The harmony search algorithm was developed in 2001 as a heuristic optimisation algorithm for use in diverse optimisation problems. After its introduction it was extensively used in multiple engineering disciplines with great success. In order to demonstrate the value of harmony search in computer vision applications I developed four novel algorithms based on harmony search that efficiently solves three problems that are commonly found in computer vision, namely visual tracking, visual correspondence matching and binary image restoration. Computer vision is a large discipline that includes solving many different kinds of optimisation problems. Many of these optimisation problems are discontinuous with derivative information difficult or impossible to come by. The most common solution is to use population based statistical optimisation algorithms like the particle filter, genetic algorithms, PSO, etc. but harmony search has never been investigated as a possible alternative. This is surprising since harmony search has been shown to be superior to these methods in several other engineering disciplines. I therefore aim to show that harmony search deserves to be included in the computer vision researcher's toolbox of optimisation algorithms through the introduction of four novel algorithms based on harmony search that solve three diverse problems in computer vision. First the harmony filter (HF) is introduced as a visual tracking algorithm that is shown to be superior to the particle filter and the unscented Kalman filter (UKF) in both speed and accuracy for robust tracking in challenging situations. The directed correspondence search (DCS) algorithm is then introduced as a solution to the visual correspondence problem. Finally, two algorithms, counterpoint harmony search (CHS) and largest error first harmony search (LEFHS), are introduced for the blind deconvolution of binary images. Comparative results from these algorithms are very promising. The harmony filter was compared with the particle filter and the UKF both of which have been extensively used in visual tracking. In challenging situations consisting of rapid and erratic target movement, extended periods of total and partial occlusion and changing light conditions, the HF proved to be more accurate and faster on average than both the particle filter and the UKF. Under various conditions I show that the HF is at least 2 times faster than a UKF implementation and 4 times faster than a particle filter implementation (using 300 particles). While there are fewer algorithms specialising in the blind deconvolution of binary images, CHS and LEFHS were compared with a current state-of-the-art method and proved to be more robust to noise and more accurate. LEFHS is the only algorithm currently available that can recover a 24 x 12 binary image using blind deconvolution to 100% accuracy without putting constraints on the point spread function (blurring kernel). During the development of these algorithms several valuable insights into the inner workings of harmony search were discovered. In each application harmony search had to be adapted in a different way and with each new adaptation a deeper understanding of the advantages of harmony search is revealed. Knowing which components may be modified without degrading performance is key to adapting harmony search for use in diverse problems and allows one to use harmony search in situations it was not originally designed for without losing its superior performance. These insights and the adaptation strategies that they lead to are the main contribution of this thesis.

The design of many engineering systems can be a complex process, which means many possibilities and factors must be considered during problem formulation. The process of searching for a design that meets both performance and safety standards with reliable impact is the goal of structural optimization. Structural optimization is an approach whereby the structural design is subjected to being optimized in terms of weight while maintaining all design constraints such as stress, strain, and stability. Structural design optimization problems involve searching for the minimum of the stated objective function, usually the weight of the structure and constructability. Trusses are triangular frame works in which the members are subjected to essentially axial forces due to externally applied load at the joints only. Truss structures can be optimized by varying the structure’s size, shape, and topology. Although combining these three prototypes of optimization can ultimately a yield better result, the underlying mathematical model becomes complicated. Over the last decade, new optimization strategies based on metaheuristic algorithms have been devised to obtain the optimal design for structural systems. Harmony search (HS) is a metaheuristic algorithm proposed by Geem et al., inspired by the observation that the aim of music is to search for a perfect state of harmony. In this research, the implementation of HS algorithm has been applied to optimize the size of truss structures that results in the weight reduction of the truss members. The results obtained with HS were compared to those obtained from the original sizes before optimization, to verify the influence on the optimal design of truss structures subjected to stresses, deflections, vertical and lateral displacements, and buckling constrains. / Civil Engineering

Design optimization of structures has become an important method to study and develop these days. Due to the fact that the world's population is increasing, and the worlds' resources are decreasing. An optimum design algorithm is a useful tool that can help to minimize the weight of a structure. Over the last four decades, several number of algorithms have been developed to solve engineering optimization problems, for example, metaheuristic algorithms. An example of metaheuristic algorithms is the Harmony Search algorithm (HS). HS algorithms make use of the analogy between the performance process of natural music and searching for solutions to optimization problems. In this research, the HS was applied on the College of Engineering Building at Temple University Main Campus in Philadelphia, PA. The HS algorithm searches for minimum cross-sectional areas that leads to find optimal steel sizes considering design constrains such as: stress, deflection, and lateral displacement limitations. The HS algorithm obtained lighter weight of steel frames by selecting a suitable steel section from the American Institute of Steel Construction (AISC) and by following the specification of Allowable Stress Design method (ASD). The results show that HS yielded lighter steel moment frames with approximately 20% weight reduction. Keywords: Harmony Search Algorithm, Steel Moment Frame, Optimization. / Civil Engineering

