A otimização topológica de estruturas está relacionada à concepção de projetos que executem suas funções com nível de segurança adequado empregando a quantidade mínima de material. Neste trabalho, determina-se a geometria ótima de estruturas planas por meio do acoplamento do Método dos Elementos de Contorno (MEC) ao Método Level Set (MLS). O algoritmo é composto por 3 etapas: problema mecânico, otimização topológica e reconstrução da estrutura. O problema mecânico é resolvido pelas equações algébricas do MEC. A otimização topológica é determinada pelo MLS, este representa a geometria do corpo e suas evoluções por meio da função Level Set (LS) avaliada em seu nível zero. Na reconstrução realiza-se o remalhamento, pois a cada iteração a estrutura é modificada. O acoplamento proposto resulta na geometria ótima da estrutura sem a necessidade da aplicação de filtros. Os exemplos analisados mostram que algoritmo desenvolvido capta adequadamente a geometria ótima das estruturas. Com esse trabalho, avança-se no campo das aplicações do acoplamento MEC-MLS e no desenvolvimento de soluções inovadoras para problemas complexos de engenharia. / In general, the topological optimization of structures is related to design projects that perform their functions with appropriate security levels using the minimum amount of material. This research determines the optimal geometry of 2D structures by coupling the Boundary Blement Method (BEM) to Level Set Method (LSM). The algorithm consists of 3 steps: mechanical model, topology optimization and structure reconstruction. The mechanical model is solved by BEM algebraic equations. The topology optimization is determined using the MLS, the geometry of the body is determined by the Level Set (LS) function evaluated at the zero level. The reconstruction achieves the remeshing, because for each iteration of the structure is modified. The proposed coupling results in the optimal geometry of the structure without the filters application. The examples show that the algorithm developed captures adequately the optimal geometry of the structures. With this dissertation, it is possible advance in the field of applications of the BEM - LSM and develop innovative solutions to complex engineering problems.

Made available in DSpace on 2016-08-10T10:40:24Z (GMT). No. of bitstreams: 1 Roberto Capparelli Marcal.pdf: 1385634 bytes, checksum: 037e447d80e3c2c33c23560ac2c75dca (MD5) Previous issue date: 2015-03-05 / This study aimed to construct a model for the simultaneous optimization of the topology and design of compressed air pipeline networks. The proposed model consists of two parts; the objective functions and a set of constraints. This model is a nonlinear mixed multiobjective programming. The function of this model is to optimize the diameters of the tubes and the topology of an air system under study, presenting a set of effective solutions while minimizing costs and pressure drop, given the constraints that enable each point of air consumption is treated in their minimum requirements of flow and pressure. For the verification of the proposed model behavior, data from a small network and obtained were applied efficient solutions for decision making. / Este trabalho teve como objetivo a construção de um modelo para a otimização simultânea da topologia e do dimensionamento de redes de ar comprimido. O modelo proposto é composto de duas partes: as funções objetivos e um conjunto de restrições. Este modelo é um modelo de programação não linear misto multiobjetivo. A função deste modelo é otimizar os diâmetros e a topologia dos tubos de uma rede de ar em estudo, apresentando um conjunto de soluções eficientes minimizando os custos e a perda de carga e atendendo as restrições que possibilitem que cada ponto de consumo de ar comprimido seja atendido em seus requerimentos mínimos de vazão e pressão. Para a verificação do comportamento do modelo proposto, foram aplicados dados de uma rede de pequeno porte e obtidos as soluções eficientes para a tomada de decisão.

