    Grebennik, I.
    Lytvynenko, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/410932.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    combinatorial generation
    k-set
    Basic combinatorial set
    random generation
    complexity
    Opis:
    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.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 4; 43-48
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Elements transpositions and their impact on the cyclic structure of permutations
    Autorzy:
    Grebennik, I.
    Chorna, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/411147.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    Permutations set
    permutation polyhedron
    adjacency criterion
    permutation properties
    transposition
    combinatorics
    Opis:
    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 arbitraży components. We consider the impact of the corresponding components on the cyclic structure of permutations depending on the type of a permutation. In this paper we formulate the assertion about the features of the impact of transpositions corresponding to the adjacency criterion on the permutations consisting of the one cycle. During the proof of statement all six types of permutations are considered and clearly demonstrated that only two types arrangement of the elements in the cycle contribute to the persistence a single cycle in the permutation after the impast of two transpositions. Research conducted in the Niven work, will be further employed in mathematical modeling and computational methods. Especially for solving combinatorial optimization problems and for the generation of combinatorial objects with a predetermined cyclic structure.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2015, 4, 3; 33-38
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Optimization of linear functions on a cyclic permutation. Based on the random search
    Autorzy:
    Grebennik, I.
    Baranov, O.
    Chorna, A.
    Gorbacheva, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/411110.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    combinatorial optimization
    linear function
    cyclic permutations
    random search
    branch and bound algorithm
    parallel computing
    Opis:
    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.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 3; 211-216
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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