Na busca de novos materiais que possuam boa resistência mecânica, baixo peso e de fácil manufatura, surgem os compósitos e os compósitos reforçados direcionando a uma ampla área de aplicações e estudos em desenvolvimento. Os materiais compósitos têm um vasto campo de aplicação, porém quando sujeitos a maiores esforços, não apresentam grande resistência e bom desempenho frente aos materiais metálicos. Os materiais compósitos quando reforçados com fibras multiplicam sua resistência consideravelmente, tornando-se um excelente substituto de materiais que possuem boa resistência mecânica como os metais, sendo um material resistente à oxidação. Em muitos casos os compósitos reforçados substituem os metais com um desempenho superior, como exemplo a aplicação de materiais reforçados com fibra de carbono. Este trabalho tem como objetivo criar uma plataforma para o desenvolvimento de um software para o cálculo otimizado das trajetórias das fibras em materiais compósitos, com fibras que venham a reforçar o mesmo e que venham a ser utilizados pela comunidade em diversas áreas como mecânica, medicina, elétrica, entre várias outras. / In the search of new materials, which have good mechanic strength, low weight and easy manufacturing, appear the composites and reinforced composites leading to an ample area of applications and studies in development. The composites materials have a vast field of application, however when subjected to a bigger effort, they do not show a great strength and a good development when compared to metallic materials. The composites materials when reinforced with fibers multiply their strength considerably, becoming an excellent substitute of materials, which have mechanic strength like metals, which in a strong material to corrosion. In many cases, the reinforced composites substitute the metals with a higher development, for example, like applications of reinforced materials with carbon fiber. This production has to objective, to create a platform to development of a software to a calculation optimization of course the fibers in a composite material, using fibers that come to reinforce it and are able to used by the community in many areas like mechanic, medicine, electric and among others.

A crescente necessidade de buscar operações mais eficientes, com menor custo e mais sustentáveis tem feito com que empresas passassem a procurar oportunidades pelas quais estes objetivos pudessem ser atingidos. Na área de transportes encontrou-se na colaboração uma oportunidade para tal. Este trabalho trata o problema de cobertura rotas com cardinalidade restrita (PCRCR), onde empresas que realizam viagens de carga cheia se unem com o objetivo de reduzir o deslocamento vazio de veículos através da formação de ciclos. É chamado de problema de cardinalidade restrita uma vez que limitamos o número de máximo de viagens no ciclo, o que torna este problema NP-Hard. Existem na literatura duas heurísticas (construtivas) e um modelo por programação linear inteira para a solução deste problema. Este trabalho apresenta uma heurística baseada em um método de busca local que reduziu em média 3,19% os melhores resultados apresentados na literatura. Também são apresentados os tempos de execução de cada um dos algoritmos e a importância de escolher de uma boa solução inicial quando se deseja implantar uma Heurística com Busca Local. / The growing need to seek more efficient, lower cost and more sustainable operations has caused industries to seek opportunities in which these objectives could be achieved. In the area of transportation, collaboration is an opportunity for that. This work deals with the cardinality constrained lane covering problem (CCLCP), where companies who uses full truck loads join efforts in order to reduce empty vehicle travel through closed cycle formation. It is known as cardinality constraint problem as the maximum number of trips in the cycle is limited to an integer number, which makes this problem NP-Hard. There are two heuristics in the literature (constructive) and an integer linear programming model for solving this problem. This work presents a heuristic based on a local search method that reduced an average of 3.19% the better results in the literature. It also presents the execution times of each algorithm and the importance of choosing a good initial solution when you want to create a Local Search Heuristic.

Remote sensors and unmanned aerial vehicles (UAVs) have the potential to dramatically improve infrastructure health monitoring in terms of accuracy of the information and frequency of data collection. UAV automation has made significant progress but that automation is also creating vast amounts of data that needs to be processed into actionable information. A key aspect of this work is the optimization (not just automation) of data collection from UAVs for targeted planning of mission objectives. This work investigates the use of camera planning for Structure from Motion for 3D modeling of infrastructure. Included in this thesis is a novel multi-scale view-planning algorithm for autonomous targeted inspection. The method presented reduced the number of photos needed and therefore reduced the processing time while maintaining desired accuracies across the test site. A second focus in this work investigates various set covering problem algorithms to use for selecting the optimal camera set. The trade-offs between solve time and quality of results are explored. The Carousel Greedy algorithm is found to be the best method for solving the problem due to its relatively fast solve speeds and the high quality of the solutions found. Finally, physical flight tests are used to demonstrate the quality of the method for determining coverage. Each of the set covering problem algorithms are used to create a camera set that achieves 95% coverage. The models from the different camera sets are comparable despite having a large amount of variability in the camera sets chosen. While this study focuses on multi-scale view planning for optical sensors, the methods could be extended to other remote sensors, such as aerial LiDAR.

