This thesis focuses on the challenges that arise from the scheduling of heat exchanger network maintenance problems which undergo fouling and run continuously over time. The original contributions of the current research consist of the development of novel optimisation methodologies for the scheduling of cleaning actions in heat exchanger network problems, the application of the novel solution methodology developed to other general maintenance scheduling problems, the development of a stochastic programming formulation using this optimisation technique and its application to these scheduling problems with parametric uncertainty. The work presented in this thesis can be divided into three areas. To efficiently solve this non-convex heat exchanger network maintenance scheduling problem, new optimisation strategies are developed. The resulting contributions are outlined below. In the first area, a novel methodology is developed for the solution of the heat exchanger network maintenance scheduling problems, which is attributed towards a key discovery in which it is observed that these problems exhibit bang-bang behaviour. This indicates that when integrality on the binary decision variables is relaxed, the solution will tend to either the lower or the upper bound specified, obviating the need for integer programming solution techniques. Therefore, these problems are in ac- tuality optimal control problems. To suitably solve these problems, a feasible path sequential mixed integer optimal control approach is proposed. This methodology is coupled with a simple heuristic approach and applied to a range of heat exchanger network case studies from crude oil refinery preheat trains. The demonstrated meth- odology is shown to be robust, reliable and efficient. In the second area of this thesis, the aforementioned novel technique is applied to the scheduling of the regeneration of membranes in reverse osmosis networks which undergo fouling and are located in desalination plants. The results show that the developed solution methodology can be generalised to other maintenance scheduling problems with decaying performance characteristics. In the third and final area of this thesis, a stochastic programming version of the feasible path mixed integer optimal control problem technique is established. This is based upon a multiple scenario approach and is applied to two heat exchanger network case studies of varying size and complexity. Results show that this methodology runs automatically with ease without any failures in convergence. More importantly due to the significant impact on economics, it is vital that uncertainty in data is taken into account in the heat exchanger network maintenance scheduling problem, as well as other general maintenance scheduling problems when there is a level of uncertainty in parameter values.

Orientador: Antonio Roberto Balbo / Banca: Edilaine Martins Soler / Banca: Leonardo Nepomuceno / Resumo: Neste trabalho apresentamos o método previsor-corretor primal-dual de pontos interiores, com barreira logarítmica modificada e estratégia de ajuste cúbico (MPIBLM-EX) e o método previsor-corretor primal-dual de pontos interiores, com barreira logarítmica modificada, com estratégias de ajuste cúbico e de convergência global (MPIBLMCG-EX). Na definição do algoritmo proposto, a função barreira logarítmica modificada auxilia o método em sua inicialização com pontos inviáveis. Porém, a inviabilidade pode ocorrer em pontos tais que o logaritmo não está definido, consequentemente, isso implica na não existência de função barreira logarítmica modificada. Para suprir essa dificuldade um polinômio cúbico ajustado ao logaritmo, que preserva as derivadas de primeira e segunda do mestre definido a partir de um ponto da região ampliada ao método previsor-corretor primal-dual de pontos interiores com barreira logarítmica modificada (MPIBML); no processo previsor são realizadas atualizações do parâmetro de barreira nos resíduos das restrições de complementaridade, considerando aproximações de primeira ordem do sistema de direções de busca, enquanto que no procedimento corretor, incluímos os termos quadráticos não-lineares dos resíduos citados, que foram desprezados no procedimento previsor. Considerando também a estratégia de convergência global para o MPIBLM-EX, a qual utiliza uma variante do método de Levenberg-Marquardt para ajustar a matriz dual normal da função lagrangiana, caso esta não seja definida positiva. A matriz dual normal é redefinida para as restrições primais de igualdade, de desigualdade e para as variáveis canalizadas, incorporando variáveis duais e matrizes diagonais relativas às restrições de complementariade. Desse estudo, o MPIBLM-EX é transformado no MPIBLMCG-EX e mostramos... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work presents a predictor primal-dual interior point method with modified log-barrier and third order extrapolation strategy (IPMLBM-EX) and also and extension of this method with the inclusion of the global convergence strategy (IPMLBGCM-EX). In the definition of the proposed algorithm, the modified log-barrier function helps the method initialize with infeasible points. However, infeasibility may occur for some point where the logarithm is not defined. The implicates in non-existence of the modified log-barrier function. To cope with such as problem, a cubic polynomial function is adjusted to the logarithmic function. Sucha polynomial function preserves first and second order derivatives in certain point defined in the extended region. This function is applied to the predictor-corretor primal-dual interior point method with modified log-barrier function. In the predictor procedure, the barrier parameter is updated in the complementarity conditions considering first-order approximations of the search direction, while the corrector procedure includes the nonlinear quadratic terms of the mentioned residuals, which were neglected in the predictor procedure. We also consider the global convergence strategy for the method, which uses a variant of the Levenberg-Marquardt method to update the normal dual matrix of the Langrangian function, should it fail to be positively defined. In this case, this matrix is redefined for equality primal constraints, bounded inequality primal constraints and bounded variables, incorporating dual variables and diagonal matrices of the complementarity constraints. From such studies, the IPMLBM-EX method is extended to include the global convergence strategy (IPMLBGCM-EX). We have show that both methods are projected gradient methods. An implementation performed with Matlab 6.1 has shown the... (Complete abstract click electronic access below) / Mestre

