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    Wyświetlanie 1-5 z 5
    Tytuł:
    On the robustness of optimal solutions for combinatorial optimization problems
    Raport Badawczy = Research Report ; RB/2/2007
    Autorzy:
    Libura, Marek
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliografia s. 15-16
    The paper considers so-called generic combinatorial optimization problem, where the set of feasible solutions is some family of subsets of a finite ground set with specified positive initial weights of elements, and the objective function represents the total weight of elements of a feasible solution. It is assumed that the weights of all elements may be perturbed simultaneously and independently up to a given percentage of their initial values. A feasible solution, which minimizes then the worst-case relative regret, is called a robust solution. The maximum percentage level of perturbations, for which an initially optimal solution remains robust, is called the robustness radius of this solution. In this paper the robustness aspect of initially optimal solutions and provide lower bounds for their robustness radii are studied.
    Bibliography p. 15-16
    16 stron ; 21 cm
    16 pages ; 21 cm
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Robustness analysis of optimal solutions for combinatorial optimization problems
    Raport Badawczy = Research Report ; RB/17/2009
    Autorzy:
    Libura, Marek
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliografia s. 13-14
    14 stron ; 21 cm
    This paper deals with so-called robustness analysis for the generic combinatorial optimization problem. Its main goal consists in finding subsets of scenarios for which an initially optimal solution of the problem remains robust. Thus, the robustness analysis may be considered as a natural extension of the standard sensitivity analysis in combinatorial optimization. Main results of the paper concern the robustness region, robustness radius and robustness tolerances, which are introduced as direct analogues of the stability region, stability radius and stability tolerances considered in the sensitivity analysis.
    14 pages ; 21 cm
    Bibliography p. 13-14
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/4/2008
    Robustness tolerances for combinatorial optimization problems
    Autorzy:
    Libura, Marek
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    Bibliografia s. 14-16
    The paper adresses the so-called generic combinatorial optimization problem, where the set of feasible solutions is some family of nonempty subsets of a finite ground set with specified positive initial weights of elements, and the objective function represents the total weight of elements of the feasible solution. It is assumed that the set of feasible solutions is fixed, but the weights of elements may be perturbed or are given with errors. All possible realizations of weights form the set of scenarios. A feasible solution, which for a given set of scenarios guarantees the minimum value of the worst-case relative regret among all the feasible solutions, is called a robust solution. The maximum percentage perturbation of a single weight, which does not destroy the robustness of a given solution, is called the robustness tolerance of this weight with respect to the solution considered. This paper presents formulae which allow calculating the robustness tolerances with respect to an optimal solution obtained for some initial weights.
    Bibliography p. 14-16
    16 stron ; 21 cm
    16 pages ; 21 cm
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/7/2010
    Sensitivity and robustness analysis in combinatorial optimization
    Autorzy:
    Libura, Marek
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    21 pages ; 21 cm
    Bibliografia s. 20-21
    This paper deals with so-called robustness analysis for the generic combinatorial optimization problem. Its main goal consists in finding subsets of scenarios for which an initially optimal solution of the problem remains robust. Thus, the robustness analysis may be considered as a natural extension of the standard sensitivity analysis in combinatorial optimization. Main results of the paper concern the robustness region, the robustness radius and the robustness tolerances, which are introduced as direct analogues of the optimality region, the optimality radius and the weigts tolerances considered in the sensitivity analysis.
    21 stron ; 21 cm
    Bibliography p. 20-21
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
    Tytuł:
    Raport Badawczy = Research Report ; RB/8/2011
    Sensitivity and robustness analysis in combinatorial optimization (revised version)
    Autorzy:
    Libura, Marek
    Wydawca:
    Instytut Badań Systemowych. Polska Akademia Nauk
    Systems Research Institute. Polish Academy of Sciences
    Powiązania:
    Raport Badawczy = Research Report
    Opis:
    24 stron ; 21 cm
    Bibliography p. 22-24
    24 pages ; 21 cm
    Bibliografia s. 22-24
    This paper is a revised version of the report RB-2010-07. Several improvements, slight changes in the presentation and corrections in proofs have been introduced, as well as short comments concerning an influence of the adopted robustness measure on the robustness analysis have been added. The paper deals with so-called robustness analysis for the generic combinatorial optirnization problem. Its main goal consists in finding subsets of scenarios for which an initially optimal solution of the problem remains robust.
    Dostawca treści:
    RCIN - Repozytorium Cyfrowe Instytutów Naukowych
    Książka
      Wyświetlanie 1-5 z 5

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