Remote sensors and unmanned aerial vehicles (UAVs) have the potential to dramatically improve infrastructure health monitoring in terms of accuracy of the information and frequency of data collection. UAV automation has made significant progress but that automation is also creating vast amounts of data that needs to be processed into actionable information. A key aspect of this work is the optimization (not just automation) of data collection from UAVs for targeted planning of mission objectives. This work investigates the use of camera planning for Structure from Motion for 3D modeling of infrastructure. Included in this thesis is a novel multi-scale view-planning algorithm for autonomous targeted inspection. The method presented reduced the number of photos needed and therefore reduced the processing time while maintaining desired accuracies across the test site. A second focus in this work investigates various set covering problem algorithms to use for selecting the optimal camera set. The trade-offs between solve time and quality of results are explored. The Carousel Greedy algorithm is found to be the best method for solving the problem due to its relatively fast solve speeds and the high quality of the solutions found. Finally, physical flight tests are used to demonstrate the quality of the method for determining coverage. Each of the set covering problem algorithms are used to create a camera set that achieves 95% coverage. The models from the different camera sets are comparable despite having a large amount of variability in the camera sets chosen. While this study focuses on multi-scale view planning for optical sensors, the methods could be extended to other remote sensors, such as aerial LiDAR.

Covering arrays for words of length t over a d letter alphabet are k × n arrays with entries from the alphabet so that for each choice of t columns, each of the dt t-letter words appears at least once among the rows of the selected columns. We study two schemes in which all words are not considered to be different. In the first case, words are equivalent if they induce the same partition of a t element set. In the second case, words of the same weighted sum are equivalent. In both cases we produce logarithmic upper bounds on the minimum size k = k(n) of a covering array. Most definitive results are for t = 2, 3, 4.

abstract: This dissertation studies three classes of combinatorial arrays with practical applications in testing, measurement, and security. Covering arrays are widely studied in software and hardware testing to indicate the presence of faulty interactions. Locating arrays extend covering arrays to achieve identification of the interactions causing a fault by requiring additional conditions on how interactions are covered in rows. This dissertation introduces a new class, the anonymizing arrays, to guarantee a degree of anonymity by bounding the probability a particular row is identified by the interaction presented. Similarities among these arrays lead to common algorithmic techniques for their construction which this dissertation explores. Differences arising from their application domains lead to the unique features of each class, requiring tailoring the techniques to the specifics of each problem. One contribution of this work is a conditional expectation algorithm to build covering arrays via an intermediate combinatorial object. Conditional expectation efficiently finds intermediate-sized arrays that are particularly useful as ingredients for additional recursive algorithms. A cut-and-paste method creates large arrays from small ingredients. Performing transformations on the copies makes further improvements by reducing redundancy in the composed arrays and leads to fewer rows. This work contains the first algorithm for constructing locating arrays for general values of $d$ and $t$. A randomized computational search algorithmic framework verifies if a candidate array is $(\bar{d},t)$-locating by partitioning the search space and performs random resampling if a candidate fails. Algorithmic parameters determine which columns to resample and when to add additional rows to the candidate array. Additionally, analysis is conducted on the performance of the algorithmic parameters to provide guidance on how to tune parameters to prioritize speed, accuracy, or a combination of both. This work proposes anonymizing arrays as a class related to covering arrays with a higher coverage requirement and constraints. The algorithms for covering and locating arrays are tailored to anonymizing array construction. An additional property, homogeneity, is introduced to meet the needs of attribute-based authorization. Two metrics, local and global homogeneity, are designed to compare anonymizing arrays with the same parameters. Finally, a post-optimization approach reduces the homogeneity of an anonymizing array. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2019

We extend Sharkovskii's theorem concerning orbit lengths of endomorphisms of the real line to endomorphisms of a path component of the solenoid and certain subspaces of the Warsawanoid. In particular, Sharkovskii showed that if there exists an orbit of length 3 then there exist orbits of all lengths. The solenoid is the inverse limit of double covers over the circle, and the Warsawanoid is the inverse limit of double covers over the Warsaw circle. We show Sharkovskii's result is true for path components of the solenoid and certain subspaces of the Warsawanoid.