Os mecanismos flexíveis são dispositivos capazes de transmitir força e movimento através da deformação elástica. Têm grande importância a uma série de aplicações nas quais os mecanismos de corpos rígidos não seriam viáveis, como por exemplo, os sistemas microeletromecânicos. Existem várias maneiras pelas quais os mecanismos flexíveis podem ser projetados, sendo a otimização topológica um método bastante difundido por ser de aplicação sistemática, ou seja, não requer do projetista qualquer ação analítica durante a etapa de projeto. Na maioria dos casos, o método da otimização topológica combina o método dos elementos finitos com um método de programação matemática. Logo, faz-se necessário discretizar a região do espaço na qual o material disponível será distribuído para determinar o mecanismo flexível adequado à aplicação desejada. Freqüentemente, o mecanismo projetado apresenta duas regiões sólidas unidas por um único nó pertencente à malha de elementos finitos. Durante a transmissão do movimento, este nó age como uma dobradiça conectada às duas regiões. Trata-se de um efeito indesejado, pois compromete a modelagem e a fabricação do componente mecânico. Assim, neste trabalho, foram estudadas técnicas destinadas à redução da ocorrência das \"dobradiças\" no projeto de mecanismos flexíveis por otimização topológica. Foi implementado em linguagem C um código que permite projetar mecanismos flexíveis submetidos a um único carregamento ou múltiplos carregamentos (mecanismos multi-flexíveis). Com o objetivo de analisar e explorar outros aspectos da formulação implementada no código, investigou-se também a sua utilização no projeto de estruturas rígidas. Como resultado, é mostrada a influência dos diversos parâmetros de otimização no projeto de mecanismos flexíveis sem dobradiças, permitindo analisar a eficácia da formulação implementada. / Compliant mechanisms are devices capable of transmitting force and displacement through elastic deformation. They are extremely important for a number of applications in which the mechanisms of rigid bodies would not be feasible, such as microelectromechanical systems. There are several ways through which compliant mechanisms can be designed, being topology optimization a highly diffused method because of its systematic application, once, it does not require from the designer any analytical action during the stage of the project. In most cases, topology optimization method combines the finite element method with a mathematical program method. Therefore, it is necessary to discretize the region of the space in which the available material will be distributed to determine the appropriate compliant mechanism for the desired application. However, the mechanism designed often presents two solid regions united by one single node. During movement transmission, this node acts as a hinge connected to both regions. This is an undesired effect, as it compromises the modeling and manufacturing of the mechanical component. Thus, this work covers techniques aiming at reducing the occurrence of hinges in the design of compliant mechanisms through topology optimization. A code in C language was implemented, which allows the design of compliant mechanisms subjected to one single load or multiple loads (multi-compliant mechanisms). With the purpose of analyzing and exploring other aspects of the formulation implemented in the code, its use in the design of rigid structures was also investigated. As a result, the influence of several optimization parameters in the design of compliant mechanisms without hinges is shown. This allows to analyze the efficiency of the formulation implemented.

Concevoir des dispositifs thermiques plus compacts, nécessitant moins de masse de matière, produisant moins de pertes de charge et présentant un rendement thermique accru représente un enjeu clé pour des performances améliorées à un coût moindre. La présente thèse étudie le potentiel et la validité de l’optimisation topologique en tant qu’outil CFD viable permettant de générer des designs thermiques optimaux par rapport aux approches conventionnelles telles que l’optimisation de forme et paramétrique. La première partie de la thèse présente une étude expérimentale de structures bi matériaux arborescentes optimales obtenues par optimisation topologique. Le problème mathématique d’optimisation topologique est formulé et implémenté dans OpenFOAM®. Il est appliqué au problème d’optimisation de la conduction thermique dans une configuration de type volume-vers-point. Des