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Optimization models for resource allocation
Franěk, Jiří ; Šeda, Miloš (referee) ; Kůdela, Jakub (advisor)
The thesis presents an overview of the issue of resource allocation optimization and construction processing of two models for the given example describing an engineering production company. The first of the created models, which was conceived as deterministic, was transformed into a stochastic one using different demand scenarios. The solution of the models itself was implemented in the Julia programming language using available optimization libraries. An analysis of the solution including its graphic representation was carried out and a production plan for the company was successfully created.
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Analysis of Impact of Covariates Entering Stochastic Optimization Problem
Volf, Petr
In the contribution we study consequences of imperfect information to precision of stochastic optimization solution. In particular, it is assumed that the characteristics of optimization problem are influenced by a set of covariates. This dependence is described via a regression model. Hence, the uncertainty is then caused by statistical estimation of regression parameters. The contribution will analyze several regression model cases, together with their application. Precision of results will be explored, both theoretically as well as with the aid of simulations.
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Stochastic optimization for electricity consumption control
Sekula, Jakub ; Popela, Pavel (referee) ; Kůdela, Jakub (advisor)
The aim of this work is to optimize charging of batteries used in an electric vehicle using electric charger control in order to decrease total costs. We will also count in scenario of using electric energy from vehicle’s batteries to run home demands because of different costs of energies during the day and night, when the batteries are usually charging. Given the uncertainty of events like the route, which will the vehicle cover, power demand of home or weather, we will use stochastic optimization, because we are able to tell with which probability would these events occur.
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Software Support for Timetabling
Macků, Veronika ; Šeda, Miloš (referee) ; Roupec, Jan (advisor)
The aim of this thesis is the analysis of the current approaches to scheduling at BUT and other institutions of higher learning and the subsequent creation of a software for semiautomatic timetabling. The first part acts as an introduction to university timetabling problems, the analysis of the given problem and an overview of possible solving algorithms. The second part deals with the creation of the sofware itself and the implementation of the chosen heuristic method.
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Benchmarking of swarm optimization algorithms
Mittaš, Eduard ; Dosoudilová, Monika (referee) ; Kůdela, Jakub (advisor)
This thesis deals with benchmarking of swarm optimization algorithms. First part handles optimization problem and it’s meaning in testing of algorithm’s performances. Next chapter describes the very benchmarking itself, it’s tools and software platforms. Afterwards individual algorithms, which were selected for implementation are described. Following this part is a program realization of solution, selected algorithms, selected testing functions and the data, which is exported by the program. The last chapter deals with results of respective performance tests, in which algorithms solved given testing problems. Eventually these results are evaluated and from them an outcome of efficiency and performance of algorithms is formed.
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Stochastic activity networks
Sůva, Pavel ; Dupačová, Jitka (advisor) ; Kaňková, Vlasta (referee)
In the present work, stochastic network models representing a project as a set of activities are studied, as well as different approaches to these models. The critical path method, stochastic network models with probability constraints, finding a reference project duration, worst-case analysis in stochastic networks and optimization of the parameters of the probability distributions of the activity durations are studied. Use of stochastic network models in telecommunications networks is also briefly presented. In a numerical study, some of these models are implemented and the~related numerical results are analyzed.
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Optimization in energy problems
Fürst, Matouš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
Title: Optimization in energy problems Author: Matouš Fürst Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis we present an optimization model of a semi-autonomous household, which aims to make energy management more efficient. The household is equipped with solar panels and an electric vehicle with a high-capacity battery. In the first part we summarize the basic properties of linear programming and two- stage stochastic linear programming. Subsequently, a two-stage stochastic linear program is formulated and solved in order to optimize the purchase, sale and storage of energy in the household during a single day. The program is formulated in two versions - with present and with departing vehicle. The final solution represents optimal decisions of the household and we discuss it with respect to the input data. In both versions the solution leads to a substantial reduction in costs compared to a household without a battery. Keywords: stochastic optimization, linear programming, domestic microgrid 1
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Robust approaches in portfolio optimization with stochastic dominance
Kozmík, Karel ; Kopa, Miloš (advisor)
We use modern approach of stochastic dominance in portfolio optimization, where we want the portfolio to dominate a benchmark. Since the distribution of returns is often just estimated from data, we look for the worst distribution that differs from empirical distribution at maximum by a predefined value. First, we define in what sense the distribution is the worst for the first and second order stochastic dominance. For the second order stochastic dominance, we use two different formulations for the worst case. We derive the robust stochastic dominance test for all the mentioned approaches and find the worst case distribution as the optimal solution of a non-linear maximization problem. Then we derive programs to maximize an objective function over the weights of the portfolio with robust stochastic dominance in constraints. We consider robustness either in returns or in probabilities for both the first and the second order stochastic dominance. To the best of our knowledge nobody was able to derive such program before. We apply all the derived optimization programs to real life data, specifically to returns of assets captured by Dow Jones Industrial Average, and we analyze the problems in detail using optimal solutions of the optimization programs with multiple setups. The portfolios calculated using...
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Market with several vendors
Trégner, Tomáš ; Lachout, Petr (advisor) ; Branda, Martin (referee)
The thesis studies the problem well-known in literature as the newsvendor problem. After summarizing the basic model we pay attention to two extensions of this problem and their combination in single model. The first extension concerns the possibility of the vendor to choose his selling price. The second extension is creation of market with several vendors. We describe both situations in the first chapter of the thesis. In the second chapter we study the combination of both extensions, which means the market with several vendors who can choose their selling prices. We touched several models of such market and we found that the problem is very complex. However we found the optimal reaction of one vendor on the strategy of the other vendor in case of special market with two vendors. That enabled us to create a programme that examines such market, mainly the dependence of the optimal decision of one vendor on the strategy of the second vendor and presence of the Nash equilibriums. 1
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Robust approaches in portfolio optimization with stochastic dominance
Kozmík, Karel ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
We use modern approach of stochastic dominance in portfolio optimization, where we want the portfolio to dominate a benchmark. Since the distribution of returns is often just estimated from data, we look for the worst distribution that differs from empirical distribution at maximum by a predefined value. First, we define in what sense the distribution is the worst for the first and second order stochastic dominance. For the second order stochastic dominance, we use two different formulations for the worst case. We derive the robust stochastic dominance test for all the mentioned approaches and find the worst case distribution as the optimal solution of a non-linear maximization problem. Then we derive programs to maximize an objective function over the weights of the portfolio with robust stochastic dominance in constraints. We consider robustness either in returns or in probabilities for both the first and the second order stochastic dominance. To the best of our knowledge nobody was able to derive such program before. We apply all the derived optimization programs to real life data, specifically to returns of assets captured by Dow Jones Industrial Average, and we analyze the problems in detail using optimal solutions of the optimization programs with multiple setups. The portfolios calculated using...
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