This work presents the state of the art in hierarchically decomposed multilevel optimization. This work is expanded with the inclusion of evidence theory with the multilevel framework for the quantification of epistemic uncertainty. The novel method, Evidence-Based Multilevel Design optimization, is then used to solve two analytical optimization problems. This method is also used to explore the effect of the belief structure on the final solution. A methodology is presented to reduce the costs of evidence-based optimization through manipulation of the belief structure. In addition, a transport aircraft wing is also solved with multilevel optimization without uncertainty. This complex, real world optimization problem shows the capability of decomposed multilevel framework to reduce costs of solving computationally expensive problems with black box analyses.

A predição de links em redes é uma tarefa com aplicações em diversos cenários. Com a automatização de processos, as redes sociais, redes tecnológicas e outras cresceram muito em número de vértices e arestas. Portanto, a utilização de preditores de links em redes com alta complexidade estrutural não é trivial, mesmo considerando algoritmos de baixa complexidade computacional. A grande quantidade de operações necessárias para que os preditores possam escolher quais arestas são promissoras torna o processo de considerar a rede toda inviável na maioria dos casos. As abordagens existentes enfrentam essa característica de diversas formas, sendo que as mais populares são as que limitam o conjunto de pares de vértices que serão considerados para existência de arestas promissoras. Este projeto aborda a criação de uma estratégia que utiliza otimização multinível para contrair as redes, executar os algoritmos de predição de links nas redes contraídas e projetar os resultados de predição para a rede original, para reduzir o número de operações necessárias à predição de links. Os resultados mostram que a abordagem consegue reduzir o tempo necessário para predição, apesar de perdas esperadas na qualidade na predição. / Link prediction in networks is a task with applications in several scenarios. With the automation of processes, social networks, technological networks, and others have grown considerably in the number of vertices and edges. Therefore, the creation of systems for link prediction in networks of high structural complexity is not a trivial process, even considering low-complexity algorithms. The large number of operations required for predicting which edges are promising makes the considering of the whole network impracticable in many cases. The existing approaches face this characteristic in several ways, and the most popular are those that limit the set of vertex pairs that will be considered for the existence of promising edges. This project addresses a strategy that uses multilevel optimization to coarse networks, execute prediction algorithms on coarsened networks and project the results back to the original network, in order to reduce the number of operations for link prediction. The experiments show that the approach can reduce the time despite some expected losses of accuracy.

A predição de links em redes é uma tarefa com aplicações em diversos cenários. Com a automatização de processos, as redes sociais, redes tecnológicas e outras cresceram muito em número de vértices e arestas. Portanto, a utilização de preditores de links em redes com alta complexidade estrutural não é trivial, mesmo considerando algoritmos de baixa complexidade computacional. A grande quantidade de operações necessárias para que os preditores possam escolher quais arestas são promissoras torna o processo de considerar a rede toda inviável na maioria dos casos. As abordagens existentes enfrentam essa característica de diversas formas, sendo que as mais populares são as que limitam o conjunto de pares de vértices que serão considerados para existência de arestas promissoras. Este projeto aborda a criação de uma estratégia que utiliza otimização multinível para contrair as redes, executar os algoritmos de predição de links nas redes contraídas e projetar os resultados de predição para a rede original, para reduzir o número de operações necessárias à predição de links. Os resultados mostram que a abordagem consegue reduzir o tempo necessário para predição, apesar de perdas esperadas na qualidade na predição. / Link prediction in networks is a task with applications in several scenarios. With the automation of processes, social networks, technological networks, and others have grown considerably in the number of vertices and edges. Therefore, the creation of systems for link prediction in networks of high structural complexity is not a trivial process, even considering low-complexity algorithms. The large number of operations required for predicting which edges are promising makes the considering of the whole network impracticable in many cases. The existing approaches face this characteristic in several ways, and the most popular are those that limit the set of vertex pairs that will be considered for the existence of promising edges. This project addresses a strategy that uses multilevel optimization to coarse networks, execute prediction algorithms on coarsened networks and project the results back to the original network, in order to reduce the number of operations for link prediction. The experiments show that the approach can reduce the time despite some expected losses of accuracy.

Derivative free optimization algorithms are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. These are designed to minimize smooth functions whose derivatives are not available or costly to compute. The trust region based multilevel optimization algorithms for solving large scale unconstrained optimization problems resulting by discretization of partial differential equations (PDEs), make use of different discretization levels to reduce the computational cost. In this thesis, a derivative free multilevel optimization algorithm is derived and its convergence behavior is analyzed. The effectiveness of the algorithms is demonstrated on a shape optimization problem.