mesures thermiques expérimentales sont effectuées sur les structures optimisées, en utilisant la thermographie infrarouge afin de quantifier leurs performances de transfert de chaleur et ainsi validé les performances des structures optimales déterminées par le code d’optimisation topologique développé. La deuxième partie de la thèse présente une technique bi-objectif innovante d’optimisation topologique des systèmes de transferts de chaleur conjugués (CHT, Conjugate Heat Transfer) en régimes d’écoulement laminaires. Pour cela, le problème est développé mathématiquement et implémenté dans le solveur OpenFOAM® basé sur une méthode directe par volumes finis. La fonction objectif est formulée par la pondération linéaire de deux fonctions objectifs, l’une pour la réduction de la perte de charge et l’autre pour l’augmentation du transfert de chaleur. Ceci représente une cible très difficile du point de vue numérique en raison de la concurrence entre les deux objectifs (minimisation de la perte de charge et maximisation de la puissance thermique récupérable). Des designs non intuitifs, mais optimaux au sens de Pareto, ont été obtenus, analysés, discutés et justifiés à l’aide de diverses méthodes d’analyses numériques globale et locale. De plus, une configuration identique à une optimisation par une méthode Lattice Boltzmann issue de la bibliographie a été optimisée en utilisant le solveur OpenFOAM® développé. L’objectif, en complément de la comparaison des solutions optimales, est également d’initier un cas de référence pour les futures études dans ce domaine de recherche et d’innovation de façon à pouvoir pleinement comparer les solutions optimales obtenues par différences méthodes et différents solveurs. Enfin, les différents points expérimentaux et numériques mis en lumière et illustrés dans cette thèse démontrent l’importance de la méthodologie et potentiel très important de l’optimisation topologique pour la conception de systèmes thermiques industriels plus performants. / Designing thermal devices that are more compact with less mass, less frictional losses and increased thermal efficiency is a key requirement for enhanced performances at a lower cost. The present PhD thesis investigates the potential and validity of topology optimization numerical method as a viable CFD tool to generate optimal thermal designs as compared to conventional approaches like shape and parametric optimization. The first part of the thesis presents an experimental investigation of topology optimized tree-like structures made of two materials. The topolgy optimization mathematical problem is formulated and implemented in OpenFOAM®. It is applied to the topolgy optimization problem of volume-to-point heat removal. Experimental thermal measurements are carried out, on the optimal structures, using infrared thermography in order to quantify their heat transfer performances and thus validate the performances of the optimal structures determined by the developed topology optimization code. The second part of the thesis presents an innovative bi-objective optimization technique for topology optimization of Conjugate Heat Transfer (CHT) systems under laminar flow regimes. For that purpose, an inequality constrained bi-objective topology optimization problem is developed mathematically and implemented inside the Finite Volume based OpenFOAM® solver. The objective function is formulated by linear combination of two objective functions for pressure drop reduction and heat transfer enhancement which is numerically a very challenging task due to a competition between the two objectives (minimization of pressure drop and maximization of recoverable thermal power). Non-intuitive Pareto-optimal designs were obtained, analyzed, discussed and justified with the help of various global and local numerical analysis methods. Additionally, a recent Lattice Boltzmann topology optimization problem form the literature was solved using the developed OpenFOAM® solver. The objective, in addition to the comparison of the optimal solutions, is also to initiate a case of reference for future studies in this field of research and innovation so as to be able to fully compare the optimal solutions obtained by different and different methods. solvers. Finally, the various experimental and numerical findings highlighted and illustrated in this PhD thesis, demonstrate the importance of the methodology and immense potential behind topology optimization method for designing efficient industrial thermal systems.

