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Wyszukujesz frazę "Schaefer, M." wg kryterium: Autor

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    Wyświetlanie 1-6 z 6
    Tytuł:
    The island model as a Markov dynamic system
    Autorzy:
    Schaefer, R.
    Byrski, A.
    Smołka, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/331253.pdf
    Data publikacji:
    2012
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    algorytm genetyczny
    analiza asymptotyczna
    optymalizacja globalna
    algorytm ewolucyjny równoległy
    łańcuch Markova
    genetic algorithms
    asymptotic analysis
    global optimization
    parallel evolutionary algorithms
    Markov chain modeling
    Opis:
    Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators. An original and crucial feature of the framework we propose is the mechanism of inter-deme agent operation synchronization. It is important from both a practical and a theoretical point of view. We show that under a mild assumption the resulting Markov chain is ergodic and the sequence of the related sampling measures converges to some invariant measure. The asymptotic guarantee of success is also obtained as a simple issue of ergodicity. Moreover, if the cardinality of each island population grows to infinity, then the sequence of the limit invariant measures contains a weakly convergent subsequence. The formal description of the island model obtained for the case of solving a single-objective problem can also be extended to the multi-objective case.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2012, 22, 4; 971-984
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the computational cost and complexity of stochastic inverse solvers
    Autorzy:
    Faliszewski, P.
    Smołka, M.
    Schaefer, R.
    Paszyński, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/305383.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    hierarchic genetic strategy
    inverse problem
    hybrid method
    Opis:
    The goal of this paper is to provide a starting point for investigations into a mainly underdeveloped area of research regarding the computational cost analysis of complex stochastic strategies for solving parametric inverse problems. This area has two main components: solving global optimization problems and solving forward problems (to evaluate the misfit function that we try to minimize). For the first component, we pay particular attention to genetic algorithms with heuristics and to multi-deme algorithms that can be modeled as ergodic Markov chains. We recall a simple method for evaluating the first hitting time for the single-deme algorithm and we extend it to the case of HGS, a multi-deme hierarchic strategy. We focus on the case in which at least the demes in the leaves are well tuned. Finally, we also express the problems of finding local and global optima in terms of a classic complexity theory. We formulate the natural result that finding a local optimum of a function is an NP-complete task, and we argue that finding a global optimum is a much harder, DP-complete, task. Furthermore, we argue that finding all global optima is, possibly, even harder (#P-hard) task. Regarding the second component of solving parametric inverse problems (i.e., regarding the forward problem solvers), we discuss the computational cost of hp-adaptive Finite Element solvers and their rates of convergence with respect to the increasing number of degrees of freedom. The presented results provide a useful taxonomy of problems and methods of studying the computational cost and complexity of various strategies for solving inverse parametric problems. Yet, we stress that our goal was not to deliver detailed evaluations for particular algorithms applied to particular inverse problems, but rather to try to identify possible ways of obtaining such results.
    Źródło:
    Computer Science; 2016, 17 (2); 225-264
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Misfit landforms imposed by ill-conditioned inverse parametric problems
    Autorzy:
    Łoś, M.
    Smołka, M.
    Schaefer, R.
    Sawicki, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/305739.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    taxonomy of ill-conditioned problems
    ill-posed global optimization problems
    fitness landscapes
    Opis:
    In this paper, we put forward a new topological taxonomy that allows us to distinguish and separate multiple solutions to ill-conditioned parametric inverse problems appearing in engineering, geophysics, medicine, etc. This taxonomy distinguishes the areas of insensitivity to parameters called the landforms of the misfit landscape, be it around minima (lowlands), maxima (uplands), or stationary points (shelves). We have proven their important separability and completeness conditions. In particular, lowlands, uplands, and shelves are pairwise disjoint, and there are no other subsets of the positive measure in the admissible domain on which the misfit function takes a constant value. The topological taxonomy is related to the second, “local” one, which characterizes the types of ill-conditioning of the particular solutions. We hope that the proposed results will be helpful for a better and more precise formulation of ill-conditioned inverse problems and for selecting and profiling complex optimization strategies used in solving these problems.
    Źródło:
    Computer Science; 2018, 19 (2); 157-178
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic guarantee of success for multi-agent memetic systems
    Autorzy:
    Byrski, A.
    Schaefer, R.
    Smołka, M.
    Cotta, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/201942.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    computational multi-agent systems
    asymptotic analysis
    global optimization
    parallel evolutionary algorithms
    Markov chain modeling
    Opis:
    The paper introduces a stochastic model for a class of population-based global optimization meta-heuristics, that generalizes existing models in the following ways. First of all, an individual becomes an active software agent characterized by the constant genotype and the meme that may change during the optimization process. Second, the model embraces the asynchronous processing of agent’s actions. Third, we consider a vast variety of possible actions that include the conventional mixing operations (e.g. mutation, cloning, crossover) as well as migrations among demes and local optimization methods. Despite the fact that the model fits many popular algorithms and strategies (e.g. genetic algorithms with tournament selection) it is mainly devoted to study memetic algorithms. The model is composed of two parts: EMAS architecture (data structures and management strategies) allowing to define the space of states and the framework for stochastic agent actions and the stationary Markov chain described in terms of this architecture. The probability transition function has been obtained and the Markov kernels for sample actions have been computed. The obtained theoretical results are helpful for studying metaheuristics conforming to the EMAS architecture. The designed synchronization allows the safe, coarse-grained parallel implementation and its effective, sub-optimal scheduling in a distributed computer environment. The proved strong ergodicity of the finite state Markov chain results in the asymptotic stochastic guarantee of success, which in turn imposes the liveness of a studied metaheuristic. The Markov chain delivers the sampling measure at an arbitrary step of computations, which allows further asymptotic studies, e.g. on various kinds of the stochastic convergence.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 1; 257-278
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An agent-oriented hierarchic strategy for solving inverse problems
    Autorzy:
    Smołka, M.
    Schaefer, R.
    Paszyński, M.
    Pardo, D.
    Álvarez-Aramberri, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/329764.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    inverse problem
    hybrid optimization method
    memetic algorithm
    multi-agent system
    magnetotelluric data inversion
    zadanie odwrotne
    optymalizacja hybrydowa
    algorytm memetyczny
    system wieloagentowy
    Opis:
    The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems’ difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 3; 483-498
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A hybrid algorithm for solving inverse problems in elasticity
    Autorzy:
    Barabasz, B.
    Gajda-Zagórska, E.
    Migórski, S.
    Paszyński, M.
    Schaefer, R.
    Smołka, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/331427.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    inverse problem
    hierarchic genetic strategy
    hybrid optimization
    automatic hp adaptive finite element method
    zagadnienie odwrotne
    strategia genetyczna
    optymalizacja hybrydowa
    metoda elementów skończonych
    Opis:
    The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 865-886
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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