Various kinds of optimization problems involve nonlinear functions of binary variables that exhibit a property of diminishing marginal returns. Such a property is known as submodularity. Vast amount of work has been devoted to the problem of submodular optimization. In this thesis, we exploit structural information for several classes of submodular optimization problems. We strive for polynomial time algorithms with improved approximation ratio and strong mixed-integer linear formulations of mixed-integer non-linear programs where the epigraph and hypograph of submodular functions of a specific form appear as a substructure together with other side constraints. In Chapter 2, we develop approximation algorithms for the expected utility knapsack problem. We use the sample average approximation framework to approximate the stochastic problem as a deterministic knapsack-constrained submodular maximization problem, and then use an approximation algorithm to solve the deterministic counterpart. We show that a polynomial number of samples are enough for a deterministic approximation that is close in relative error. Then, exploiting the strict monotonicity of typical utility functions, we present an algorithm that maximizes an increasing submodular function over a knapsack constraint with approximation ratio better than the classical $(1-1/e)$ ratio. In Chapter 3, we present polyhedral results for the expected utility knapsack problem. We study a mixed-integer nonlinear set that is the hypograph of $f(a'x)$ together together with a knapsack constraint. We propose a family of inequalities for the convex hull of the nonlinear set by exploiting both the structure of the submodular function $f(a'x)$ and the knapsack constraint. Effectiveness of the proposed inequalities is shown by computational experiments on expected utility maximization problem with budget constraint using a branch-and-cut framework. In Chapter 4, we study a mixed-integer nonlinear set that is the epigraph of $f(a'x)$ together with a cardinality constraint. This mixed-integer nonlinear set arises as a substructure in various constrained submodular minimization problems. We develop a strong linear formulation of the convex hull of the nonlinear set by exploiting both the submodularity of $f(a'x)$ and the cardinality constraint. We provide a full description of the convex hull of the nonlinear set when the vector a has identical components. We also develop a family of facet-defining inequalities when the vector a has nonidentical components. We demonstrate the effectiveness of the proposed inequalities by solving mean-risk knapsack problems using a branch-and-cut framework.

Pessoas portadoras de deficiências encontram enormes dificuldades ao tentarem entrar no mercado de trabalho. De fato, sobretudo em países em desenvolvimento, esta parcela significativa da população representa uma fração ínfima dos trabalhadores empregados. Dentre as iniciativas que tentam reverter este quadro, destaca-se a criação de Centros de Trabalhadores Deficientes (CTDs), empresas sem fins lucrativos que empregam pessoas portadoras de deficiências, geralmente em linhas de produção. Um dos fins últimos dos CTDs é expor os trabalhadores a situações encontradas em uma gama diversa de contextos produtivos, de modo que eles possam, eventualmente, vir a compor o quadro de empresas convencionais. A organização e planejamento da operação de CTDs envolve uma série de dificuldades. Questões ligadas à ergonomia do trabalho ou ao gerenciamento de qualidade, por exemplo, adquirem características particulares neste ambiente. Da mesma forma, problemas clássicos de balanceamento de linhas de produção ganham novas particularidades devido, sobretudo, à enorme heterogeneidade existente entre os trabalhadores. Neste contexto, nos interessamos por problemas referentes ao balanceamento da linha de produção com trabalhadores deficientes, onde se busca obter a maior eficiência produtiva dadas as habilidades específicas de cada trabalhador. De maneira mais precisa, o problema de balanceamento de linhas de produção em CTDs, conhecido na literatura como problema de balanceamento e designação de trabalhadores em linhas de produção (ALWABP, na sigla em inglês) consiste em alocar tarefas e trabalhadores a estações de trabalho, de modo a minimizar o gargalo produtivo e levando em consideração que cada tarefa tem um tempo de duração que depende do trabalhador escolhido para sua execução. Isto dá ao problema um caráter de dupla alocação, aumentando seu caráter combinatório e, consequentemente, sua dificuldade de resolução. Nesta dissertação, estudamos uma variedade de técnicas de resolução do ALWABP. Os objetivos deste estudo são, primeiramente, obter métodos diversos para resolução do problema que sejam eficazes tanto em termos do tempo computacional necessário para sua utilização como em termos da qualidade da solução obtida. Dentre as abordagens propostas e testadas encontram-se versões de algoritmos com diferentes complexidades, indo desde heurísticas construtivas e estratégias de busca monotônica em vizinhança até meta-heurísticas como GRASP e Busca Tabu. A variedade de técnicas desenvolvidas permitiu a resolução de um problema ainda mais complexo que o ALWABP, que consiste em programar a linha para diversos períodos produtivos, levando em consideração a rotação de tarefas entre os trabalhadores. Deste modo, os trabalhadores podem ser expostos ao maior número de tarefas possível (atendendo, assim, o fim de treinamento almejado no ambiente dos CTDs). Para resolução do problema de rotação de tarefas, as técnicas desenvolvidas foram utilizadas em um esquema de otimização híbrido que faz uso de um pool