The study of non-Newtonian flow is presents itself as relevant in bioengineering field, specially for design of devices that conduct blood, as arterial bypass grafts. Improvements in reducing energy dissipation and blood cell damage caused by artificial flows can be achieved by using numerical simulation and optimization methods. Thus, the present work proposes the study of design channels for steady, incompressible non-Newtonian flow, by using Topology Optimization Method based on the density method. The fluid flow is modeled with the Navier-Stokes equations coupled with Carreau-Yasuda constitutive equation for the dynamic viscosity to take into account the effects of the non-Newtonian blood properties. The Topology Optimization Method distributes regions of solid and fluid, given a volume constraint, within a specified domain in order to obtain a geometry and layout that minimizes energy dissipation, shear stress and vorticity by using the material pseudo-density as design variable. To apply this method to fluidic systems design, a fictional porous media based on Darcy equation is introduced. The flow model is implemented in its discrete form by using the Finite Element Method through the OpenSource platform FEniCS, applied to automate the solution of mathematical models based on differential equations. The optimization problem is solved by using the library DOLFIN-adjoint and IPOpt optimizer. Optimized topologies of channels for blood flow, focusing in arterial bypass grafts, are presented to illustrate the proposed method. / O estudo de escoamento de fluidos não-Newtonianos apresenta-se relevante no campo de bioengenharia, em especial no projeto de dispositivos para condução de sangue, como bypass arterial. Melhorias na redução de dissipação de energia e no dano às células sanguíneas causados por fluxos artificiais podem ser obtidas através do uso de técnicas de simulação e otimização numéricas. Deste modo, este trabalho propõe o estudo do projeto de canais para escoamentos incompressíveis em regime permanente de fluidos não-Newtonianos através do Método de Otimização Topológica baseado no método de densidade. O escoamento é modelado com as equações de Navier-Stokes acopladas com a equação constitutiva de Carreau-Yasuda para a viscosidade dinâmica, para que sejam considerados os efeitos das propriedades não-Newtonianas do sangue. O Método de Otimização Topológica distribui regiões de sólido e fluido, dada uma restrição de volume, dentro de um domínio especificado de modo a obter uma geometria e configuração que minimize a dissipação de energia, tensão de cisalhamento e vorticidade, utilizando a pseudo-densidade do material como variável de projeto. Para aplicar este método a sistemas fluidos, um meio poroso fictício, baseado na equação de Darcy, é introduzido. O modelo de escoamento é implementado em sua forma discreta utilizando o Método de Elementos Finitos através da plataforma OpenSource FEniCS, aplicada para automatizar a solução dos modelos matemáticos baseados em equações diferenciais, e o problema de otimização é resolvido utilizando a biblioteca DOLFIN-adjoint e otimizador IPOpt. Topologias otimizadas de canais para fluxo de sangue, com foco em bypass arterial, são apresentadas para ilustrar o método proposto.

O projeto de um componente mecânico é uma atividade muito complexa, onde muitas vezes se tem restrições de projeto como peso do componente e rigidez máxima, e também restrições de manufatura, associada aos processos de fabricação disponíveis para serem utilizados. É fato conhecido que a Otimização Topológica (OT), apesar de ser um método extremamente eficiente para a obtenção de soluções ótimas, gera soluções com geometrias complexas que são ou muito caras de se fabricar ou infactíveis. A técnica de projeção foi escolhida como adequada para implementar as restrições propostas neste trabalho. Esta técnica resolve o problema posto num domínio de variáveis de projeto e projeta essa solução num domínio de pseudo-densidades, que são a resposta do problema. A relação entre os dois domínios e determinada pela função de projeção e pelo mapeamento das variáveis definidos de forma diferente para cada restrição. Neste trabalho foram implementadas restrições de manufatura para OT de modo a restringir a gama possível de soluções no problema de otimização. Como exemplo foi considerado o problema de maximização de rigidez, com restrição de volume. Todas as implementações foram realizadas em linguagem de programação C, e o algoritmo de otimização utilizado é o critério de optimalidade. Foram implementadas as seguintes restrições de manufatura com a técnica de projeção: membro mínimo, buraco mínimo, simetria, extrusão, é revolução, repetição de padrões, fundição, forjamento, e laminação. Estas restrições mostram a grande capacidade da técnica de projeção para controlar a solução do problema de otimização sem implicar num grande aumento do custo computacional. Os resultados encontrados mostram a potencialidade de utilizar restrições de manufatura na OT, porém estão longe de esgotarem o assunto, nesse tema recente que vem sendo explorado no Método de Otimização Topológica (MOT). / The design of a mechanical component is a very complex task, which includes constraints such as maximum weight and maximum stiffness, and also manufacturing constraints, associated with the manufacturing processes required at the shop floor. It is known that Topology Optimization (TO), despite of being a very effective and powerful method to obtain optimal solutions, generates solutions with complex geometries that are too much expensive to be manufactured or just can not be made. The projection scheme has been chosen as the most appropriate technique for implementing the proposed constraints. This scheme solves the proposed problem in a domain of design variables and then projects these results into a pseudo-density domain to find the solution. The relation between both domains is defined by the projection function and variable mapping defined in a different way for each constraint. In this work, manufacturing constraints for TO are implemented in a way that the possible solutions of the optimization problem are restricted. As an example, the traditional stiffness maximization problem is considered. All implementations have been done using C programming language, and the optimization algorithm applied is the optimality criteria. The following manufacturing constraints have been implemented using the projection scheme: minimal member size, minimal hole size, symmetry, extrusion, revolution, pattern repetition, casting, forging and lamination. These constraints show the large capacity of the projection scheme to control the solution for the optimization without adding a large computational cost. The results that have been found show the great power of using manufacturing constraints in the TO, however, they are far from exhausting this topic that has been recently explored in the Topology Optimization Method (TOM).