Dans le contexte de l’avion plus électrique, les réseaux électriques aéronautiques sont en pleine évolution. Cette évolution est poussée par le besoin d’une intégration à forte densité énergétique ce qui pose des défis aux concepteurs en termes d’architectures, de systèmes et de méthodes de dimensionnement.Un réseau de bord est composé d’un ensemble de systèmes électriques multidisciplinaire qui proviennent de différents fournisseurs dont le design est actuellement effectué en répondant à des standards de qualité spécifiés par l’agrégateur. L’objectif de la thèse est de proposer de nouvelles approches intégrées qui permettent de gérer la complexité des réseaux électriques tout en convergeant vers un résultat optimal, offrant des gains de masses en référence à un design par des « approches mécanistes » reposant sur un agrégat de boucles d’optimisation locales. Une approche multiniveau a été développée en s’inspirant des travaux sur la MDO « Multidisciplinary Design Optimization ». L’élaboration de cette approche a été le résultat d’une expertise accumulée en appliquant différentes méthodes disponibles dans la bibliographie. L’optimisation porte plus spécifiquement sur les filtres d’entrée des charges du réseau ainsi que sur le filtre de sortie du canal de génération du réseau électrique embarqué. L’optimisation multiniveau vise, dans un contexte collaboratif, à itérer entre le niveau agrégateur (niveau réseau) et le niveau équipementier (charges et source du réseau). L’utilisation d’une formulation agrégée au niveau réseau et le respect des causalités au niveau des sous-problèmes sont les principaux atouts de cette approche qui conduit à des solutions proches de l’optimum global de masse de filtres. / Within more electric aircraft context, electric systems and networks have to evolve. High energy density integration pushes designers to reconsider their systems, architectures and tools.An aircraft network contains a large number of multidisciplinary systems which come from different manufacturers. Each manufacturer designs its system separately following quality standards specified by the aggregator. The goal of this thesis is to provide system approaches which could deal with the high-level of complexity of the network while reaching the optimal design of all the system and so reduce the total weight in comparison with mechanistic approaches based on independent optimization loops for the different subsystems.Consulting MDO “Multidisciplinary Design Optimization” researches, we have developed a multilevel approach based on our previous studies and conclusions on classical approaches used in the design of electrical systems. The optimization concerns the input filters of the loads connected to the HVDC bus and the output filter of the generating channel which supply the electric power. The multilevel collaborative optimization allows an automated exchange of data between the aggregator (system level) and manufacturers (sub-system level) and thanks to that, the optimal design of all the system is joined. The strong points of this approach are the aggregated formulation and causality connections between sub-systems.

Les avantages que présentent les systèmes électriques par rapport aux autres systèmes (mécaniques, hydrauliques et pneumatiques) ont permis d’intensifier l’électrification des systèmes embarqués à bord des aéronefs : c’est le concept d’avion plus électrique. Dans ce contexte, l’approche de conception intégrée par optimisation (CIO) de ces systèmes s’avère aujourd’hui une nécessité pour pouvoir répondre aux exigences en termes d’efficacité énergique, de fiabilité et de masse... Dans cette thèse, nous avons appliqué la CIO à une chaine de conversion électromécanique utilisée dans le système de conditionnement d’air d’un avion. Deux objectifs sont ciblés : la minimisation de la masse du système et l’augmentation de son efficacité énergétique. Ces objectifs sont intégrés à diverses contraintes hétérogènes, allant de la qualité réseau au respect de la mission de vol dans le plan couple – vitesse, en passant par la thermique,… Compte tenu de la complexité du système étudié et de son caractère multidisciplinaire, des approches de conception par optimisation dites « MDO » (pour Multidisciplinary Design Optimization) sont étudiées. En effet, au delà des compétences physiques et techniques, la conception intégrée par optimisation des systèmes complexes nécessite des efforts supplémentaires en termes de méthodologies de conception. Nous avons présenté dans cette thèse trois approches : Approches mono-niveau : séquentielle et globale ; Approche multi-niveaux, couplant niveaux système et niveau constituants (filtre, onduleur, machine) ; des formulations adaptées à notre problème de conception sont présentées afin de résoudre les problèmes liés aux optimisations mono-niveau. Les performances des différentes approches de conception sont présentées analysées et comparées. Les résultats obtenus montrent clairement les avantages que présente la formulation multi-niveaux par rapport aux approches classiques de conception. / The benefits of electrical systems compared to other systems (mechanical, hydraulic and pneumatic) are a serious motivation for the electrification of embedded systems in “more electric aircraft”. In this framework, the integrated optimal design of these systems appears necessary to meet requirements in terms of efficiency, reliability and weight reduction. In this thesis, we have applied the integrated optimal design to an electromechanical system used in the air conditioning system of a more electric aircraft. Two objectives are targeted: the minimization of the system weight and the increase of its efficiency. Both objectives are integrated with several heterogeneous constraints, from network quality till flight mission fulfilment in the torque vs speed plan. Because of the complexity of the studied system and its multidisciplinary nature, "MDO" approaches (for multidisciplinary Design Optimization) are studied. In fact, beyond physical and technical skills, integrated optimal design of complex systems requires additional efforts in terms of design methodologies. Three approaches are presented in this thesis: One-level Approaches: sequential and global; Multilevel approach, coupling “system” level with “device” level (filter, inverter, electric machine); a set of formulations adapted to our design problem are presented to solve the issues associated to the one-level approaches. The performance of these design approaches are presented, analyzed and compared. The results clearly show the advantages that involves multilevel formulation compared to conventional design approaches.