
Advanced Decomposition Methods in Stochastic Convex Optimization
Kůdela, Jakub ; Fabian, Csaba (referee) ; Šmíd,, Martin (referee) ; Popela, Pavel (advisor)
Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warmstart” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích.


Models and methods for routing problems in logistics
Muna, Izza Hasanul ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
The thesis focuses on how to optimize vehicle routes for distributing logistics. This vehicle route optimization is known as a vehicle routing problem (VRP). The VRP has been extended in numerous directions for instance by some variations that can be combined. One of the extension forms of VRP is a capacitated VRP with stochastics demands (CVRPSD), where the vehicle capacity limit has a nonzero probability of being violated on any route. So, a failure to satisfy the amount of demand can appear. A strategy is required for updating the routes in case of such an event. This strategy is called as recourse action in the thesis. The main objective of the research is how to design the model of CVRPSD and find the optimal solution. The EEV (Expected Effective Value) and FCM (Fuzzy CMeans) – TSP (Travelling Salesman Problem) approaches are described and used to solve CVRPSD. Results have confirmed that the EEV approach has given a better performance than FCMTSP for solving CVRPSD in small instances. But EEV has disadvantage, that the EEV is not capable to solve big instances in an acceptable running time because of complexity of the problem. In the real situation, the FCM –TSP approach is more suitable for implementations than the EEV because the FCM – TSP can find the solution in a shorter time. The disadvantage of this algorithm is that the computational time depends on the number of customers in a cluster.

 

Hybrid Algorithms in Optimization
Zamazal, Petr ; Hrabec, Pavel (referee) ; Popela, Pavel (advisor)
This work deals with the solution of an integer programming task using a hybrid algorithm. Mentioned task is a minimum cost network flow problem with option of adding new edges. The hybrid algorithm is based on a genetic algorithm using the network simplex method. Implementation is in the Python programming language.


Statistics Control of Process Described by Attributive and Continues Variable
Svobodová, Hana ; Popela, Pavel (referee) ; Bednář, Josef (advisor)
This thesis aimes at approaching the problem of control diagrams. The first part summarizes the theoretical knowledge about the control diagrams, including their sorting based on the type of the monitored quantity. The different types of diagrams are described in detail. The second part deals with the practical use of control diagrams using actual data. Tests of definable causes are used on these data, and the causes of failure are sought. The key is to assess process stability.


Modelling Languages for Optimization Problems
Talpa, Jaroslav ; Roupec, Jan (referee) ; Popela, Pavel (advisor)
This bachelor thesis is concerned with the area of modeling and solving of optimization problems, mainly by the use of modeling languages. For the solving of two selected types of complex optimization problems, sensitivity analysis and multistage optimization, two original software solutions in Java using the GAMS modeling language, are described in the paper, which are further tested and applied to real problems. The thesis also describes the issue of parallelism which is implemented by the proposed programs.


Network simplex method
Khýr, Lukáš ; Janošťák, František (referee) ; Popela, Pavel (advisor)
This thesis is focused on summary knowledges relating to mathematical modeling in optimization area. We will deal with simplex method in detail and especially its network modification, which is used in various practical applications. We will solve tasks of various sizes and compare their solutions using implementation these two methods in Matlab. There is solved a task with real data provided by the Institute of Process Engineering at the end of the work.


Correlation coefficients and their field of application
Rudžík, Matej ; Popela, Pavel (referee) ; Žák, Libor (advisor)
This bachelor’s thesis deals with different types of correlation coefficients and their properties depending on the data layout. The theoretical part of this work contains definitions of various types of correlation coefficients and tests related with this issue. The practical part compares the behaviour of parametric and nonparametric correlation coefficients in different situations. This comparison is realised in program MATLAB.


Mathematical Programs for Blending Problems
Kalenský, Vít ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
This diploma thesis deals with optimization models with design of a new waste management infrastructure in the Czech Republic, such that combustible waste, which is not utilized by the material recovering, can be used by energy recovering. This task is handled by optimization models, including trac and mixing problems. First of all, the concepts of graph theory and optimization are presented in this paper. Subsequently, some of the GAMS functions are discussed, and later the VBA programming language used to handle the larger data quickly is presented. In the main part, three gradually expanding models are developed. At the end the data from the waste management information system are implemented into them.


Advanced Optimization of Network Flows
Cabalka, Matouš ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
The master’s thesis focuses on the optimization models in logistics with emphasis on the network interdiction problem. The brief introduction is followed by two overview chapters  graph theory and mathematical programming. Important definitions strongly related to network interdiction problems are introduced in the chapter named Basic concepts of graph theory. Necessary theorems used for solving problems are following the definitions. Next chapter named Introduction to mathematical programming firstly contains concepts from linear programming. Definitions and theorems are chosen with respect to the following maximum flow problem and the derived dual problem. Concepts of stochastic optimization follow. In the fifth chapter, we discuss deterministic models of the network interdiction. Stochastic models of the network interdiction follow in the next chapter. All models are implemented in programmes written in the programming language GAMS, the codes are attached.