de soluções (obtidas pelos métodos heurísticos) que são integradas através de modelos de otimização linear inteira mista. Os resultados obtidos sugerem que as técnicas desenvolvidas são eficientes e flexíveis para o problema ALWABP e que a sua integração permite a obtenção de soluções eficientes para o problema de rotação de tarefas. Deste modo, esta dissertação propõe um esquema completo para o balanceamento de linhas de produção em CTDs / Disabled workers face enormous difficulties when trying to enter to the labor market. At the present moment, in particular in developing countries, this group constitutes a small portion of the labor force in productive processes. Among the initiatives that attempt to reverse this situation, we highlight the creation of sheltered work centers for the disabled (referred to as SWD henceforth), which are non-profit companies that employ people with disabilities, often in assembly lines. The organization and planning of the operation of a SWD involves a number of challenges. Issues related to ergonomy or production quality management, for instance, acquire particular characteristics in this environment. Likewise, classic assembly lines balancing modeling and solving techniques have to be modified, due to the significant heterogeneity among workers. In this context, we are concerned with problems related to the assembly line balancing with disabled workers, which attempts to achieve the higher production efficiency as possible, given the specific skills of each worker. More precisely, the assembly line balancing problem in SWD, known in the literature as the assembly line worker assignment and balancing problem (ALWABP), consists in assigning tasks and workers to workstations, in order to minimize the bottleneck of the production line while considering that each task duration time depends on the worker chosen for its execution. This double assignment structure leads to a much more complex problem. In this dissertation, we study a variety of techniques for solving the ALWABP. The goals of this study are, first of all, the development of a number of efficient techniques for solving the problem, both in terms of computational time required for their use and in terms of the quality of the obtained solutions. Among the techniques proposed and tested, we have versions of algorithms with different complexities, ranging from constructive heuristics and monotonic neighborhood search strategies to metaheuristics such as Tabu Search and GRASP. The diversity of the developed techniques allowed the resolution of a problem even more complex than the ALWABP, which consists of programming the line for a set of periods, taking into account the rotation of tasks among workers. The objective of this new problem is to propose a solution for a given production period that considers the fact that it might be positive to expose the workers to as many tasks as possible (for training, therapeutical and motivational reasons). In order to solve this job rotation problem, the techniques developed were integrated into a hybrid optimization scheme that uses a pool of solutions (obtained with the heuristic methods) which become inputs of mixed integer linear optimization models. The results suggest that the techniques developed are efficient and flexible to the ALWABP and their integration allows the obtention of efficient solutions to the job rotation problem. Thus, this dissertation proposes a complete scheme for the resolution of the balancing problem in SWD production lines

Pessoas portadoras de deficiências encontram enormes dificuldades ao tentarem entrar no mercado de trabalho. De fato, sobretudo em países em desenvolvimento, esta parcela significativa da população representa uma fração ínfima dos trabalhadores empregados. Dentre as iniciativas que tentam reverter este quadro, destaca-se a criação de Centros de Trabalhadores Deficientes (CTDs), empresas sem fins lucrativos que empregam pessoas portadoras de deficiências, geralmente em linhas de produção. Um dos fins últimos dos CTDs é expor os trabalhadores a situações encontradas em uma gama diversa de contextos produtivos, de modo que eles possam, eventualmente, vir a compor o quadro de empresas convencionais. A organização e planejamento da operação de CTDs envolve uma série de dificuldades. Questões ligadas à ergonomia do trabalho ou ao gerenciamento de qualidade, por exemplo, adquirem características particulares neste ambiente. Da mesma forma, problemas clássicos de balanceamento de linhas de produção ganham novas particularidades devido, sobretudo, à enorme heterogeneidade existente entre os trabalhadores. Neste contexto, nos interessamos por problemas referentes ao balanceamento da linha de produção com trabalhadores deficientes, onde se busca obter a maior eficiência produtiva dadas as habilidades específicas de cada trabalhador. De maneira mais precisa, o problema de balanceamento de linhas de produção em CTDs, conhecido na literatura como problema de balanceamento e designação de trabalhadores em linhas de produção (ALWABP, na sigla em inglês) consiste em alocar tarefas e trabalhadores a estações de trabalho, de modo a minimizar o gargalo produtivo e levando em consideração que cada tarefa tem um tempo de duração que depende do trabalhador escolhido para sua execução. Isto dá ao problema um caráter de dupla alocação, aumentando seu caráter combinatório e, consequentemente, sua dificuldade de resolução. Nesta dissertação, estudamos uma variedade de técnicas de resolução do ALWABP. Os objetivos deste estudo são, primeiramente, obter métodos diversos para resolução do problema que sejam eficazes tanto em termos do tempo computacional