Otimização estrutural é uma área relativamente nova que vem sendo cada vez mais explorada. Existem muitos métodos clássicos, e outros mais recentes vem surgindo para disputar em eficiência, confiabilidade e rapidez na obtenção de um resultado ótimo. Os algoritmos são classificados em algoritmos determinísticos, que utilizam a informação do gradiente, ou seja, usam os valores das funções e suas derivadas, e os meta-heurísticos, algoritmos de otimização aleatórios que são métodos probabilísticos não baseados em gradiente, ou seja, usam somente a avaliação da função objetivo. São apresentados dois algoritmos meta-heurísticos relativamente recentes: o Harmony Search, baseado na improvisação musical em busca da harmonia perfeita, e o Firefly Algorithm, que é inspirado no comportamento da luz dos vagalumes. Vários exemplos clássicos de treliças 2-D e 3-D considerando otimização paramétrica e de forma, com restrições de tensão, deslocamento, flambagem e frequência natural, são apresentados para demonstrar a eficiência dos métodos. Os resultados são comparados aos de outros autores usando diferentes métodos encontrados na literatura. Os resultados indicam que os algoritmos de otimização estudados neste trabalho são melhores ou tão eficientes quanto os demais. Por fim, os métodos são aplicados à estrutura de um projeto de engenharia adaptado. / Structural optimization is a relatively new area that has been increasingly exploited. There are many classical methods, and newer are emerging to compete on efficiency, reliability and speed in obtaining an optimal result. The algorithms are classified into deterministic algorithms, which use the gradient information, i.e., use the values of the functions and their derivatives, and meta-heuristic algorithms, random optimization methods which are probabilistic methods not based on gradient, i.e., they use only objective function evaluation. Two relatively recent meta-heuristics algorithms are presented, Harmony Search, based on musical improvisation in search of the perfect harmony, and Firefly Algorithm, which is inspired by the behavior of the light of fireflies. Several benchmarks of 2-D and 3-D trusses considering size and shape optimization, with stress, displacement, buckling and natural frequency constraints, are presented to demonstrate the effectiveness of the methods. The results are compared to the others authors using different methods found in the literature. The results indicate that optimization algorithms studied in this work are better than or as efficient as others. Finally, the methods are applied to the structure of an adapted engineering design.

Otimização estrutural é uma área relativamente nova que vem sendo cada vez mais explorada. Existem muitos métodos clássicos, e outros mais recentes vem surgindo para disputar em eficiência, confiabilidade e rapidez na obtenção de um resultado ótimo. Os algoritmos são classificados em algoritmos determinísticos, que utilizam a informação do gradiente, ou seja, usam os valores das funções e suas derivadas, e os meta-heurísticos, algoritmos de otimização aleatórios que são métodos probabilísticos não baseados em gradiente, ou seja, usam somente a avaliação da função objetivo. São apresentados dois algoritmos meta-heurísticos relativamente recentes: o Harmony Search, baseado na improvisação musical em busca da harmonia perfeita, e o Firefly Algorithm, que é inspirado no comportamento da luz dos vagalumes. Vários exemplos clássicos de treliças 2-D e 3-D considerando otimização paramétrica e de forma, com restrições de tensão, deslocamento, flambagem e frequência natural, são apresentados para demonstrar a eficiência dos métodos. Os resultados são comparados aos de outros autores usando diferentes métodos encontrados na literatura. Os resultados indicam que os algoritmos de otimização estudados neste trabalho são melhores ou tão eficientes quanto os demais. Por fim, os métodos são aplicados à estrutura de um projeto de engenharia adaptado. / Structural optimization is a relatively new area that has been increasingly exploited. There are many classical methods, and newer are emerging to compete on efficiency, reliability and speed in obtaining an optimal result. The algorithms are classified into deterministic algorithms, which use the gradient information, i.e., use the values of the functions and their derivatives, and meta-heuristic algorithms, random optimization methods which are probabilistic methods not based on gradient, i.e., they use only objective function evaluation. Two relatively recent meta-heuristics algorithms are presented, Harmony Search, based on musical improvisation in search of the perfect harmony, and Firefly Algorithm, which is inspired by the behavior of the light of fireflies. Several benchmarks of 2-D and 3-D trusses considering size and shape optimization, with stress, displacement, buckling and natural frequency constraints, are presented to demonstrate the effectiveness of the methods. The results are compared to the others authors using different methods found in the literature. The results indicate that optimization algorithms studied in this work are better than or as efficient as others. Finally, the methods are applied to the structure of an adapted engineering design.

CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior / The wind resource assessment is a key step in the development of wind power generation projects. Minimizing errors in this step brings significant reliability gains for the whole project. In this study we sought a reduction in the errors associated with the adjustment of the Weibull distribution with respect to data collected by an improvement of this setting. With this purpose, it was applied the optimization algorithm of Harmonic Search (HS) to find the Weibull distribution parameters with the best fit. The HS was used to find the Weibull distribution parameters for two sets of data from the Sistema de OrganizaÃÃo de Dados Ambientais (SONDA) of the cities of Petrolina-PE and SÃo Martinho da Serra-RS. The parameters of the HS were selected by two methods, one being a result of the novel combination of two other already presented in the literature. We therefore compared the errors for each one to determine which method provides better optimization. For evaluating the quality setting, the root mean square error (RMSE) and the correlation coefficient were used. The HS-PA method uses a selection of random parameters but, results showed more stable than the IHS. It was found for the IHS method one RMSE = 0.006418 for Petrolina and RMSE = 0.008303 for SÃo Martinho da Serra. The HS-PA method presented a RMSE = 0.006419 for Petrolina and RMSE = 0.008303 for SÃo Martinho da Serra. The RMSE values for the traditional methods applied to the same data set, there were two or more times greater than those found by employing the Harmonic search. / A anÃlise de recurso eÃlico à uma etapa fundamental no desenvolvimento de projetos de geraÃÃo de energia eÃlica. A minimizaÃÃo dos erros nesta etapa traz ganhos significativos de confiabilidade para o projeto como um todo. Neste trabalho foi buscada uma diminuiÃÃo dos erros associados ao ajuste da distribuiÃÃo de Weibull em relaÃÃo aos dados coletados atravÃs de uma melhora deste ajuste. Visando tal intento, foi aplicado o algoritmo de otimizaÃÃo da Busca HarmÃnica (HS) para encontrar os parÃmetros da distribuiÃÃo de Weibull com o melhor ajuste. A HS foi utilizada para encontrar os parÃmetros da distribuiÃÃo de Weibull para dois conjuntos de dados provenientes do Sistema de OrganizaÃÃo de Dados ambientais (SONDA) das cidades de Petrolina-PE e SÃo Martinho da Serra-RS. Os parÃmetros da HS foram selecionados atravÃs de duas metodologias, sendo uma delas inovadora por resultar da combinaÃÃo de outras duas jà apresentadas anteriormente em literatura. Foram, portanto, comparados os erros referentes a cada uma para determinar qual mÃtodo fornecia uma melhor otimizaÃÃo. Para a avaliaÃÃo da qualidade do ajuste, foram utilizados o erro mÃdio quadrÃtico (RMSE) e o coeficiente de correlaÃÃo. O mÃtodo HS-PA, embora utilize uma seleÃÃo de parÃmetros aleatÃria, apresentou resultados mais estÃveis do que o IHS. Foi encontrado para o mÃtodo IHS um RMSE = 0,006418 para Petrolina e RMSE = 0,008303 para SÃo Martinho da Serra. O mÃtodo HS-PA apresentou um RMSE = 0,006419 para Petrolina e RMSE = 0,008303 para SÃo Martinho da Serra. Os valores de RMSE para os mÃtodos tradicionais aplicados ao mesmo conjunto de dados, foram duas ou mais vezes maiores do que os encontrados, empregando a Busca HarmÃnica.

Otimização estrutural é uma área relativamente nova que vem sendo cada vez mais explorada. Existem muitos métodos clássicos, e outros mais recentes vem surgindo para disputar em eficiência, confiabilidade e rapidez na obtenção de um resultado ótimo. Os algoritmos são classificados em algoritmos determinísticos, que utilizam a informação do gradiente, ou seja, usam os valores das funções e suas derivadas, e os meta-heurísticos, algoritmos de otimização aleatórios que são métodos probabilísticos não baseados em gradiente, ou seja, usam somente a avaliação da função objetivo. São apresentados dois algoritmos meta-heurísticos relativamente recentes: o Harmony Search, baseado na improvisação musical em busca da harmonia perfeita, e o Firefly Algorithm, que é inspirado no comportamento da luz dos vagalumes. Vários exemplos clássicos de treliças 2-D e 3-D considerando otimização paramétrica e de forma, com restrições de tensão, deslocamento, flambagem e frequência natural, são apresentados para demonstrar a eficiência dos métodos. Os resultados são comparados aos de outros autores usando diferentes métodos encontrados na literatura. Os resultados indicam que os algoritmos de otimização estudados neste trabalho são melhores ou tão eficientes quanto os demais. Por fim, os métodos são aplicados à estrutura de um projeto de engenharia adaptado. / Structural optimization is a relatively new area that has been increasingly exploited. There are many classical methods, and newer are emerging to compete on efficiency, reliability and speed in obtaining an optimal result. The algorithms are classified into deterministic algorithms, which use the gradient information, i.e., use the values of the functions and their derivatives, and meta-heuristic algorithms, random optimization methods which are probabilistic methods not based on gradient, i.e., they use only objective function evaluation. Two relatively recent meta-heuristics algorithms are presented, Harmony Search, based on musical improvisation in search of the perfect harmony, and Firefly Algorithm, which is inspired by the behavior of the light of fireflies. Several benchmarks of 2-D and 3-D trusses considering size and shape optimization, with stress, displacement, buckling and natural frequency constraints, are presented to demonstrate the effectiveness of the methods. The results are compared to the others authors using different methods found in the literature. The results indicate that optimization algorithms studied in this work are better than or as efficient as others. Finally, the methods are applied to the structure of an adapted engineering design.

