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Evolutionary Algorithms for Multiobjective Optimization
Pilát, Martin ; Neruda, Roman (advisor) ; Schoenauer, Marc (referee) ; Pošík, Petr (referee)
Multi-objective evolutionary algorithms have gained a lot of atten- tion in the recent years. They have proven to be among the best multi-objective optimizers and have been used in many industrial ap- plications. However, their usability is hindered by the large number of evaluations of the objective functions they require. These can be expensive when solving practical tasks. In order to reduce the num- ber of objective function evaluations, surrogate models can be used. These are a simple and fast approximations of the real objectives. In this work we present the results of research made between the years 2009 and 2013. We present a multi-objective evolutionary algo- rithm with aggregate surrogate model, its newer version, which also uses a surrogate model for the pre-selection of individuals. In the next part we discuss the problem of selection of a particular type of model. We show which characteristics of the various models are im- portant and desirable and provide a framework which combines sur- rogate modeling with meta-learning. Finally, in the last part, we ap- ply multi-objective optimization to the problem of hyper-parameters tuning. We show that additional objectives can make finding of good parameters for classifiers faster. 1
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Mathematical models in strategic decision-making
Khýr, Lukáš ; Popela, Pavel (referee) ; Pavlas, Martin (advisor)
This master thesis deals with various mathematical models, which can be used for designing the location of collection points for various fractions of municipal waste with consideration of walking distance, economic demands and utilization of allocated capacities. Scripts for generating input datasets for applied models from basic input data, which are address points with population and GPS coordinates, is also included in the thesis. The model was implemented in GAMS and the script was written in VBA in Microsoft Excel. Model was used in case study. Results of single and multi-criteria approaches are analyzed and compared.
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Risk aversion in portfolio efficiency
Puček, Samuel ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
This thesis deals with selecting the optimal portfolio for a risk averse investor. Firstly, we present the risk measures, specifically spectral risk me- asures which consider an individual risk aversion of the investor. Then we propose a diversification-consistent data envelopment analysis model. The model is searching for an efficient portfolio with respect to second-order sto- chastic dominance. The crux of the thesis is a model based on the theory of multi-criteria optimization and spectral risk measures. The presented mo- del is searching for an optimal portfolio suitable for the investor with a given risk aversion. In addition, the optimal portfolio is also consistent with second- order stochastic dominance efficiency. The topic of the practical part is a nu- merical study in which both models are implemented in MATLAB. Models are applied to a dataset from real financial markets. Personal contribution lies in comparing the diversification-consistent data envelopment analysis model and model based on multi-criteria optimization, both with respect to second order stochastic dominance efficiency.
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Advanced optimisation model for circular economy
Pluskal, Jaroslav ; Bednář, Josef (referee) ; Šomplák, Radovan (advisor)
This diploma thesis deals with application optimization method in circular economy branch. The introduction is focused on explaining main features of the issue and its benefits for economy and environment. Afterwards are mentioned some obstacles, which are preventing transition from current waste management. Mathematical apparatus, which is used in practical section, is described in the thesis. Core of the thesis is mathematical optimization model, which is implemented in the GAMS software, and generator of input data is made in VBA. The model includes all of significant waste management options with respect to economic and enviromental aspect, including transport. Functionality is then demostrated on a small task. Key thesis result is application of the model on real data concerning Czech Republic. In conclusion an analysis of computation difficulty, given the scale of the task, is accomplished.
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Multicriteria and robust extension of news-boy problem
Šedina, Jaroslav ; Kopa, Miloš (advisor) ; Kaňková, Vlasta (referee)
This thesis studies a classic single-period stochastic optimization problem called the newsvendor problem. A news-boy must decide how many items to order un- der the random demand. The simple model is extended in the following ways: endogenous demand in the additive and multiplicative manner, objective func- tion composed of the expected value and Conditional Value at Risk (CVaR) of profit, multicriteria objective with price-dependent demand, multiproduct exten- sion under dependent and independent demands, distributional robustness. In most cases, the optimal solution is provided. The thesis concludes with the nu- merical study that compares results of two models after applying the Sample Average Approximation (SAA) method. This study is conducted on the real data. 1
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Evolutionary Algorithms for Multiobjective Optimization
Pilát, Martin ; Neruda, Roman (advisor) ; Schoenauer, Marc (referee) ; Pošík, Petr (referee)
Multi-objective evolutionary algorithms have gained a lot of atten- tion in the recent years. They have proven to be among the best multi-objective optimizers and have been used in many industrial ap- plications. However, their usability is hindered by the large number of evaluations of the objective functions they require. These can be expensive when solving practical tasks. In order to reduce the num- ber of objective function evaluations, surrogate models can be used. These are a simple and fast approximations of the real objectives. In this work we present the results of research made between the years 2009 and 2013. We present a multi-objective evolutionary algo- rithm with aggregate surrogate model, its newer version, which also uses a surrogate model for the pre-selection of individuals. In the next part we discuss the problem of selection of a particular type of model. We show which characteristics of the various models are im- portant and desirable and provide a framework which combines sur- rogate modeling with meta-learning. Finally, in the last part, we ap- ply multi-objective optimization to the problem of hyper-parameters tuning. We show that additional objectives can make finding of good parameters for classifiers faster. 1
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Multiobjective portfolio optimization
Malá, Alena ; Kopa, Miloš (advisor) ; Dupačová, Jitka (referee)
The goal of this thesis is to summarize three basic principles of solving multi-objective programming problems. We focus on three approaches: a linear combination of objective functions, ε-constrained approach and a goal programming. All these methods are subsequently applied to US data. We consider monthly excess returns of ten US representative portfolios based on individual stock market capitalization of equity that serve as basic assets. Our aim is to find the efficient portfolios. Next we investigate a structure of these portfolios and their mutual relationships. Graphic representation of efficient frontiers is also included in the thesis. All calculations were performed using Mathematica software version 8.