necessário para sua utilização como em termos da qualidade da solução obtida. Dentre as abordagens propostas e testadas encontram-se versões de algoritmos com diferentes complexidades, indo desde heurísticas construtivas e estratégias de busca monotônica em vizinhança até meta-heurísticas como GRASP e Busca Tabu. A variedade de técnicas desenvolvidas permitiu a resolução de um problema ainda mais complexo que o ALWABP, que consiste em programar a linha para diversos períodos produtivos, levando em consideração a rotação de tarefas entre os trabalhadores. Deste modo, os trabalhadores podem ser expostos ao maior número de tarefas possível (atendendo, assim, o fim de treinamento almejado no ambiente dos CTDs). Para resolução do problema de rotação de tarefas, as técnicas desenvolvidas foram utilizadas em um esquema de otimização híbrido que faz uso de um pool de soluções (obtidas pelos métodos heurísticos) que são integradas através de modelos de otimização linear inteira mista. Os resultados obtidos sugerem que as técnicas desenvolvidas são eficientes e flexíveis para o problema ALWABP e que a sua integração permite a obtenção de soluções eficientes para o problema de rotação de tarefas. Deste modo, esta dissertação propõe um esquema completo para o balanceamento de linhas de produção em CTDs / Disabled workers face enormous difficulties when trying to enter to the labor market. At the present moment, in particular in developing countries, this group constitutes a small portion of the labor force in productive processes. Among the initiatives that attempt to reverse this situation, we highlight the creation of sheltered work centers for the disabled (referred to as SWD henceforth), which are non-profit companies that employ people with disabilities, often in assembly lines. The organization and planning of the operation of a SWD involves a number of challenges. Issues related to ergonomy or production quality management, for instance, acquire particular characteristics in this environment. Likewise, classic assembly lines balancing modeling and solving techniques have to be modified, due to the significant heterogeneity among workers. In this context, we are concerned with problems related to the assembly line balancing with disabled workers, which attempts to achieve the higher production efficiency as possible, given the specific skills of each worker. More precisely, the assembly line balancing problem in SWD, known in the literature as the assembly line worker assignment and balancing problem (ALWABP), consists in assigning tasks and workers to workstations, in order to minimize the bottleneck of the production line while considering that each task duration time depends on the worker chosen for its execution. This double assignment structure leads to a much more complex problem. In this dissertation, we study a variety of techniques for solving the ALWABP. The goals of this study are, first of all, the development of a number of efficient techniques for solving the problem, both in terms of computational time required for their use and in terms of the quality of the obtained solutions. Among the techniques proposed and tested, we have versions of algorithms with different complexities, ranging from constructive heuristics and monotonic neighborhood search strategies to metaheuristics such as Tabu Search and GRASP. The diversity of the developed techniques allowed the resolution of a problem even more complex than the ALWABP, which consists of programming the line for a set of periods, taking into account the rotation of tasks among workers. The objective of this new problem is to propose a solution for a given production period that considers the fact that it might be positive to expose the workers to as many tasks as possible (for training, therapeutical and motivational reasons). In order to solve this job rotation problem, the techniques developed were integrated into a hybrid optimization scheme that uses a pool of solutions (obtained with the heuristic methods) which become inputs of mixed integer linear optimization models. The results suggest that the techniques developed are efficient and flexible to the ALWABP and their integration allows the obtention of efficient solutions to the job rotation problem. Thus, this dissertation proposes a complete scheme for the resolution of the balancing problem in SWD production lines

The problem of risk-averse decision making under uncertainties is studied from both modeling and computational perspectives. First, we consider a framework for constructing coherent and convex measures of risk which is inspired by infimal convolution operator, and prove that the proposed approach constitutes a new general representation of these classes. We then discuss how this scheme may be effectively employed to obtain a class of certainty equivalent measures of risk that can directly incorporate decision maker's preferences as expressed by utility functions. This approach is consequently utilized to introduce a new family of measures, the log-exponential convex measures of risk. Conducted numerical experiments show that this family can be a useful tool when modeling risk-averse decision preferences under heavy-tailed distributions of uncertainties. Next, numerical methods for solving the rising optimization problems are developed. A special attention is devoted to the class p-order cone programming problems and mixed-integer models. Solution approaches proposed include approximation schemes for $p$-order cone and more general nonlinear programming problems, lifted conic and nonlinear valid inequalities, mixed-integer rounding conic cuts and new linear disjunctive cuts.

