2021

Постійне посилання на фонд

https://ela.kpi.ua/handle/123456789/46699

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Перегляд 2021 за Автор "Romanuke, V. V."

Зараз показуємо 1 - 4 з 4
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    Finite approximation of zero-sum games played in staircase-function continuous spaces
    (КПІ ім. Ігоря Сікорського, 2021) Romanuke, V. V.
    Background. There is a known method of approximating continuous zero-sum games, wherein an approximate solution is considered acceptable if it changes minimally by changing the sampling step minimally. However, the method cannot be applied straightforwardly to a zero-sum game played with staircase-function strategies. Besides, the independence of the player’s sampling step selection should be taken into account. Objective. The objective is to develop a method of finite approximation of zero-sum games played in staircase-function continuous spaces by taking into account that the players are likely to independently sample their pure strategy sets. Methods. To achieve the said objective, a zero-sum game, in which the players’ strategies are staircase functions of time, is formalized. In such a game, the set of the player’s pure strategies is a continuum of staircase functions of time, and the time is thought of as it is discrete. The conditions of sampling the set of possible values of the player’s pure strategy are stated so that the game becomes defined on a product of staircase-function finite spaces. In general, the sampling step is different at each player and the distribution of the sampled points (function-strategy values) is non-uniform. Results. A method of finite approximation of zero-sum games played in staircase-function continuous spaces is pre sented. The method consists in irregularly sampling the player’s pure strategy value set, solving smaller-sized matrix games, each defined on a subinterval where the pure strategy value is constant, and stacking their solutions if they are consistent. The stack of the smaller-sized matrix game solutions is an approximate solution to the initial staircase game. The (weak) consistency of the approximate solution is studied by how much the payoff and optimal situation change as the sampling density minimally increases by the three ways of the sampling increment: only the first player’s increment, only the second player’s increment, both the players’ increment. The consistency is decomposed into the payoff, opti mal strategy support cardinality, optimal strategy sampling density, and support probability consistency. It is practically reasonable to consider a relaxed payoff consistency. Conclusions. The suggested method of finite approximation of staircase zero-sum games consists in the independent samplings, solving smaller-sized matrix games in a reasonable time span, and stacking their solutions if they are con sistent. The finite approximation is regarded appropriate if at least the respective approximate (stacked) solution is e-payoff consistent.
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    Optimization of lstm networks for time series forecasting
    (КПІ ім. Ігоря Сікорського, 2021) Romanuke, V. V.
    Background. LSTM neural networks are a very promising means to develop time series analysis and forecasting. However, s well as neural networks for other fields and applications, LSTM networks have a lot of architecture ver sions, training parameters, and hyperparameters, whose inappropriate selection may lead to unacceptably poor perfor mance (poor or badly unreliable forecasts). Thus, optimization of LSTM networks is still an open question. Objective. The goal is to ascertain whether the best forecasting accuracy is achieved at such a number of LSTM layer neurons, which can be determined by the time series lag. Methods. To achieve the said goal, a set of benchmark time series for testing the forecasting accuracy is presented. Then, a set-up of the computational study for various versions of the LSTM network is defined. Finally, the computa tional study results are clearly visualized and discussed. Results. Time series with a linear trend are forecasted worst, whereas defining the LSTM layer size by the lag in a time series does not help much. The best-forecasted are time series with only repeated random subsequences, or seasonality, or exponential rising. Compared to the single LSTM layer network, the forecasting accuracy is improved by 15 % to 19 % by applying the two LSTM layers network. Conclusions. The approximately best forecasting accuracy may be expectedly achieved by setting the number of LSTM layer neurons at the time series lag. However, the best forecasting accuracy cannot be guaranteed. LSTM networks for time series forecasting can be optimized by using only two LSTM layers whose size is set at the time series lag. Some discrepancy is still acceptable, though. The size of the second LSTM layer should not be less than the size of the first layer.
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    Sorting approaches in the heuristic based on remaining available and processing periods to minimize total weighted tardiness in progressive idling-free 1-machine preemptive scheduling
    (КПІ ім. Ігоря Сікорського, 2021) Romanuke, V. V.
    Background. In preemptive job scheduling, total weighted tardiness minimization is commonly reduced to solving a combinatorial problem, which becomes practically intractable as the number of jobs and the numbers of their processing periods increase. To cope with this challenge, heuristics are used. A heuristic, in which the decisive ratio is the weighted reciprocal of the maximum of a pair of the remaining processing period and remaining available period, is closely the best one. However, the heuristic may produce schedules of a few jobs whose total weighted tardiness is enormously huge compared to the real minimum. Therefore, this heuristic needs further improvements, one of which already exists for jobs without priority weights with a sorting approach where remaining processing periods are minimized. Three other sorting approaches still can outperform it, but such exceptions are quite rare. Objective. The goal is to determine the influence of the four sorting approaches and try to select the best one in the case where jobs have their priority weights. The heuristic will be applied to tight-tardy progressive idling-free 1-machine preemptive scheduling, where the release dates are given in ascending order starting from 1 to the number of jobs, and the due dates are tightly set after the release dates. Methods. To achieve the said goal, a computational study is carried out with applying each of the four heuristic approaches to minimize total weighted tardiness. For this, two series of 4151500 scheduling problems are generated. In the solution of a scheduling problem, a sorting approach can “win” solely or “win” in a group of approaches, producing the heuristically minimal total weighted tardiness. In each series, the distributions of sole-and-group “wins” are ascertained. Results. The sole “wins” and non-whole-group “wins” are rare: the four sorting approaches produce schedules with the same total weighted tardiness in over 98.39 % of scheduling problems. Although the influence of these approaches is different, it is therefore not really significant. Each of the sorting approaches has heavy disadvantages leading sometimes to gigantic inaccuracies, although they occur rarely. When the inaccuracy occurs to be more than 30 %, this implies that 3 to 9 jobs are scheduled. Conclusions. Unlike the case when jobs do not have their priority weights, it is impossible to select the best sorting approach for the case with job priority weights. Instead, a hyper-heuristic comprising the sorting approaches (i. e., the whole group, where each sorting is applied) may be constructed. If a parallelization can be used to process two or even four sorting routines simultaneously, the computation time will not be significantly affected.