Na presente tese é resolvida a equação de difusão de nêutrons estacionária, bem como problemas de cinética, em geometria unidimensional cartesiana multi-região considerando o modelo de multigrupos de energia. Um dos objetivos e inovação neste trabalho é a obtenção de uma solução aproximada com estimativa de erro, controle de precisão e na forma de uma expressão analítica. Com esse tipo de solução não há a necessidade de recorrer a esquemas de interpolação, geralmente necessários em caso de discretizações do domínio. O fluxo de nêutrons é expandido em uma série de Taylor cujos coeficientes são encontrados utilizando a equação diferencial e as condições de contorno e interface. O domínio é dividido em várias células, cujo tamanho e o grau do polinômio são ajustáveis de acordo com a precisão requerida. Para resolver o problema de autovalor é utilizado o método da potência. A metodologia é aplicada em um benchmark que consiste na solução da equação de difusão como condição inicial e na solução de problemas de cinética para diferentes transientes. Os resultados são comparados com sucesso com resultados da literatura. A convergência da série é garantida pela aplicação de um raciocínio baseado no critério de Lipschitz para funções contínuas. Cabe ressaltar que a solução obtida, em conjunto com a análise da convergência, mostra a solidez e a precisão dessa metodologia. / In the present dissertation the one-dimensional neutron diffusion equation for stationary and kinetic problems in a multi-layer slab has been solved considering the multi-group energy model. One of the objectives and innovation in this work is to obtain an approximate solution with error estimation, accuracy control and in the form of an analytical expression. With this solution there is no need for interpolation schemes, which are usually needed in case of discretization of the domain. The neutron flux is expanded in a Taylor series whose coefficients are found using the differential equation and the boundary and interface conditions. The domain is divided into several layers, whose size and the polynomial order can be adjusted according to the required accuracy. To solve the eigenvalue problem the conventional power method has been used. The methodology is applied in a benchmark problem consisting of the solution of the diffusion equation as an initial condition and solving kinetic problems for different transients. The results are compared successfully with the ones in the literature. The convergence of the series is guaranteed by applying a criterion based on the Lipschitz criterion for continuous functions. Note that the solution obtained, together with the convergence analysis, shows the robustness and accuracy of this methodology.

Harmony search method based optimum design algorithm is presented for the grillage systems. This numerical optimization technique imitates the musical performance process that takes place when a musician searches for a better state of harmony. For instance, jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The design algorithm considers the displacement and strength constraints which are implemented from LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction). It selects the appropriate W (Wide Flange)-sections for the transverse and longitudinal beams of the grillage system among 272 discrete W-section designations given in LRFD-AISC so that the design limitations described in LRFD are satisfied and the weight of the system is confined to be minimal. Number of design examples is considered to demonstrate the efficiency of the algorithm presented.

Harmony search method based optimum topology design algorithm is presented for single layer lamella domes. The harmony search method is a numerical optimization technique developed recently that imitates the musical performance process which takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The optimum design algorithm developed imposes the behavioral and performance constraints in accordance with LRFD-AISC. The optimum number of rings, the height of the crown and the tubular cross-sectional designations for dome members are treated as design variables. The member grouping is allowed so that the same section can be adopted for each group. The design algorithm developed has a routine that build the data for the geometry of the dome automatically that covers the numbering of joints, and member incidences, and the computation of the coordinates of joints. Due to the slenderness and the presence of imperfections in dome structures it is necessary to consider the geometric nonlinearity in the prediction of their response under the external loading. Design examples are considered to demonstrate the efficiency of the algorithm presented.