
Multiobjective shortest path problem with interval costs
Březina, Jiří ; Hladík, Milan (advisor) ; Fink, Jiří (referee)
The multiobjective shortest path problem with interval costs is a gener alization of the singlepair shortest path problem. In this problem, the edge weights are represented as tuples of intervals. The aim is to find the path that minimizes the maximum regret. We present theorems regarding the compu tation of the regret and the efficiency of a feasible solution to the problem. The main result of the thesis is an algorithm seeking for the solution with the least regret in the interval multiobjective shortest path problem. 1


Geometry of interval linear systems
Kotecký, Cyril ; Hladík, Milan (advisor) ; Rada, Miroslav (referee)
Interval linear systems of equalities and inequalities are linear systems, where the real numbered entries of the vectors and matrices are replaced with closed intervals of real numbers. The sets of solutions to these systems have interesting properties, mainly that they are unions of exponentially many convex polyhedra. This makes solving many problems hard, while on the other hand, the solution sets have a form that is convenient to analyze. This thesis deals with studying the geometry of such sets. We will begin by reviewing known properties of these sets, such as boundedness and connectedness. But mostly, we will focus on the conditions for convexity and the characterization of the convex hull, which are both known for the special case of systems with invertible interval matrices. Using polyhedral theory, we will broaden these results, mostly to general systems of interval linear inequalities. We will present illustrative examples, some serving as counterexamples in cases where generalizations are not possible. 1


Determination of risks, benefits and efficiency in the implementation of the information manufacturing system MES in production
Hladík, Milan ; Luňáček, Jiří (referee) ; Osička, Karel (advisor)
This master thesis deals with the analysis of the possibilities of implementing the MES manufacturing information system in a company that focuses on the production of medical devices. The thesis is divided into several parts. Firstly, the theoretical background of the thesis is described and then the current situation in the company is mapped out in detail, especially the area of using paper documentation, the socalled DHR. In the practical part of the thesis, the time and financial savings for the company in case of implementation of the system are then quantified, as well as the cost of the investment. Subsequently, the benefits and risks that may arise in such a largescale project are identified, and at the same time measures are proposed to eliminate these risks completely or reduce their impact. It also includes a proposal for the time allocation necessary for implementation, including the division into individual phases in which the system would be deployed for production. The thesis concludes with a calculation of the return on investment and a proposal for a solution.

 

Results of the autumn extended research of the ichthyofauna of the lakes Laka and Čertovo, including the adjacent streams.
Blabolil, Petr ; Bartoň, Daniel ; Draštík, Vladislav ; Jůza, Tomáš ; Hladík, Milan ; Holubová, Michaela ; Hůda, J. ; Kočvara, Luboš ; Muška, Milan ; Peterka, Jiří ; Vrba, Jaroslav
The report describes the results of a unique survey of the ichthyofauna in two areas of the Šumava National Park, where catches were made by an electric generator in the autumn of 2021.


Search in Imperfect Information Games
Schmid, Martin ; Hladík, Milan (advisor) ; Szepesvari, Csaba (referee) ; Bošanský, Branislav (referee)
From the very dawn of the field, search with value functions was a fun damental concept of computer games research. Turing's chess algorithm from 1950 was able to think two moves ahead, and Shannon's work on chess from 1950 includes an extensive section on evaluation functions to be used within a search. Samuel's checkers program from 1959 already combines search and value functions that are learned through selfplay and bootstrapping. TDGammon improves upon those ideas and uses neural networks to learn those complex value functions  only to be again used within search. The combination of decisiontime search and value functions has been present in the remarkable milestones where computers bested their human counterparts in long standing challenging games  DeepBlue for Chess and AlphaGo for Go. Until recently, this powerful framework of search aided with (learned) value functions has been limited to perfect information games. As many interesting problems do not provide the agent perfect information of the environment, this was an unfortunate limitation. This thesis introduces the reader to sound search for imperfect information games. 1


Integer programming and its applications
Eliáš, Marek ; Pergel, Martin (advisor) ; Hladík, Milan (referee)
In this thesis we present and implement several graph algorithms. In the rst part, we discus algorithm for the minimum weighted perfect matching in bipartite and general graphs based on the primaldual method and their modi cations. In the second part, there are algorithms for the maxcut in planar graphs and Christo des' heuristic for TSP. We present full descriptions of these algorithms providing either proof of correctness or reference to the literature. The last part deals with two approaches which we use to visualise these algorithms with di erent degree of interactivity both allowing custom graph on input.


Operation optimization in wholesale warehouses
Kolárik, Jan ; Pangrác, Ondřej (advisor) ; Hladík, Milan (referee)
The goal of this work is to choose a strategy for given warehouse that will increase the efficiency of its operation. This is primarily about reducing customer downtime and minimizing the distance travelled by handling machines. The final program can generate warehouse structure according to given parameters and then evaluate monitored variables from simulated operations based on optimization techniques used. There is also a planar and spatial warehouse model available, which helps to visualize what is actually happening in the warehouse. The program could serve as an auxiliary tool in the organizing of wholesale warehouse operations and reduce costs required for its operation.


Orthogonal contrator
Krejčová, Kristýna ; Hladík, Milan (advisor) ; Pilát, Martin (referee)
The thesis proposes an orthogonal contractors. At the beginning we define the basic concepts of interval analysis and interval linear algebra. Then, we pro pose several contractor methods. Based on propagation techniques, we propose contraction according to bilinear and quadratic terms of the conditions that we get from the properties of orthogonal matrices. We also linearize bilinear terms and use linear programming. The known contractors by eigenvalues we employed to the construction contractor by the determinant. The proposed methods are implemented in Matlab with the use of the toolbox Intlab and the library Versoft. Finally, we test and compare the presented methods. Based on the comparison of particular techniques we build a final contractor. 1


Visualisation of phenomena related to linear programming
Gregor, Jan ; Pergel, Martin (advisor) ; Hladík, Milan (referee)
This thesis introduces design and implementation of scripting language especially focused on visualization of phenomena related to linear programming. We describe a construction of an interpreter and a theory around it. Further we specify what the linear programming is and we show the simplex method. Regarding requierements of manipulation and visualization in vector space of dimension greater than three, there could not be used standard methods, e.g., from computer graphic. That is why there is also a description of modified algorithms used in this cases. Namely projection, transformation and drawing of ndimensional polyhedron. This thesis also contains examples of scripts showing possibilities of the language and its interpreter.
