This report will look at optimization under parameters of uncertainties. It will describe the subject in its wider form, then two model examples will be studied, followed by an application to an ABB product. The Monte Carlo method will be described and scrutinised, with the quasi-Monte Carlo method being favoured for large problems. An example will illustrate how the choice of Monte Carlo method will affect the efficiency of the simulation when evaluating  functions of different dimensions. Then an overview of mathematical optimization is given, from its simplest form to nonlinear, nonconvex  optimization problems containing uncertainties.A Monte Carlo simulation is applied to the design process and cost function for a custom made ABB transformer, where the production process is assumed to contain some uncertainties.The result from optimizing an ABB cost formula, where the in-parameters contains some uncertainties, shows how the price can vary and is not fixed as often assumed, and how this could influence an accept/reject decision.

Alexander A. Razborov (2007) developed the theory of flag algebras to compute the minimum asymptotic density of triangles in a graph as a function of its edge density. The theory of flag algebras, however, can be used to study the asymptotic density of several combinatorial objects. In this dissertation, we present two original results obtained in the theory of tournaments through application of flag algebra proof techniques. The first result concerns minimization of the asymptotic density of transitive tournaments in a sequence of tournaments, which we prove to occur if and only if the sequence is quasi-random. As a byproduct, we also obtain new quasi-random characterizations and several other flag algebra elements whose density is minimized if and only if the sequence is quasi-random. The second result concerns a class of equivalent properties of a sequence of tournaments that we call quasi-carousel properties and that, in a similar fashion as quasi-random properties, force the sequence to converge to a specific limit homomorphism. Several quasi-carousel properties, when compared to quasi-random properties, suggest that quasi-random sequences and quasi-carousel sequences are the furthest possible from each other within the class of almost balanced sequences. / Alexander A. Razborov (2007) desenvolveu a teoria de álgebras de flags para calcular a densidade assintótica mínima de triângulos em um grafo em função de sua densidade de arestas. A teoria das álgebras de flags, contudo, pode ser usada para estudar densidades assintóticas de diversos objetos combinatórios. Nesta dissertação, apresentamos dois resultados originais obtidos na teoria de torneios através de técnicas de demonstração de álgebras de flags. O primeiro resultado compreende a minimização da densidade assintótica de torneios transitivos em uma sequência de torneios, a qual provamos ocorrer se e somente se a sequência é quase aleatória. Como subprodutos, obtemos também novas caracterizações de quase aleatoriedade e diversos outros elementos da álgebra de flags cuja densidade é minimizada se e somente se a sequência é quase aleatória. O segundo resultado compreende uma classe de propriedades equivalentes sobre uma sequência de torneios que chamamos de propriedades quase carrossel e que, de uma forma similar às propriedades quase aleatórias, forçam que a sequência convirja para um homomorfismo limite específico. Várias propriedades quase carrossel, quando comparadas às propriedades quase aleatórias, sugerem que sequências quase aleatórias e sequências quase carrossel estão o mais distantes possível umas das outras na classe de sequências quase balanceadas.

