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.

O conteúdo deste trabalho trata da formulação para solução do problema de otimização estrutural com minimização de massa em estruturas unifilares, sujeitas a restrição de tensão, flambagem das barras isoladas e fadiga. São considerados três casos de otimização: paramétrica, de forma e dimensional. Os problemas de singularidades nas restrições de tensão e flambagem são evitados através de uma formulação que faz uso de programação inteira para solução do problema. Outra singularidade encontrada na otimização topológica é a singularidade na matriz de rigidez da estrutura. Este problema foi evitado através de uma formulação que considera a existência de matriz de rigidez regular como restrição do problema. O método de solução utilizado para resolver problema de otimização é o método dos algoritmos genéticos. As restrições do problema são impostas através da penalização da função objetivo. O método de solução mostrou-se adequado para solução dos problemas estudados. A formulação implementada é validada através da solução de problemas clássicos de otimização estrutural. Os resultados obtidos são comparados com a literatura onde verificou-se a coerência dos mesmos. Após realizar a validação, a formulação é utilizada em um estudo que tem como base uma estrutura real: uma torre de queima de gases (flare) oriundos do processo de extração e armazenagem de petróleo em uma unidade flutuante. Para o problema da torre as restrições foram determinadas com base em critérios de falha estabelecido na norma DNV. A otimização do flare permitiu minimizar a massa da estrutura sem que os critérios de falha fossem violados. Verificou-se que a metodologia proposta é adequada para solução com grande número de restrições e com diversos casos de carregamento. / The purpose of this work is the development of a methodology to solve the structural optimization problem of frame structures subject to stress, buckling of isolated members, and fatigue constraints. Three types of structural optimization problems are considered: sizing, shape and topological. The stress and buckling singularity problems are avoided by an integer design variable formulation, using integer programing to obtain the optimization problem solution. Another issue found in optimization problems is the stiffness matrix singularity. The proposed formulations include the linear system stability as a constraint in the optimization problem. A genetic algorithm is used to solve the general optimization problem. All constraints of the problem are included with a penalization equation. The results show that genetic algorithm is a good approach to solve the proposed formulation. The proposed formulation is tested for solving classical optimization problems. The obtained results are consistent with the literature. A real engineering problem is solved with proposed methodology: a gas burning tower (flare). In this problem, all constraints are based on failure criteria recommended by DNV standards. The structural optimization of this problem shows that structural mass minimization is possible without violating the failure criteria. It is observed that solution methodology deals successfully with problems with multiple constraints and load cases