O objetivo deste trabalho é otimizar formulações de estabilizantes térmicos para PVC (policloreto de vinila) pelo uso de técnicas de projetos de mistura, estendida a problemas com informação incompleta. O problema de mistura consiste em minimizar o custo de formulação enquanto se obtém um produto que satisfaça especificações técnicas e de mercado. No caso estudado, as formulações são misturas de 8 a 10 componentes, em sua grande maioria, escolhidos a partir de 16 compostos básicos. Cada composto confere diferente característica à formulação final, podendo existir interação entre eles. As características de interesse das misturas foram obtidas a partir das análises reológicas do composto de PVC, obtidas em um reômetro de torque (modelo Haake), em que foram usadas as formulações dos estabilizantes. Resultados contidos em um banco de dados, em que muitos testes diferentes e formulações comerciais foram analisados, foram aproveitados para a construção dos modelos correlacionando estas características com a composição. Como o número de experimentos que seriam necessários para obter a informação completa para a descrição da mistura seria proibitivo, modelos de mistura foram construídos usando regressão por componentes principais (PCR) e mínimos quadrados parciais (PLS). O problema de projeto de misturas foi traduzido em termos de problemas de programação linear e não linear, dependendo do tipo do modelo. Para evitar problemas de extrapolação que poderiam resultar devido à pobreza da informação, equações adicionais que restringem a solução ao conjunto onde a informação foi avaliada (o espaço gerado pelos componentes principais, definidos a partir da correlação) foram adicionados ao problema. Este procedimento corresponde a uma inovação com relação ao problema de mistura. Os resultados obtidos com os modelos são comparados com experimentos para validação do estudo executado. / The objective of this work is to optimize the formulations of heat stabilizers for PVC (Poly Vinyl Chloride) by means of mixture design techniques extended to deal with problems with incomplete information. The mixture design problem consists in minimizing the cost of the formulation while obtaining a product that satisfies technical and market specifications. In the case studied, the formulations are mixtures of 8 to 10 components chosen out from 16 basic compounds. Each of the compounds confers different characteristics to the final formulation, and there can be interactions between them. The characteristics of interest of the mixtures are obtained from assays performed in a standard torque rheometer (Haake model) for different stabilizer formulations. Data from a database, in which many different test and commercial formulations are recorded, were used in order to build models that correlate the properties with the compositions. As the number of data points that would be needed in order to obtain the necessary information for a complete description of the mixture would be prohibitive, mixture models were built using Principal Components Regression (PCR) and Pseudo-Least Squares Regression (PLS). The mixture design problem was expressed in terms of Linear and Nonlinear programming techniques, depending on the type of model used. In order to avoid extrapolation problems that would result from the poor availability of information, additional equations that confines the solution to the subset where information is available (the space spanned by the main loading vectors retained for correlation) are added to the problem. This is an extension to the standard mixture design problem. Solutions obtained are compared to validation experiments.