Alexander A. Razborov (2007) developed the theory of flag algebras to compute the minimum asymptotic density of triangles in a graph as a function of its edge density. The theory of flag algebras, however, can be used to study the asymptotic density of several combinatorial objects. In this dissertation, we present two original results obtained in the theory of tournaments through application of flag algebra proof techniques. The first result concerns minimization of the asymptotic density of transitive tournaments in a sequence of tournaments, which we prove to occur if and only if the sequence is quasi-random. As a byproduct, we also obtain new quasi-random characterizations and several other flag algebra elements whose density is minimized if and only if the sequence is quasi-random. The second result concerns a class of equivalent properties of a sequence of tournaments that we call quasi-carousel properties and that, in a similar fashion as quasi-random properties, force the sequence to converge to a specific limit homomorphism. Several quasi-carousel properties, when compared to quasi-random properties, suggest that quasi-random sequences and quasi-carousel sequences are the furthest possible from each other within the class of almost balanced sequences. / Alexander A. Razborov (2007) desenvolveu a teoria de álgebras de flags para calcular a densidade assintótica mínima de triângulos em um grafo em função de sua densidade de arestas. A teoria das álgebras de flags, contudo, pode ser usada para estudar densidades assintóticas de diversos objetos combinatórios. Nesta dissertação, apresentamos dois resultados originais obtidos na teoria de torneios através de técnicas de demonstração de álgebras de flags. O primeiro resultado compreende a minimização da densidade assintótica de torneios transitivos em uma sequência de torneios, a qual provamos ocorrer se e somente se a sequência é quase aleatória. Como subprodutos, obtemos também novas caracterizações de quase aleatoriedade e diversos outros elementos da álgebra de flags cuja densidade é minimizada se e somente se a sequência é quase aleatória. O segundo resultado compreende uma classe de propriedades equivalentes sobre uma sequência de torneios que chamamos de propriedades quase carrossel e que, de uma forma similar às propriedades quase aleatórias, forçam que a sequência convirja para um homomorfismo limite específico. Várias propriedades quase carrossel, quando comparadas às propriedades quase aleatórias, sugerem que sequências quase aleatórias e sequências quase carrossel estão o mais distantes possível umas das outras na classe de sequências quase balanceadas.

Un grand nombre d'études ont été faites dans le domaine de l'Optimisation Stochastique en général et les Algorithmes Génétiques en particulier. L'essentiel des nouveaux développements ou des améliorations faites sont alors testés sur des jeux de tests très connus tels que BBOB, CEC, etc. conçus de telle manière que soient présents les principaux défis que les optimiseurs doivent relever : non séparabilité, multimodalité, des vallées où le gradient est quasi-nul, et ainsi de suite. La plupart des études ainsi faites se déroulent via une application directe sur le jeu de test, optimisant un nombre donné de variables pour atteindre un critère précis. La première contribution de ce travail consiste à étudier l'impact de la remise en cause de ce fonctionnement par deux moyens : le premier repose sur l'introduction d'un grand nombre de variables qui n'ont pas d'impact sur la valeur de la fonction optimisée ; le second quant à lui relève de l'étude des conséquences du mauvais conditionnement d'une fonction en grande dimension sur les performances des algorithmes d'optimisation stochastique. Une deuxième contribution se situe dans l'étude de l'impact de la modification des mutations de l'algorithme CMA-ES,où, au lieu d'utiliser des mutations purement aléatoires, nous allons utiliser des mutations quasi-aléatoires. Ce travail introduit également la ``Sieves Method'', bien connue des statisticiens. Avec cette méthode, nous commençons par optimiser un faible nombre de variables, nombre qui est ensuite graduellement incrémenté au fil de l'optimisation.Bien que les jeux de tests existants sont bien sûr très utiles, ils ne peuvent constituer que la première étape : dans la plupart des cas, les jeux de tests sont constitués d'un ensemble de fonctions purement mathématiques, des plus simples comme la sphère, aux plus complexes. Le but de la conception d'un nouvel optimiseur, ou l'amélioration d'un optimiseur existant, doit pourtant in fine être de répondre à des problèmes du monde réel. Ce peut-être par exemple la conception d'un moteur plus efficace, d'identifier les bons paramètres d'un modèle physique ou encore d'organiser des données en groupes.Les optimiseurs stochastiques sont bien évidemment utilisés sur de tels problèmes, mais dans la plupart des cas, un optimiseur est choisi arbitrairement puis appliqué au problème considéré. Nous savons comment les optimiseurs se comparent les uns par rapport aux autres sur des fonctions artificielles, mais peu de travaux portent sur leur efficacité sur des problèmes réels. L'un des principaux aspects de des travaux présentés ici consiste à étudier le comportement des optimiseurs les plus utilisés dans la littérature sur des problèmes inspirés du monde réel, voire des problèmes qui en viennent directement. Sur ces problèmes, les effets des mutations quasi-aléatoires de CMA-ES et de la``Sieves Method'' sont en outre étudiés. / A lot of research is being done on Stochastic Optimisation in general and Genetic Algorithms in particular. Most of the new developments are then tested on well know testbeds like BBOB, CEC, etc. conceived to exhibit as many pitfalls as possible such as non-separability, multi-modality, valleys with an almost null gradient and so on. Most studies done on such testbeds are pretty straightforward, optimising a given number of variables for there cognized criterion on the testbed. The first contribution made here is to study the impact of some changes in those assumptions, namely the effect of supernumerary variables that don't change anything to a function evaluation on the one hand, and the effect of a change of the studied criterion on the other hand. A second contribution is in the modification of the mutation design for the algorithm CMA-ES, where we will use Quasi-Random mutations instead of purely random ones. This will almost always result in a very clear improvement ofthe observed results. This research also introduces the Sieves Method well known in statistics, to stochastic optimisers: by first optimising a small subset of the variables and gradually increasing the number of variables during the optimization process, we observe on some problems a very clear improvement. While artificial testbeds are of course really useful, they can only be the first step: in almost every case, the testbeds are a collection of purely mathematical functions, from the simplest one like the sphere, to some really complex functions. The goal of the design of new optimisers or the improvement of an existing one is however, in fine, to answer some real world question. It can be the design of a more efficient engine, finding the correct parameters of a physical model or even to organize data in clusters. Stochastic optimisers are used on those problems, in research or industry, but in most instances, an optimiser ischosen almost arbitrarily. We know how optimisers compare on artificial functions, but almost nothing is known abouttheir performances on real world problems. One of the main aspect of the research exposed here will be to compare someof the most used optimisers in the literature on problems inspired or directly coming from the real-world. On those problems, we will additionally test the efficiency of quasi-random mutations in CMA-ES and the Sieves-Method.