This report aimed to develop algorithms for solving the optimization problem of matchingbuy and sell orders in call auctions while minimizing the number of transactions. The developed algorithms were evaluated based on their execution time and solution accuracy.The study found that the problem was more difficult to solve than initially anticipated, and commercial solvers were inadequate for the task. The data’s characteristics werecritical to the algorithms’ performance, and the lack of specifications for instruments andexchange posed a challenge. The algorithms were tested on a broad range of datasets with different characteristics, as well as real trades of stocks from the Stockholm Stock Exchange. Evaluating the best-performing algorithm became a trade-off between time and accuracy, where the quickest algorithm did not have the highest solution accuracy. Therefore, the importance of these factors should be considered before deciding which algorithm to implement. Eight algorithms were evaluated: four greedy algorithms and four clusteralgorithms capable of identifying 2-1 and 3-1 matches. If execution time is the single most crucial factor, the Unsorted Greedy Algorithm should be considered. However, if accuracyi s a priority, the Cluster 3-1 & 1-3 Algorithm should be considered, even though it takes longer to find a solution. Ultimately, the report concluded that while no single algorithm can be definitively la-beled as the best, the Cluster 2-1 Algorithm strikes the most effective balance between execution time and solution accuracy, while also remaining relatively stable in perfor-mance for all test cases. The recommendation was based on the fact that the Cluster 2-1 Algorithm proved to be the quickest of the developed cluster algorithms, and that cluster algorithms were able to find the best solutions for all tested data sets. This study successfully addressed its purpose by developing eight algorithms that solved the given problem and suggested an appropriate algorithm that strikes a balance between execution time and solution quality.

A complexidade de alguns sistemas biotecnológicos impossibilita seu estudo sem o uso de técnicas de programação matemática avançadas. A quantificação de fluxos metabólicos e a síntese e projeto ótimos de plantas multiproduto são problemas com esta característica, abordados na presente tese. A quantificação de fluxos metabólicos empregando balanços de marcações é representada como um problema de otimização não-linear, o qual se resolve através da minimização da diferença entre as medidas experimentais e as predições do modelo da rede metabólica. Este problema surge da necessidade de se caracterizar o metabolismo mediante a estimação das velocidades das reações bioquímicas. O modelo matemático para problemas deste tipo é composto basicamente por balanços de metabólitos e de isótopos; os primeiros são lineares, enquanto os segundos introduzem não-linearidades ao problema e, neste trabalho, são modelados mediante uma modificação da técnica de matrizes de mapeamento de átomos. Para quantificar os fluxos metabólicos considerando a existência de ótimos locais, desenvolveu-se um algoritmo branch & bound espacial, no qual a busca global é feita mediante a divisão da região de busca (branching) e a geração de seqüências de limites (bounding) que convergem para a solução global. Como estudo de caso, estimaram-se os fluxos no metabolismo central de Saccharomyces cerevisiae. Os resultados confirmam a existência de soluções locais e a necessidade de desenvolver uma estratégia de busca global; a solução global obtida apresenta semelhanças, nos fluxos centrais, com a melhor solução obtida por um algoritmo evolucionário. Quanto aos problemas de síntese e projeto de sistemas biotecnológicos multiproduto, As abordagens mais empregadas para resolve-los são a definição e dimensionamento seqüencial das operações unitárias, e a fixação dos parâmetros de dimensionamento e de estimação do tempo de operação (com valores obtidos em laboratório ou planta piloto); porém ambas abordagens fornecem soluções subótimas. Por outro lado, a solução simultânea da síntese e projeto de sistemas biotecnológicos multiproduto gera modelos misto-inteiros não-lineares (MINLP) de grande porte, devido à combinação das decisões, ligadas à existência de alternativas no processo, com as restrições