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Mathematical models in logistics
Nevrlý, Vlastimír ; Holešovský, Jan (referee) ; Popela, Pavel (advisor)
The aim of the bachelor thesis is to model and generate test transportation networks, which are similar to real-world waste management networks. Several software tools (Mathematica, GAMS, Excel, VBA) are used to develop suitable procedures. The next task is to analyze dependence of computational complexity on the size of network by using statistical test computations. The existing original optimization model called NERUDA that supports decision-making in the eld of waste management is utilized. The obtained results are processed, analysed and interpreted in detail.
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Interval data and sample variance: computational aspects
Sokol, Ondřej ; Černý, Michal (advisor) ; Rada, Miroslav (referee)
This thesis deals with the calculation of the upper limit of the sample variance when the exact data are not known but intervals which certainly contain them are available. Generally, finding the upper limit of the sample variance knowing only interval data is an NP-hard problem, but under certain conditions imposed on the input data an appropriate efficient algorithm can be used. In this work algorithms were modified so that, even at the cost of exponential complexity, one can always find the optimal solution. The goal of this thesis is to compare selected algorithms for calculating the upper limit of sample variance over interval data from the perspective of the average computational complexity on the generated data. Using simulations it is shown that if the data meets certain conditions, the complexity of the average case is polynomial.
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Inconspicuous Appeal of Amorphous Computing Systems
Wiedermann, Jiří
Amorphous computing systems typically consist of myriads of tiny simple processors that are randomly distributed at fixed positions or move randomly in a confined volume. The processors are “embodied” meaning that each of them has its own source of energy, has a “body” equipped with various sensors and communication means and has a computational control part. Initially, the processors have no identifiers and from the technological reasons, in the interest of their maximal simplicity, their computational, communication, sensory and locomotion (if any) parts are reduced to an absolute minimum. The processors communicate wirelessly, e.g., in an airborne medium they communicate via a short-range radio, acoustically or optically and in a waterborne medium via molecular communication. In the extreme cases the computational part of the processors can be simplified down to probabilistic finite state automata or even combinatorial circuits and the system as a whole can still be made universally programmable. From the theoretical point of view the structure and the properties of the amorphous systems qualify them among the simplest (non-uniform) universal computational devices. From the practical viewpoint, once technology will enable a mass production of the required processors a host of new applications so far inaccessible to classical approaches to computing will follow.
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Modified Chinese Postman Problems - Experiments
Jelínek, Tomáš ; Fábry, Jan (advisor) ; Pelikán, Jan (referee)
This master's thesis describes modified Chinese Postman Problems. These Problems are solved by (mixed) integer linear programming. The modified problems and also used approach (integer programming) belong at least to the NP complexity class. The thesis analyzes, compares and estimates computational complexity of each model. Based on this analysis, usability of described models for solving real-life problems is deduced. The models are focused on problems in urban environment. Therefore, it is possible to apply these models on problems like optimization of a waste collection or road maintenance. Graph and problem generator is programmed for purposes of this thesis.
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Algorithms for solving of special knapsack problems and their computational complexity
Sem, Štěpán ; Ivánek, Jiří (advisor) ; Kalčevová, Jana (referee)
The thesis deals with knapsack problems variants and possibility of their solving, furthermore with the impact of particular task (instance) special structure on the effciency of tested approach. The thesis also proposes conversion possibility between described tasks and their continuous extension (continuous relaxation). It describes L3 algorithm and superdecreasing knapsack problem solving from the common sort of algorithms and Monte Carlo Method, simulated annealing and genetic algorithms from the sort of probability ones. Other possibilities are also discussed. Integral part of this thesis is the accompanying application, which was used to create groundwork used in the text and which can be also used to solve other instances.
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Optimalizace příznakového prostoru
Klimešová, Dana
The contribution deals with the problem of feature selection strategies for the case of high dimensional feature space. In this paper an effective method of feature selection is proposed where two different measures are considered and time and storage complexity is acceptable.
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