This work presents a new test case generation methodology, which has a high degree of automation (cost reduction); while providing increased power in terms of defect detection (benefits increase). Our solution is a variation of model-based testing, which takes advantage of symbolic grammars (a context-free grammar where terminals are replaced by regular expressions that represent their solution space) and quasi-random sequences to generate test cases. Previous test case generation techniques are enhanced with adaptive random testing to maximize input space coverage; and selective and directed sentence generation techniques to optimize sentence generation. Our solution was tested by generating 200 firewall policies containing up to 20 000 rules from a generic firewall grammar. Our results show how our system generates test cases with superior coverage of the input space, increasing the probability of defect detection while reducing considerably the needed number the test cases compared with other previously used approaches. / Software Engineering and Intelligent Systems

In this thesis work, importance of radome structures for antenna systems is emphasized. Structural and electromagnetic requirements of various types of radome structures are analyzed and specific properties are given. Electromagnetic scattering analysis of sandwich type radome seams has been done. Total antenna system far electromagnetic field expression, which is the combination of original antenna far electromagnetic field and the scattered electromagnetic field of the framework of the sandwich radome structure has been found and simulated. To enhance electromagnetic transparency of sandwich type radomes two sandwich radome design methods are proposed which are expressed as Geometrical Randomization and Tuning the Seams. Electromagnetic scattering level minimizations advanced by these design methods are presented with related simulations.

No description available.

This thesis deals with the method of distributed ray tracing focusing on optimalization of this method. The method uses simulation of some attributes of light by distributing rays of lights and it produces high quality and partly realistic images. The price for realitic effects is the high computational complexity of the method. The thesis analysis the theory connected with these aspects. A large part describes optimalizations of this method, i.e. searching for the nearest triangle intersection using kd-trees, quasi random sampling with faster convergence, the use of SSE instruction set and fast ray - triangle intersection. These optimalizations brought a noticable speed - up. The thesis includes description of implementation of these techniques. The implementation itself emphasises the practical usability including generating some advanced animations and universal description of objects.