The problem of packing ellipsoids consists in arranging a given collection of ellipsoids within a particular set. The ellipsoids can be freely rotated and translated, and must not overlap each other. A particular case of this problem arises when the ellipsoids are balls. The problem of packing balls has been the subject of intense theoretical and empirical research. In particular, many works have tackled the problem with optimization tools. On the other hand, the problem of packing ellipsoids has received more attention only in the past few years. This problem appears in a large number of practical applications, such as the design of high-density ceramic materials, the formation and growth of crystals, the structure of liquids, crystals and glasses, the flow and compression of granular materials, the thermodynamics of liquid to crystal transition, and, in biological sciences, in the chromosome organization in human cell nuclei. In this work, we deal with the problem of packing ellipsoids within compact sets from an optimization perspective. We introduce continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space. We present two different models for the non-overlapping of ellipsoids. As these models have quadratic numbers of variables and constraints, we also propose an implicit variables models that has a linear number of variables and constraints. We also present models for the inclusion of ellipsoids within half-spaces and ellipsoids. By applying a simple multi-start strategy combined with a clever choice of starting guesses and a nonlinear programming local solver, we present illustrative numerical experiments that show the capabilities of the proposed models. / O problema de empacotamento de elipsoides consiste em arranjar uma dada coleção de elipsoides dentro de um determinado conjunto. Os elipsoides podem ser rotacionados e transladados e não podem se sobrepor. Um caso particular desse problema surge quando os elipsoides são bolas. O problema de empacotamento de bolas tem sido alvo de intensa pesquisa teórica e experimental. Em particular, muitos trabalhos têm abordado esse problema com ferramentas de otimização. O problema de empacotamento de elipsoides, por outro lado, começou a receber mais atenção apenas recentemente. Esse problema aparece em um grande número de aplicações práticas, como o projeto de materiais cerâmicos de alta densidade, na formação e crescimento de cristais, na estrutura de líquidos, cristais e vidros, no fluxo e compressão de materiais granulares e vidros, na termodinâmica e cinética da transição de líquido para cristal e em ciências biológicas, na organização de cromossomos no núcleo de células humanas. Neste trabalho, tratamos do problema de empacotamento de elipsoides dentro de conjuntos compactos do ponto de vista de otimização. Introduzimos modelos de programação não-linear contínuos e diferenciáveis e algoritmos para o empacotamento de elipsoides no espaço n-dimensional. Apresentamos dois modelos diferentes para a não-sobreposição de elipsoides. Como esses modelos têm números quadráticos de variáveis e restrições em função do número de elipsoides a serem empacotados, também propomos um modelo com variáveis implícitas que possui uma quantidade linear de variáveis e restrições. Também apresentamos modelos para a inclusão de elipsoides em semi-espaços e dentro de elipsoides. Através da aplicação de uma estratégia multi-start simples combinada com uma escolha inteligente de pontos iniciais e um resolvedor para otimização local de programas não-lineares, apresentamos experimentos numéricos que mostram as capacidades dos modelos propostos.

<p>Embedded computing systems in portable devices need to be energy efficient, yet they have to deliver adequate performance to the often computationally expensive applications. Dynamic voltage scaling is a technique that offers a speed versus power trade-off, allowing the application to achieve considerable energy savings and, at the same time, to meet the imposed time constraints.</p><p>In this thesis, we explore the possibility of using optimal voltage scaling algorithms based on nonlinear programming at the system level, for a complex multiprocessor scheduling problem. We present an optimization approach to the modeled nonlinear programming formulation of the continuous voltage selection problem excluding the consideration of transition overheads. Our approach achieves the same optimal results as the previous work using the same model, but due to its speed, can be efficiently used for design space exploration. We validate our results using numerous automatically generated benchmarks.</p>