Mecanismo Flexível é um dispositivo mecânico utilizado para transformar movimento, força ou energia entre as portas de entrada e saída sem a presença de juntas, pinos baseados em uma estrutura em monolítica, em outras palavras, a transformação do movimento é dada pela flexibilidade de sua estrutura. Deste modo a transformação pode ser direcionada em uma direção em específico, amplificando ou reduzindo o deslocamento ou força aplicados. Por este motivo mecanismos flexíveis tem grandes aplicações em micromanipulação e nano posicionamento. A concepção deste tipo de mecanismo é complexa e uma das possibilidades de elaboração deste dispositivo mecânico é através da distribuição de flexibilidade ou rigidez dentro do domínio de projeto utilizando o Método de Otimização Topológica (MOT), que essencialmente combina algoritmos de otimização numéricos como Método de Elementos Finitos (MEF), por exemplo. A grande maioria das classes de mecanismos flexíveis existentes trabalha sob pequenos deslocamentos, na ordem de micro ou nano metros, no entanto, existe uma classe de mecanismos que utiliza o recurso da flambagem não linear para operar com grandes deslocamentos. O procedimento de concepção desta de classe de mecanismo é complexa e ainda se encontra em estagio inicial, necessitando de aprimoramentos que permitam o seu projeto completo via métodos computacionais. Portanto, esta tese foi desenvolvida como objetivo desenvolver uma metodologia computacional para projetar esta classe de mecanismo flexível inovador que emprega a flambagem não linear na sua estrutura como meio para obter sob grandes deslocamentos na porta de saída. A metodologia desenvolvida se baseia no MOT para obter a topologia da estrutura que satisfaça as restrições de projeto. A modelagem do comportamento físico da estrutura utiliza uma formulação variacional não linear do problema elástico, considerando a cinemática não linear com um modelo constitutivo policonvexo. O modelo de material aplicado para obter a topologia da estrutura do mecanismo foi o Solid IsotropicMaterial with Penalization (SIMP) com um algoritmo de otimização numérico baseado no método de ponto interior, onde foi utilizada a implementação do IpOpt em conjunto com a plataforma Python FEniCS de soluções de Equações Diferenciais Parciais (EDPs). São apresentados resultados bidimensionais de mecanismos considerando algumas configurações de geometria, condições de contorno e restrições de flambagem não-linear, como incremento de carga. / The compliant mechanism is a mechanical device used to transform displacement, force or energy between the input and output ports without joints, pins based on a monolithic structure, in other words, the motion transformation is given by the flexibility of its structure. In this way the movement can be defined to a specific axis direction, amplifying or reducing the applied displacement or force. For this reason, the compliant mechanism has significant applications in micromanipulation and nanopositioning system. The design of this type of device is intricate, and one way to achieve such design is trying to distribution flexibility or rigidity within the design domain using the Topology Optimization Method (TOM), which essentially combines numerical optimization algorithms with Finite ElementMethod (FEM), for example. Most models of existing compliant mechanism work under small displacements, in the order of micro or nanometers, nevertheless, there is a class of such mechanisms that uses the nonlinear buckling behavior to operate under large displacements. The design process of this mechanism type is complicated and is still at early stages, requiring improvements that allow a complete design process via computational methods. Therefore, this thesis goal is to develop a computational methodology to create this class of innovative compliant mechanism that employs nonlinear buckling behavior to work under large displacement at the output port. The approach developed is based on TOM to achieve the optimal structure topology that satisfies the design and optimization constraints. The modeling of the elasticity behavior of the structure relies on the nonlinear variational formulation, applying the nonlinear kinematics with a polyconvex constitutive model. The SIMP is employed as a material model to obtain the optimal topology of the mechanismstructure with a numeric optimization algorithm based on the interior point method, where the IpOpt implementation was used with the high-level Python interfaces to FEniCS to solve the partial differential equations (PDEs) problem. Two-dimensional results ofmechanisms are presented considering some geometric, boundary configuration, and including nonlinear buckling as design constraints.