não-lineares geradas dos modelos das operações. Como estudo de caso considera-se uma planta para produção de insulina, vacina para hepatite B, ativador de plasminogênio tecidual (tissue plasminogen activator) e superóxido dismutase, mediante três hospedeiros diferentes: levedura (S. cerevisiae) com expressão extra ou intracelular, Escherichia coli e células de mamíferos. O projeto deve satisfazer a meta de produção para cada produto, minimizando os custos de capital e selecionando os hospedeiros, as operações e o arranjo dos equipamentos em cada estágio. Os resultados obtidos mostram que a formulação das decisões por abordagem big-M permite resolver o modelo MINLP gerado e que a consideração de múltiplos produtos com seqüências e condições de processamento diferentes gera grande ociosidade nos equipamentos e aumenta o custo total do projeto. Para o estudo de caso observou-se que a alocação de tanques intermediários tem um efeito limitado na diminuição do custo do projeto, porém a implementação simultânea da flexibilização do scheduling, do projeto de equipamentos auxiliares e tanques intermediários permite obter projetos satisfatórios. / The complexity of biotechnological systems does not allow their study without the use of advanced mathematical programming techniques. Metabolic flux quantification and optimal synthesis and design of multiproduct plants are problems with this characteristic, and are addressed in this thesis. The metabolic flux quantification employing labeling balances is formulated as a nonlinear optimization problem that is solved by the minimization of the difference between experimental measurements and predictions of the metabolic network model. This problem is generated by the necessity of estimating the rates of biochemical reactions that characterize the metabolism. The mathematical model for this class of problems is composed by balances of metabolites and isotopes; the former are linear whereas the latter are nonlinear and, in this work, are modeled by a modification of the atom mapping matrix technique. A spatial branch & bound algorithm was developed to quantify the metabolic fluxes, that considers the existence of local optima; in this algorithm, the global search is developed by the division of the searching region (branching) and the generation of sequences of bounds (bounding) that converge to the global solution. As a case study, fluxes in central metabolism of Saccharomyces cerevisiae were estimated. The results confirm the existence of local solutions and the necessity of develop a global search strategy; the central fluxes in the obtained global solution are similar to those ones obtained by an evolutionary algorithm. To solve problems of synthesis and design of multiproduct biotechnological systems, the most employed approaches are the sequential selection and sizing of the unit operations, and the fixing of sizing and time parameters (employing values from laboratory or pilot plants); nevertheless, both approaches generate suboptimal solutions. On the other hand, the simultaneous solution of the synthesis and design of multiproduct biotechnological systems generates large size mixed-integer nonlinear models (MINLP), due to the combination of options into the processing with nonlinear constraints from the operation models. As case study, a plant for production of insulin, hepatitis B vaccine, tissue plasminogen activator and superoxide dismutase was considered, by three hosts: yeast (S. cerevisiae) with extra or intracellular expression, Escherichia coli and mammalian cells. The design must satisfy the production target for each product, minimizing the capital cost and considering the selection of hosts, the operations and the number of parallel units in each stage. The obtained results show that the formulation of decisions by the big-M approach allows the solution of the generated MINLP model and that consideration of several products with different processing sequences and conditions generates large idleness at the equipment and increases the total cost of the design. In the case study it was observed that the allocation of storage tanks has a limited effect on cost reduction, but the simultaneous implementation of flexible scheduling, design of auxiliary equipments and intermediate storage tanks allow the generation of satisfactory designs.