In combinatorial optimization, covering problems are those problems where given a ground set and a family of subsets of the ground set, the objective is to find a minimum cost set of subsets whose union contains the ground set. We consider covering problems in the context of Computational Geometry, which is a subfield of Computer Science that deals with problems associated with geometric objects such as points, lines, disks, polygons etc. In particular, geometric covering is an active research area, where the ground set and the family of subsets are induced by geometric objects. Covering problems in combinatorial optimizations often have a geometric analogue that arises naturally, and though such problems remain NP-hard, it is often possible to exploit the geometric properties of the set system to obtain better approximation algorithms. In this work, the fundamental problem that we consider is a generalization of geometric covering, where each element in the ground set may need to covered by more than one subset. To be precise, the problem is defined as follows: given two sets of points X, Y and a coverage function κ : X → Z+ ∪ {0}, construct balls centered on the points in Y such that each point in X is covered by at least κ(x) distinct balls. The objective in this problem is to minimize the total cost, which is a function of the radii of the balls. This problem is termed as the metric multi-cover (MMC) problem. We first consider version of the MMC problem where κ(x) = 1 for all clients, i.e. the 1-covering case. The known results that give a constant factor approximation for this problem are variations of LP-based primal-dual algorithm. We use a modified local search technique, motivated by geometric idea, to derive a simple, constant- factor approximation for this problem in Chapter 2. We then look at the MMC problem where the point sets X,Y are in the Euclidean plane, and each client x ∈ X needs to be covered by at least κ(x) distinct disks centered on the points in Y . In Chapter 4, we give the first polynomial time constant factor approximation for this problem, in which the constant is independent of the coverage function κ. Our solution also has an incremental property, which allows the algorithm to handle increases in the coverage requirement by increasing the radii of the current server disks, without affecting the approximation factor. In the next problem, we move from the Euclidean plane to arbitrary metric spaces where we consider the uniform MMC problem. In this problem, each client x has the demand κ(x) = k, where k > 0 is an integer. We give the first constant factor approximation (independent of k) for this problem. The key contribution that led to this result is the formulation of a partitioning scheme of the servers in the uniform MMC problem, that reduces the uniform MMC problem to k instances of 1-covering problem, while preserving the optimality of the solution to a constant multiplicative factor. We present the partitioning scheme as an independent result in Chapter 5, which we then use to solve the uniform MMC problem in Chapter 6. The MMC problem with arbitrary coverage function κ is then considered in Chapter 7. The key challenge that the non-uniform version presents is that the symmetry of the server partitioning scheme breaks down as the coverage demands of clients are independent of each other. We present a constant factor algorithm for this problem in Chapter 7. The last problem that we consider is the t-MMC problem, which is a restricted version of the uniform MMC problem. The objective is to compute a cover in which each client is covered by at least k distinct server disks, using atmost t server disks in total. This problem is a generalization of the clustering problem (where k = 1), and to our knowledge this is the first time this generalization has been considered. We give a constant factor approximation for this problem in Chapter 8.

This thesis presents and develops a theory of self-reduction. This process is used to map instances of combinatorial optimisation problems onto smaller, more easily solvable instances in such a way that a solution of the former can be readily re-constructed, without loss of information or quality, from a solution of the latter. Self-reduction rules are surveyed for the Graph Colouring Problem, the Maximum Clique Problem, the Steiner Problem in Graphs, the Bin Packing Problem and the Set Covering Problem. This thesis introduces the problem of determining the maximum sequence of self-reductions on a given structure, and shows how the theory of confluence can be adapted from term re-writing to solve this problem by identifying rule sets for which all maximal reduction sequences are equivalent. Such confluence results are given for a number of reduction rules on problems on discrete systems. In contrast, NP-hardness results are also presented for some reduction rules. A probabilistic analysis of self-reductions on graphs is performed, showing that the expected number of self-reductions on a graph tends to zero as the order of the graph tends to infinity. An empirical study is performed comparing the performance of self-reduction, graph decomposition and direct methods of solving the Graph Colouring and Set Covering Problems. The results show that self-reduction is a potentially valuable, but sometimes erratic, method of finding exact solutions to combinatorial problems.

Artifacts are moved to museums after the excavations in order to provide an indoor protection, while the immovable findings remain exposed to environmental conditions and human activity. In order to conserve these architectural remains made of vulnerable material, mosaics and wall paintings in situ, covering structures are designed offering temporary or long-term sheltering, preserving and exhibiting facilities. The aim of the study is to evaluate these protective structures. In this study, national and international approaches in the conservation of archaeological sites are studied in order to form the theoretical framework. Following the theoretical research, problems facing excavation sites, in situ conservation, interventions and the presentation of the archaeological sites are studied. New building in an archaeological site is discussed in architectural and conservation perspectives and evaluation criteria are defined. Selected cases are studied according to their material selection, functional and physical efficiency, compatibility with the remaining and its urban context in terms of the determined principles. The study is concluded with the general remarks for a new protective structure for the preservation and presentation of the architectural remains in an archaeological site.