This thesis consists of an introduction and seven appended papers. The purpose of the introduction is to give an overview of the field of topology optimization of discretized load carrying continuum structures. It is assumed that the design domain has been discretized by the finite element method and that the design variable vector is a binary vector indicating presence or absence of material in the various finite elements. Common to all papers is the incorporation of von Mises stresses in the problem formulations. In the first paper the design variables are binary but it is assumed that the void structure can actually take some load. This is equivalent to adding a small positive value, epsilon, to all design variables, both those that are void and those that are filled with material. With this small positive lower bound the stiffness matrix becomes positive definite for all designs. If only one element is changed (from material to void or from void to material) the new global stiffness matrix is just a low rank modification of the old one and thus the Sherman-Morrison-Woodbury formula can be used to compute the displacements in the neighbouring designs efficiently. These efficient sensitivity calculations can then be applied in the context of a neighbourhood search method. Since the computed displacements are exact in the 1-neighbourhood (when one design variable is changed) the neighbourhood search method will find a local optimum with respect to the 1-neighbourhood. The second paper presents globally optimal zero-one solutions to some small scale topology optimization problems defined on discretized continuum design domains. The idea is that these solutions can be used as benchmarks when testing new algorithms for finding pure zero-one solutions to topology optimization problems. In the third paper the results from the first paper are extended to include also the case where there is no epsilon>0. In this case the stiffness matrix will no longer be positive definite which means that the Sherman-Morrison-Woodbury formula can no longer be applied. The changing of one or two binary design variables to their opposite binary values will still result in a low rank change, but the size of the reduced stiffness matrix will change with the design. It turns out, however, that it is possible to compute the effect of these low rank changes efficiently also without the positive lower bound. These efficient sensitivity calculations can then be used in the framework of a neighbourhood search method. In this case the complete 1-neighbourhood and a subset of the 2-neighbourhood is investigated in the search for a locally optimal solution. In the fourth paper the sensitivity calculations developed in the third paper are used to generate first and partial second order approximations of the nonlinear functions usually present in topology optimization problems. These approximations are then used to generate subproblems in two different sequential integer programming methods (SLIP and SQIP, respectively). Both these methods generate a sequence of iteration points that can be proven to converge to a local optimum with respect to the 1-neighbourhood. The methods are tested on some different topology optimization problems. The fifth paper demonstrates that the SLIP method developed in the previous paper can be applied also to the mechanism design problem with stress constraints. In order to generate the subproblems in a fast way small displacements are assumed, which implies that the efficient sensitivity calculations derived in the third paper can be used. The numerical results indicate that the method can be used to lower the stresses and still get a functional mechanism. In the sixth paper the SLIP method developed in the fourth paper is used as a post processor to obtain locally optimal zero-one solutions starting from a rounded solution to the corresponding continuous problem. The numerical results indicate that the method can perform well as a post processor. The seventh paper is a theoretical paper that investigates the validity of the commonly used positive lower bound epsilon on the design variables when stating and solving topology optimization problems defined on discretized load carrying continuum structures. The main result presented here is that an optimal "epsilon-1" solution to an "epsilon-perturbed" discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to zero-one, to the corresponding "unperturbed" discrete problem. This holds if the constraints in the perturbed problem are carefully defined and epsilon>0 is sufficiently small. / QC 20100917