A complexidade de alguns sistemas biotecnológicos impossibilita seu estudo sem o uso de técnicas de programação matemática avançadas. A quantificação de fluxos metabólicos e a síntese e projeto ótimos de plantas multiproduto são problemas com esta característica, abordados na presente tese. A quantificação de fluxos metabólicos empregando balanços de marcações é representada como um problema de otimização não-linear, o qual se resolve através da minimização da diferença entre as medidas experimentais e as predições do modelo da rede metabólica. Este problema surge da necessidade de se caracterizar o metabolismo mediante a estimação das velocidades das reações bioquímicas. O modelo matemático para problemas deste tipo é composto basicamente por balanços de metabólitos e de isótopos; os primeiros são lineares, enquanto os segundos introduzem não-linearidades ao problema e, neste trabalho, são modelados mediante uma modificação da técnica de matrizes de mapeamento de átomos. Para quantificar os fluxos metabólicos considerando a existência de ótimos locais, desenvolveu-se um algoritmo branch & bound espacial, no qual a busca global é feita mediante a divisão da região de busca (branching) e a geração de seqüências de limites (bounding) que convergem para a solução global. Como estudo de caso, estimaram-se os fluxos no metabolismo central de Saccharomyces cerevisiae. Os resultados confirmam a existência de soluções locais e a necessidade de desenvolver uma estratégia de busca global; a solução global obtida apresenta semelhanças, nos fluxos centrais, com a melhor solução obtida por um algoritmo evolucionário. Quanto aos problemas de síntese e projeto de sistemas biotecnológicos multiproduto, As abordagens mais empregadas para resolve-los são a definição e dimensionamento seqüencial das operações unitárias, e a fixação dos parâmetros de dimensionamento e de estimação do tempo de operação (com valores obtidos em laboratório ou planta piloto); porém ambas abordagens fornecem soluções subótimas. Por outro lado, a solução simultânea da síntese e projeto de sistemas biotecnológicos multiproduto gera modelos misto-inteiros não-lineares (MINLP) de grande porte, devido à combinação das decisões, ligadas à existência de alternativas no processo, com as restrições não-lineares geradas dos modelos das operações. Como estudo de caso considera-se uma planta para produção de insulina, vacina para hepatite B, ativador de plasminogênio tecidual (tissue plasminogen activator) e superóxido dismutase, mediante três hospedeiros diferentes: levedura (S. cerevisiae) com expressão extra ou intracelular, Escherichia coli e células de mamíferos. O projeto deve satisfazer a meta de produção para cada produto, minimizando os custos de capital e selecionando os hospedeiros, as operações e o arranjo dos equipamentos em cada estágio. Os resultados obtidos mostram que a formulação das decisões por abordagem big-M permite resolver o modelo MINLP gerado e que a consideração de múltiplos produtos com seqüências e condições de processamento diferentes gera grande ociosidade nos equipamentos e aumenta o custo total do projeto. Para o estudo de caso observou-se que a alocação de tanques intermediários tem um efeito limitado na diminuição do custo do projeto, porém a implementação simultânea da flexibilização do scheduling, do projeto de equipamentos auxiliares e tanques intermediários permite obter projetos satisfatórios. / The complexity of biotechnological systems does not allow their study without the use of advanced mathematical programming techniques. Metabolic flux quantification and optimal synthesis and design of multiproduct plants are problems with this characteristic, and are addressed in this thesis. The metabolic flux quantification employing labeling balances is formulated as a nonlinear optimization problem that is solved by the minimization of the difference between experimental measurements and predictions of the metabolic network model. This problem is generated by the necessity of estimating the rates of biochemical reactions that characterize the metabolism. The mathematical model for this class of problems is composed by balances of metabolites and isotopes; the former are linear whereas the latter are nonlinear and, in this work, are modeled by a modification of the atom mapping matrix technique. A spatial branch & bound algorithm was developed to quantify the metabolic fluxes, that considers the existence of local optima; in this algorithm, the global search is developed by the division of the searching region (branching) and the generation of sequences of bounds (bounding) that converge to the global solution. As a case study, fluxes in central metabolism of Saccharomyces cerevisiae were estimated. The results confirm the existence of local solutions and the necessity of develop a global search strategy; the central fluxes in the obtained global solution are similar to those ones obtained by an evolutionary algorithm. To solve problems of synthesis and design of multiproduct biotechnological systems, the most employed approaches are the sequential selection and sizing of the unit operations, and the fixing of sizing and time parameters (employing values from laboratory or pilot plants); nevertheless, both approaches generate suboptimal solutions. On the other hand, the simultaneous solution of the synthesis and design of multiproduct biotechnological systems generates large size mixed-integer nonlinear models (MINLP), due to the combination of options into the processing with nonlinear constraints from the operation models. As case study, a plant for production of insulin, hepatitis B vaccine, tissue plasminogen activator and superoxide dismutase was considered, by three hosts: yeast (S. cerevisiae) with extra or intracellular expression, Escherichia coli and mammalian cells. The design must satisfy the production target for each product, minimizing the capital cost and considering the selection of hosts, the operations and the number of parallel units in each stage. The obtained results show that the formulation of decisions by the big-M approach allows the solution of the generated MINLP model and that consideration of several products with different processing sequences and conditions generates large idleness at the equipment and increases the total cost of the design. In the case study it was observed that the allocation of storage tanks has a limited effect on cost reduction, but the simultaneous implementation of flexible scheduling, design of auxiliary equipments and intermediate storage tanks allow the generation of satisfactory designs.

