Ústav matematiky

Browse

Now showing 1 - 5 of 89

Network Flow Problem Heuristic Reduction Using Machine Learning
(Springer Nature, 2023-09-23) Rosecký, Martin; Pluskal, Jaroslav; Šomplák, Radovan
Most of the supporting tools developed for logistic optimization and processing infrastructure planning are based on the network flow problem. The real-world application of these instruments can provide great insight and help to ensure long-term sustainability. The main limitation of these tools lies in great computing demand when there is the necessity of solving large-scale tasks in great detail. It means that the ability to find the optimal solution for real-world problems is limited. Thus, the detail of infrastructure is often reduced by data aggregation or heuristic approaches are used to find a suboptimal solution. This paper proposes a machine learning classification model to reduce the number of variables for an exact solution algorithm. First, the design of experiments is used to create a set of smaller problems that are possible to solve exactly. Artificial data are used at this stage, while domain knowledge is used to set appropriate distribution and parameters. Second, the classification model estimates the probability of the presence of each arc in the optimal solution. Features, which are related to costs and capacity, of each arc are utilized in the classification model. Models created on a subset of generated problems are then tested on the other problems. Finally, the proposed framework is applied to the waste management problem in the Czech Republic. The results of the verification show, that it is possible to remove 95 % of arcs without impact on strategic decisions and without significant change of an objective function. The computing time of the reduced problem takes only 7 % of the original task.
Optimal control of combined heat and power station operation
(Springer Nature, 2023-09-13) Kůdela, Jakub; Suja, Jerguš; Šomplák, Radovan; Pluskal, Jaroslav; Hrabec, Dušan
Combined heat and power stations have become one of the most utilized units of district heating systems. These stations usually contain several boilers for burning fossil fuels and renewable resources used for heating up steam, which can be used either for residential and commercial heating or electricity generation. To ensure efficiency, a boiler should either run continuously (for at least a given period) on a power output higher than a given threshold or switch off. The optimal control of the plant operations should combine an efficient setup for the turbine and boilers in operation, reflecting the demand for steam and the price of electricity, and a schedule that describes which boilers should be in operation at a given time. This paper proposes a method for optimal control of combined heat and power station operation for a given time horizon. The method is based on a two-level approach. The lower-level models correspond to finding the optimal setup of the combined heat and power station parameters for an hourly demand for different kinds of steam. The upper-level model corresponds to the optimal schedule of the operations of the individual boilers, which is planned for the entire time horizon. The lower-level model is modeled as a mixed-integer linear programming problem and is solved using parametric programming. A dynamic programming algorithm solves the upper-level model with a rolling horizon. The validity of the proposed method and its computational complexity for different granularity of the time horizon, different ranges of the parameters, varying demand for various kinds of steam, and varying electricity prices are investigated in a case study. The presented approach can be readily applied to other control problems with a similar structure.
Forecasting the waste production hierarchical time series with correlation structure
(SPRINGER, 2024-07-02) Eryganov, Ivan; Rosecký, Martin; Šomplák, Radovan; Smejkalová, Veronika
Continuous increase in society's prosperity causes overwhelming growth of the produced municipal solid waste. Circular economy initiatives help to solve this problem by creating closed production cycles, where the produced waste is recycled, or its energy is recovered. An embedment of such principles requires implementation of new waste management strategies. However, these novel strategies must be based on the accurate forecasts of future waste flows. Municipal solid waste production data demonstrate behavior of hierarchical time series. Among all possible approaches to hierarchical times series forecasting, this article is focused on the reconciliation of the base waste generation forecasts. The novel method, that is based on the game-theoretically optimal reconciliation of hierarchical time series, is presented. The modified approach enables to incorporate interdependencies between time series using correlation matrix and to obtain the forecasts corresponding to the unique solution of the optimization problem. The potential of the proposed abstract approach is demonstrated on the waste production data of paper, plastics (both primarily sorted by households), and mixed municipal solid waste from the Czech Republic.
Mathematical models for machining optimization of Ampcoloy 35 with different thicknesses using WEDM to improve the surface properties of mould parts
(MDPI, 2023-01-14) Mouralová, Kateřina; Bednář, Josef; Beneš, Libor; Prokeš, Tomáš; Zahradníček, Radim; Fries, Jiří
Wire electrical discharge machining (WEDM) is an unconventional machining technology that can be used to machine materials with a minimum electrical conductivity. The technology is often employed in the automotive industry, as it makes it possible to produce mould parts of complex shapes. Copper alloys are commonly used as a electrodes for their high thermal conductivity. The subject of this study was creating mathematical models for machining optimization of Ampcoloy 35 with different thicknesses (ranging from 5 to 160 mm with a step of 5 mm) using WEDM to improve the surface properties of mould parts.The Box-Behnken type experiment was used with a total of 448 samples produced. The following machining parameters were altered over the course of the experiment: Pulse on and off time, Discharge current, and material thickness. The cutting speed was measured and the topography of the machined surfaces in the centre and at the margins of the samples, were analysed. The morphology and subsurface layer were also studied. What makes this study unique is the large number of the tested thicknesses, ranging from 5 to 160 mm with a step of 5 mm. The contribution of this study to the automotive industry and plastic injection mould production is therefore significant. The regression models for cutting speed and surface topography allow for efficient defect-free machining of Ampcoloy 35 of 5-160 mm thicknesses, both in the surface and subsurface layer.
Exploring the Influence of Soil Types on the Mineral Profile of Honey: Implications for Geographical Origin Prediction
(MDPI, 2024-07-26) Schmidlová, Simona; Javůrková, Zdeňka; Tremlová, Bohuslava; Hernik, Józef; Prus, Barbara; Marcinčák, Slavomír; Marcinčáková, Dana; Štarha, Pavel; Čížková, Helena; Kružík, Vojtěch; Bodor, Zsanett; Benedek, Csilla; Titěra, Dalibor; Boržíková, Jana; Pospiech, Matej
Honey contains a wide range of inorganic substances. Their content can be influenced, i.e., by the type of soil on which the bee pasture is located. As part of this study, the mineral profile of 32 samples of honey from hobby beekeepers from the Czech Republic wasevaluated and then compared with soil types in the vicinity of the beehive location. Pearson's correlation coefficient was used to express the relationship between mineral substances and soil type. There was a high correlation between antroposol and Zn (R = 0.98), Pb (R = 0.96), then between ranker and Mn (0.95), then regosol and Al (R = 0.97) (p < 0.05). A high negative correlation was found between regosol and Mg (R = -0.97), Cr (R = -0.98) and between redzinas and Al (R = -0.97) (p < 0.05). Both positive and negative high correlations were confirmed for phaeozem. The CART method subsequently proved that the characteristic elements for individual soil types are B, Ca, Mg, Ni, and Mn. The soil types of cambisol, fluvisol, gleysol, anthrosol, and kastanozem had the closest relationship with the elements mentioned, and it can therefore be assumed that their occurrence indicates the presence of these soil types within the range of beehive location.

Browse

Recent Submissions