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    Wyświetlanie 1-3 z 3
    Tytuł:
    Combinatorial approaches to the capital-budgeting problem
    Autorzy:
    Pichugina, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/411221.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    capital-budgeting problem
    integer programming
    knapsack problem
    combinatorial optimization
    Branch and Bound
    Opis:
    Optimization approaches, combinatorial and continuous, to a capital-budgeting problem (CBP) are presented. This NP-hard problem, traditionally modelled as a linear binary problem, is represented as a biquadratic over an intersection of a sphere and a supersphere. This allows applying nonlinear optimization to it. Also, the method of combinatorial and surface cuttings (MCSC) is adopted to (CBP). For the single constrained version (1CBP), new combinatorial models are introduced based on joint analysis of the constraint, objective function, and feasible region. Equivalence of (1CBP) to the multichoice knapsack problem (MCKP) is shown. Peculiarities of Branch&Bound techniques to (1CBP) are described.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 4; 29-36
    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
    Tytuł:
    Development the methods of optimum placement undirected planar objects with piecewise non-linear boundaries in the multiply area
    Autorzy:
    Chaplya, Yu.
    Sobol, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/411345.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    optimal placement
    object with piecewise linear boundary
    multiply area
    mathematical model
    branch and bound method
    method of simulated annealing
    Opis:
    In this paper the statement of the problem is formulated and the mathematical model of optimization the placement of the undirected planar geometrical objects with piecewise non-linear boundaries in the multiply area is developed. It is shown the geometrical interpretation and derived the estimate of the number of restrictions in the model. On the basis of a mathematical model for finding the global extremum of the objective function was proposed modified method of branches and boundaries. It is also shown the solutions tree that takes into account the problems of optimal placement of undirected planar geometrical object with piecewise nonlinear boundaries in the multiply area, and received the complexity of this method. For locally optimal solutions of the problem modified simulated annealing method has been developed. Thus the analytical expressions for the function of energy system were received, the function, that describes the decrease of temperature over time, function that forms a new state of system. The method of formation the new state of the system was investigated in more detail, which is based on a random permutation of numbers the pair of the objects, it is also based on a consistent placement of objects according to reshuffle their numbers and determining the probability of transition to a new state. It is shown the example of determining permissible points of placement the local coordinate system of the specific geometrical object. The conclusion is that to solve practical optimization problems of placement of the undirected planar geometrical objects with piecewise non-linear boundaries in the multiply area should be used the modified simulated annealing method.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 2; 39-44
    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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