L'optimisation topologique vise à concevoir une structure en recherchant la disposition optimale du matériau dans un espace de conception donné, permettant ainsi de proposer des designs optimaux innovants. Cette thèse est centrée sur l'optimisation topologique pour des problèmes de conception de structures prenant en compte des contraintes de flambage. Dans une large variété de domaines de l'ingénierie, la conception innovante de structures est cruciale. L'allègement des structures lors la phase de conception tient une place prépondérante afin de réduire les coûts de fabrication. Ainsi l'objectif est souvent la minimisation de la masse de la structure à concevoir. En ce qui concerne les contraintes, en plus des contraintes mécaniques classiques (compression, tension), il est nécessaire de prendre en compte des phénomènes dits de flambage, qui se caractérisent par une amplification des déformations de la structure et une potentielle annihilation des capacités de la structure à supporter les efforts appliqués. Dans le but d'adresser un large panel de problèmes d'optimisation topologique, nous considérons les deux types de représentation d'une structure : les structures treillis et les structures continues. Dans le cadre de structures treillis, l'objectif est de minimiser la masse en optimisant le nombre d'éléments de la structure et les dimensions des sections transversales associées à ces éléments. Nous considérons les structures constituées d'éléments poutres et nous introduisons une formulation du problème comme un problème d'optimisation non-linéaire en variables mixtes. Afin de prendre en compte des contraintes de manufacturabilité, nous proposons une fonction coût combinant la masse et la somme des seconds moments d'inertie de chaque poutre. Nous avons développé un algorithme adapté au problème d'optimisation considéré. Les résultats numériques montrent que l'approche proposée mène à des gains de masses significatifs par rapport à des approches existantes. Dans le cas des structures continues, l'optimisation topologique vise à discrétiser le domaine de conception et à déterminer les éléments de ce domaine discrétisé qui doivent être composés de matière, définissant ainsi un problème d'optimisation discret. [...] / Topology optimization aims to design a structure by seeking the optimal material layout within a given design space, thus making it possible to propose innovative optimal designs. This thesis focuses on topology optimization for structural problems taking into account buckling constraints. In a wide variety of engineering fields, innovative structural design is crucial. The lightening of structures during the design phase holds a prominent place in order to reduce manufacturing costs. Thus the goal is often the minimization of the mass of the structure to be designed. Regarding the constraints, in addition to the conventional mechanical constraints (compression, tension), it is necessary to take into account buckling phenomena which are characterized by an amplification of the deformations of the structure and a potential annihilation of the capabilities of the structure to support the applied efforts. In order to adress a wide range of topology optimization problems, we consider the two types of representation of a structure: lattice structures and continuous structures. In the framework of lattice structures, the objective is to minimize the mass by optimizing the number of elements of the structure and the dimensions of the cross sections associated to these elements. We consider structures constituted by a set of frame elements and we introduce a formulation of the problem as a mixed-integer nonlinear problem. In order to obtain a manufacturable structure, we propose a cost function combining the mass and the sum of the second moments of inertia of each frame. We developed an algorithm adapted to the considered optimization problem. The numerical results show that the proposed approach leads to significant mass gains over existing approaches. In the case of continuous structures, topology optimization aims to discretize the design domain and to determine the elements of this discretized domain that must be composed of material, thus defining a discrete optimization problem. [...]