A unique mathematical tool is developed to deal with global optimization of a set of engineering problems. These include image processing, mechanical topology optimization, and optimal path planning in a variational framework, as well as some benchmark problems in parameter optimization. The optimization tool in these applications is based on the level set theory by which an evolving contour converges toward the optimum solution. Depending upon the application, the objective function is defined, and then the level set theory is used for optimization. Level set theory, as a member of active contour methods, is an extension of the steepest descent method in conventional parameter optimization to the variational framework. It intrinsically suffers from trapping in local solutions, a common drawback of gradient based optimization methods. In this thesis, methods are developed to deal with this drawbacks of the level set approach. By investigating the current global optimization methods, one can conclude that these methods usually cannot be extended to the variational framework; or if they can, the computational costs become drastically expensive. To cope with this complexity, a global optimization algorithm is first developed in parameter space and compared with the existing methods. This method is called "Spiral Bacterial Foraging Optimization" (SBFO) method because it is inspired by the aggregation process of a particular bacterium called, Dictyostelium Discoideum. Regardless of the real phenomenon behind the SBFO, it leads to new ideas in developing global optimization methods. According to these ideas, an effective global optimization method should have i) a stochastic operator, and/or ii) a multi-agent structure. These two properties are very common in the existing global optimization methods. To improve the computational time and costs, the algorithm may include gradient-based approaches to increase the convergence speed. This property is particularly available in SBFO and it is the basis on which SBFO can be extended to variational framework. To mitigate the computational costs of the algorithm, use of the gradient based approaches can be helpful. Therefore, SBFO as a multi-agent stochastic gradient based structure can be extended to multi-agent stochastic level set method. In three steps, the variational set up is formulated: i) A single stochastic level set method, called "Active Contours with Stochastic Fronts" (ACSF), ii) Multi-agent stochastic level set method (MSLSM), and iii) Stochastic level set method without gradient such as E-ARC algorithm. For image processing applications, the first two steps have been implemented and show significant improvement in the results. As expected, a multi agent structure is more accurate in terms of ability to find the global solution but it is much more computationally expensive. According to the results, if one uses an initial level set with enough holes in its topology, a single stochastic level set method can achieve almost the same level of accuracy as a multi-agent structure can obtain. Therefore, for a topology optimization problem for which a high level of calculations (at each iteration a finite element model should be solved) is required, only ACSF with initial guess with multiple holes is implemented. In some applications, such as optimal path planning, objective functions are usually very complicated; finding a closed-form equation for the objective function and its gradient is therefore impossible or sometimes very computationally expensive. In these situations, the level set theory and its extensions cannot be directly employed. As a result, the Evolving Arc algorithm that is inspired by "Electric Arc" in nature, is proposed. The results show that it can be a good solution for either unconstrained or constrained problems. Finally, a rigorous convergence analysis for SBFO and ACSF is presented that is new amongst global optimization methods in both parameter and variational framework.

Disertacijoje nagrinėjamos santvarų globalaus optimizavimo problemos. Pagrindinis darbo tikslas – sukurti technologiją ir ją aprašančius algoritmus santvarų topologijos optimizavimui ir sinchroniniam topologijos ir formos optimizavimui. Optimizavimui naudojami genetiniai algoritmai. Topologijai optimizuoti pasirinkta perdėtai sujungtos struktūros strategija (angl. ground structure approach). / The dissertation deals with the topology optimization problems of the truss systems. The main aim of the work is to create a technology and implementing algorithms for topology optimization and for simultaneous topology and shape optimization of truss systems. The genetic algorithms are used as the main tool for optimization. The topology optimization problems are formulated using the so-called ground structure approach.