The thesis concentrates on a methodological research on categorical structural optimization by means of manifold learning. The main difficulty of handling the categorical optimization problems lies in the description of the design variables: they are presented in a discrete manner and do not have any orders. Thus the treatment of the design space is a key issue. In this thesis, the non-ordinal categorical variables are treated as multi-dimensional discrete variables, thus the dimensionality of corresponding design space becomes high. In order to reduce the dimensionality, the manifold learning techniques are introduced to find the intrinsic dimensionality and map the original design space to a reduced-order space. The mechanisms of both linear and non-linear manifold learning techniques are firstly studied. Then numerical examples are tested to compare the performance of manifold learning techniques. It is found that Principal Component Analysis (PCA) and Multi-dimensional Scaling (MDS) can only deal with linear or globally approximately linear cases. Isomap preserves the geodesic distances for non-linear manifold, however, its time consuming is the most. Locally Linear Embedding (LLE) preserves the neighbour weights and can yield good results in a short time. Kernel Principal Component Analysis (KPCA) works as a non-linear classifier and we proves the reason why it cannot preserve distances or angles in some cases.Based on the reduced-order representation obtained by Isomap, the graph-based evolutionary crossover and mutation operators are proposed to deal with categorical structural optimization problems, including the design of dome, six-story rigid frame and dame-like structures. The results show that the proposed graph-based evolutionary approach constructed on the reduced-order space performs more efficiently than traditional methods including simplex approach or evolutionary approach without reduced-order space.The Locally Linear Embedding is applied to reduce the data dimensionality and a polynomial interpolation helps to construct the responding surface from lower dimensional representation to original data. Then the continuous search method of moving asymptotes is executed and yields a competitively good but inadmissible solution within only a few of iteration numbers. Then in the second stage, a discrete search strategy is proposed to find out better solutions based on a neighbour search. The ten-bar truss and dome structural design problems are tested to show the validity of the method. In the end, this method is compared to the Simulated Annealing algorithm and Covariance Matrix Adaptation Evolutionary Strategy, showing its better optimization efficiency.In order to deal with the case in which the categorical design instances are distributed on several manifolds, we propose a k-manifolds learning method based on the Weighted Principal Component Analysis. The obtained manifolds are integrated in the lower dimensional design space. Then the two-stage search method is applied to solve the ten-bar truss, the dome and the dam-like structural design problems. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Recent advances in the field of computational intelligence have led to a numberof promising optimization algorithms. These algorithms have the potential to findoptimal or near-optimal solutions to complex problems within a reasonable timeframe. Structural optimization is a research field where such algorithms are appliedto optimally design structures. Although a significant amount of research has been published in the field ofstructural optimization since the 1960s, little of the research effort has been utilizedin structural design practice. One reason for this is that only a small portion ofthe research targets real-world applications. Therefore there is a need to conductresearch on cost optimization of realistic structures, particularly large structureswhere significant cost savings may be possible. To address this need, a software application for cost optimization of beam bridgeswas developed. The software application was limited to road bridges in concretethat are straight and has a constant width of the bridge deck. Several simplificationswere also made to limit the scope of the thesis. For instance, a rough design ofthe substructure was implemented, and the design of some structural parts wereneglected. This thesis introduces the subject of cost optimization, treats fundamentaloptimization theory, explains how the software application works, and presents acase study that was carried out to evaluate the application. The result of the case study suggests a potential for significant cost savings. Yet,the speeding up of the design process is perhaps the major benefit that should inclinedesigners to favor optimization. These findings mean that current optimizationalgorithms are robust enough to decrease the cost of beam bridges compared to aconventional design. However, the software application needs several improvementsbefore it can be used in a real design situation, which is a topic for future research. / Nya framsteg inom forskningen har lett till ett antal lovande optimeringsalgoritmer.Dessa algoritmer har potentialen att hitta optimala eller nästan optimala lösningartill komplexa problem inom rimlig tid. Strukturoptimering är ett forskningsområdedär dessa algoritmer tillämpas för att dimensionera konstruktioner på ett optimaltsätt. Även om en betydande mängd forskning har publicerats inom området strukturoptimeringsedan 1960-talet, så har endast lite av forskningsinsatserna kommit tillanvändning i praktiken. Ett skäl till detta är att endast en liten del av forskningenär inriktad mot verklighetsförankrade tillämpningar. Därför finns det ett behov avatt bedriva forskning på kostnadsoptimering av realistiska konstruktioner, särskiltstora konstruktioner där betydande kostnadsbesparingar kan vara möjligt. För att möta detta behov har ett datorprogram för kostnadsoptimering avbalkbroar utvecklats. Programmet begränsades till vägbroar i betong som är rakaoch har en konstant bredd. Flera förenklingar gjordes också för att begränsaomfattningen av arbetet. Till exempel implementerades en grov dimensionering avunderbyggnaden, och dimensioneringen av vissa komponenter försummades helt ochhållet. Detta examensarbete presenterar ämnet kostnadsoptimering, behandlar grundläggandeoptimeringsteori, förklarar hur programmet fungerar, och presenterar enfallstudie som genomfördes för att utvärdera programmet. Resultatet av fallstudien visar en potential för betydande kostnadsbesparingar.Trots det så är tidsbesparingarna i dimensioneringsprocessen kanske den störstafördelen som borde locka konstruktörer att använda optimering. Dessa upptäckterinnebär att aktuella optimeringsalgoritmer är tillräckligt robusta för att minskakostnaden för balkbroar jämfört med en konventionell dimensionering. Dock måsteprogrammet förbättras på flera punkter innan det kan användas i en verklig dimensioneringssituation,vilket är ett ämne för framtida forskning.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21757号 / 工博第4574号 / 新制||工||1713(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 髙田 滋, 教授 鈴木 基史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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The goal of this research is to compare performance of three analysis methods and three optimization methods for core-megacolumn-outrigger, or CMO skyscrapers. The three analysis methods include a 1D stick analysis, 2D frame analysis, and 3D finite element analysis. The three optimization methods include a trial and error optimization, optimality criteria optimization, and genetic algorithm. Each of these methods was compared by applying an example CMO skyscraper. The 1D stick analysis proved to be the most accurate when compared with the 3D finite element results. The genetic algorithm was recommended as the best optimization method in this research. The 1D stick method in this thesis introduces a new analysis involving an outrigger modification factor. The comparison of these optimization methods for skyscrapers has not been reported in the literature.

A Displacement Based Optimization (DBO) approach was applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the approach to solve such problem. Various truss sizing problems with holonomic (path-independent) elastoplastic laws were investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. A computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics was developed to solve this type of problems. For comparison, we chose an important class of minimum-weight truss design problems, where holonomic linear strain hardening behavior was used. Additional examples of optimum design of trusses with elastic perfectly plastic material response that could be easily solved by Limit Design approach using linear programming were investigated for comparison. All demonstrated examples were tested successfully using the DBO approach. Solutions of comparable examples were consistent with the available results by other methods. Computational effort associated with the DBO approach was minimal for all the examples studied. Optimum solutions of several examples proved that the DBO approach is particularly suited for truss topology design where removal of truss members is essential. / Master of Science

No / This paper presents a two-stage hybrid optimization algorithm based on a modified genetic algorithm. In the first stage, a global search is carried out over the design search space using a modified GA. The proposed modifications on the basic GA includes dynamically changing the population size throughout the GA process and the use of different forms of the penalty function in constraint handling. In the second stage, a local search based on the genetic algorithm solution is executed using a discretized form of Hooke and Jeeves method. The hybrid algorithm and the modifications to the basic genetic algorithm are examined on the design optimization of reinforced concrete flat slab buildings. The objective function is the total cost of the structure including the cost of concrete, formwork, reinforcement and foundation excavation. The constraints are defined according to the British Standard BS8110 for reinforced concrete structures. Comparative studies are presented to study the effect of different parameters of handling genetic algorithm on the optimized flat slab building. It has been shown that the proposed hybrid algorithm can improve genetic algorithm solutions at the expense of more function evaluations.