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Planning and Drawing Module for Matches
Jelínek, Zdeněk ; Soukup, Ondřej (referee) ; Křivka, Zbyněk (advisor)
This bachelors thesis consists of description of a design and implementation of a module for drawing tournaments in competitive sports. The goal of the module is to match competitors in such a way that the repetitions of matches are minimal and the quality of the individual matches is the best, and that each competitor plays appropriate number of matches. The worst-case asymptotic time complexity of the resulting drawing algorithm is polynomial.
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Approximations in Stochastic Optimization and Their Applications
Mrázková, Eva ; Horová, Ivana (referee) ; Štěpánek, Petr (referee) ; Karpíšek, Zdeněk (advisor)
Mnoho inženýrských úloh vede na optimalizační modely s~omezeními ve tvaru obyčejných (ODR) nebo parciálních (PDR) diferenciálních rovnic, přičemž jsou v praxi často některé parametry neurčité. V práci jsou uvažovány tři inženýrské problémy týkající se optimalizace vibrací a optimálního návrhu rozměrů nosníku. Neurčitost je v nich zahrnuta ve formě náhodného zatížení nebo náhodného Youngova modulu. Je zde ukázáno, že dvoustupňové stochastické programování nabízí slibný přístup k řešení úloh daného typu. Odpovídající matematické modely, zahrnující ODR nebo PDR omezení, neurčité parametry a více kritérií, vedou na (vícekriteriální) stochastické nelineární optimalizační modely. Dále je dokázáno, pro jaký typ úloh je nutné použít stochastické programování (EO reformulace), a kdy naopak stačí řešit jednodušší deterministickou úlohu (EV reformulace), což má v praxi význam z hlediska výpočetní náročnosti. Jsou navržena výpočetní schémata zahrnující diskretizační metody pro náhodné proměnné a ODR nebo PDR omezení. Matematické modely odvozené pomocí těchto aproximací jsou implementovány a řešeny v softwaru GAMS. Kvalita řešení je určena na základě intervalových odhadů "optimality gapu" spočtených pomocí metody Monte Carlo. Parametrická analýza vícekriteriálního modelu vede na výpočet "efficient frontier". Jsou studovány možnosti aproximace modelu zahrnujícího pravděpodobnostní členy související se spolehlivostí pomocí smíšeného celočíselného nelineárního programování a reformulace pomocí penalizační funkce. Dále je vzhledem k budoucím možnostem paralelních výpočtů rozsáhlých inženýrských úloh implementován a testován PHA algoritmus. Výsledky ukazují, že lze tento algoritmus použít, i když nejsou splněny matematické podmínky zaručující konvergenci. Na závěr je pro deterministickou verzi jedné z úloh porovnána metoda konečných diferencí s metodou konečných prvků za použití softwarů GAMS a ANSYS se zcela srovnatelnými výsledky.
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Multiobjective optimization of electromagnetic structures based on self-organizing migration
Kadlec, Petr ; Prof. Hans L. Hartnagel (referee) ; Škvor,, Zbyněk (referee) ; Raida, Zbyněk (advisor)
Práce se zabývá popisem nového stochastického vícekriteriálního optimalizačního algoritmu MOSOMA (Multiobjective Self-Organizing Migrating Algorithm). Je zde ukázáno, že algoritmus je schopen řešit nejrůznější typy optimalizačních úloh (s jakýmkoli počtem kritérií, s i bez omezujících podmínek, se spojitým i diskrétním stavovým prostorem). Výsledky algoritmu jsou srovnány s dalšími běžně používanými metodami pro vícekriteriální optimalizaci na velké sadě testovacích úloh. Uvedli jsme novou techniku pro výpočet metriky rozprostření (spread) založené na hledání minimální kostry grafu (Minimum Spanning Tree) pro problémy mající více než dvě kritéria. Doporučené hodnoty pro parametry řídící běh algoritmu byly určeny na základě výsledků jejich citlivostní analýzy. Algoritmus MOSOMA je dále úspěšně použit pro řešení různých návrhových úloh z oblasti elektromagnetismu (návrh Yagi-Uda antény a dielektrických filtrů, adaptivní řízení vyzařovaného svazku v časové oblasti…).
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