The number of technology alternatives has lately grown to satisfy the increasingly demanding goals in modern engineering. These technology alternatives are handled in the design process as either concepts or categorical design inputs. Additionally, designers desire to bring into early design more and more accurate, but also computationally burdensome, simulation tools to obtain better performing initial designs that are more valuable in subsequent design stages. It constrains the computational budget to optimize the design space. These two factors unveil the need of a conceptual design methodology to use more efficiently sophisticated tools for engineering problems with several concept solutions and categorical design choices. Enhanced initial designs and discrete alternative selection are pursued. Advances in computational speed and the development of Bayesian adaptive sampling techniques have enabled the industry to move from the use of look-up tables and simplified models to complex physics-based tools in conceptual design. These techniques focus computational resources on promising design areas. Nevertheless, the vast majority of the work has been done on problems with continuous spaces, whereas concepts and categories are treated independently. However, observations show that engineering objectives experience similar topographical trends across many engineering alternatives. In order to address these challenges, two meta-models are developed. The first one borrows the Hamming distance and function space norms from machine learning and functional analysis, respectively. These distances allow defining categorical metrics that are used to build an unique probabilistic surrogate whose domain includes, not only continuous and integer variables, but also categorical ones. The second meta-model is based on a multi-fidelity approach that enhances a concept prediction with previous concept observations. These methodologies leverage similar trends seen from observations and make a better use of sample points increasing the quality of the output in the discrete alternative selection and initial designs for a given analysis budget. An extension of stochastic mixed-integer optimization techniques to include the categorical dimension is developed by adding appropriate generation, mutation, and crossover operators. The resulted stochastic algorithm is employed to adaptively sample mixed-integer-categorical design spaces. The proposed surrogates are compared against traditional independent methods for a set of canonical problems and a physics-based rotor-craft model on a screened design space. Next, adaptive sampling algorithms on the developed surrogates are applied to the same problems. These tests provide evidence of the merit of the proposed methodologies. Finally, a multi-objective rotor-craft design application is performed in a large domain space. This thesis provides several novel academic contributions. The first contribution is the development of new efficient surrogates for systems with categorical design choices. Secondly, an adaptive sampling algorithm is proposed for systems with mixed-integer-categorical design spaces. Finally, previously sampled concepts can be brought to construct efficient surrogates of novel concepts. With engineering judgment, design community could apply these contributions to discrete alternative selection and initial design assessment when similar topographical trends are observed across different categories and/or concepts. Also, it could be crucial to overcome the current cost of carrying a set of concepts and wider design spaces in the categorical dimension forward into preliminary design.

La conception d'un système électrique est une tâche très complexe qui relève d’expertises dans différents domaines de compétence. Dans un contexte compétitif où l’avance technologique est un facteur déterminant, l’industrie cherche à réduire les temps d'étude et à fiabiliser les solutions trouvées par une approche méthodologique rigoureuse fournissant une solution optimale systémique.Il est alors nécessaire de construire des modèles et de mettre au point des méthodes d'optimisation compatibles avec ces préoccupations. En effet, l’optimisation unitaire de sous-systèmes sans prendre en compte les interactions ne permet pas d'obtenir un système optimal. Plus le système est complexe plus le travail est difficile et le temps de développement est important car il est difficile pour le concepteur d'appréhender le système dans toute sa globalité. Il est donc nécessaire d'intégrer la conception des composants dans une démarche systémique et globale qui prenne en compte à la fois les spécificités d’un composant et ses relations avec le système qui l’emploie.Analytical Target Cascading est une méthode d'optimisation multi niveaux de systèmes complexes. Cette approche hiérarchique consiste à décomposer un système complexe en sous-systèmes, jusqu’au niveau composant dont la conception relève d’algorithmes d'optimisation classiques. La solution optimale est alors trouvée par une technique de coordination qui assure la cohérence de tous les sous-systèmes. Une première partie est consacrée à l'optimisation de composants électriques. L'optimisation multi niveaux de systèmes complexes est étudiée dans la deuxième partie où une chaîne de traction électrique est choisie comme exemple / The design of an electrical system is a very complex task which needs experts from various fields of competence. In a competitive environment, where technological advance is a key factor, industry seeks to reduce study time and to make solutions reliable by way of a rigorous methodology providing a systemic solution.Then, it is necessary to build models and to develop optimization methods which are suitable with these concerns. Indeed, the optimization of sub-systems without taking into account the interaction does not allow to achieve an optimal system. More complex the system is more the work is difficult and the development time is important because it is difficult for the designer to understand and deal with the system in its complexity. Therefore, it is necessary to integrate the design components in a systemic and holistic approach to take into account, in the same time, the characteristics of a component and its relationship with the system it belongs to.Analytical Target Cascading is a multi-level optimization method for handling complex systems. This hierarchical approach consists on the breaking-down of a complex system into sub-systems, and component where their optimal design is ensured by way of classical optimization algorithms. The optimal solution of the system must be composed of the component's solutions. Then a coordination strategy is needed to ensure consistency of all sub-systems. First, the studied and proposed optimization algorithms are tested and compared on the optimization of electrical components. The second part focuses on the multi-level optimization of complex systems. The optimization of railway traction system is taken as a test case