This thesis consists of four independent papers concerningdifferent aspects of interior methods for optimization. Threeof the papers focus on theoretical aspects while the fourth oneconcerns some computational experiments. The systems of equations solved within an interior methodapplied to a convex quadratic program can be viewed as weightedlinear least-squares problems. In the first paper, it is shownthat the sequence of solutions to such problems is uniformlybounded. Further, boundedness of the solution to weightedlinear least-squares problems for more general classes ofweight matrices than the one in the convex quadraticprogramming application are obtained as a byproduct. In many linesearch interior methods for nonconvex nonlinearprogramming, the iterates can "falsely" converge to theboundary of the region defined by the inequality constraints insuch a way that the search directions do not converge to zero,but the step lengths do. In the sec ond paper, it is shown thatthe multiplier search directions then diverge. Furthermore, thedirection of divergence is characterized in terms of thegradients of the equality constraints along with theasymptotically active inequality constraints. The third paper gives a modification of the analytic centerproblem for the set of optimal solutions in linear semidefiniteprogramming. Unlike the normal analytic center problem, thesolution of the modified problem is the limit point of thecentral path, without any strict complementarity assumption.For the strict complementarity case, the modified problem isshown to coincide with the normal analytic center problem,which is known to give a correct characterization of the limitpoint of the central path in that case. The final paper describes of some computational experimentsconcerning possibilities of reusing previous information whensolving system of equations arising in interior methods forlinear programming. <b>Keywords:</b>Interior method, primal-dual interior method,linear programming, quadratic programming, nonlinearprogramming, semidefinite programming, weighted least-squaresproblems, central path. <b>Mathematics Subject Classification (2000):</b>Primary90C51, 90C22, 65F20, 90C26, 90C05; Secondary 65K05, 90C20,90C25, 90C30.

Manufacturing outsourcing in the U.S. has never been stronger than it is today. Increased outsourcing has led to significant changes in the design of the retail distribution network. While the traditional distribution network had the manufacturing plants supplying goods to the retail stores directly, the off-shore manufacturing has increased the network's demand for transportation and warehousing to deliver the goods. Thus, most companies have a complex distribution network with several import and regional distribution centers (RDC). In this thesis, we study an integrated facility location and inventory allocation problem for designing a distribution network with multiple national (import) distribution centers (NDC) and retailers. The key decisions are where to locate the RDCs and how much inventory to hold at the different locations such that the total network cost is minimized under a pre-defined operational rule for the distribution of goods. In particular, the inventory cost analysis is based on the continuous review batch ordering policy and the base-stock policy. Both Type-I (probability of stock-outs) and Type-II (fill-rate) service level measures are used in the analysis. Two different models are presented in this thesis for solving the integrated facility location-inventory allocation problem. The first model, continuous approximation (CA), assumes the distribution network to be located in a continuous region and replaces the discrete store locations with a store density function. The second model is a discrete representation of the problem as a mixed integer programming problem. Both the models take a nonlinear form and solution techniques are developed using the theory of nonlinear programming and linear reformulation of nonlinear problems. The goal of the first part of the thesis is to model the problem using a modified CA approach and an iterative solution scheme is presented to solve it. The main contribution of this work lies in developing a refined CA modeling technique when the discrete data cannot be modeled by a continuous function. In addition, the numerical analysis suggests that the total network cost is significantly lower in the case of the integrated model as compared with the non-integrated model. It is also shown that the regular CA approach leads to a solution which is inferior to the solution obtained by the modified CA approach. Our analysis shows that the type of service measure used affects the network design. In the second part of the thesis, the problem is modeled as a nonlinear mixed integer program and a linear reformulation solution technique is proposed to obtain a lower bound on the original problem. Computational results are presented for small problem instances. We conclude this part of the thesis by presenting an integrated model when a base stock inventory policy is used. A drop-decomposition heuristic is proposed to solve this problem.

Inferring and anticipation of genetic networks based on experimental data and environmental measurements is a challenging research problem of mathematical modeling. In this thesis, we discuss gene-environment network models whose dynamics are represented by a class of time-continuous systems of ordinary differential equations containing unknown parameters to be optimized. Accordingly, time-discrete version of that model class is studied and improved by using different numerical methods. In this aspect, 3rd-order Heun&rsquo / s method and 4th-order classical Runge-Kutta method are newly introduced, iteration formulas are derived and corresponding matrix algebras are newly obtained. We use nonlinear mixed-integer programming for the parameter estimation and present the solution of a constrained and regularized given mixed-integer problem. By using this solution and applying the 3rd-order Heun&rsquo / s and 4th-order classical Runge-Kutta methods in the timediscretized model, we generate corresponding time-series of gene-expressions by this thesis. Two illustrative numerical examples are studied newly with an artificial data set and a realworld data set which expresses a real phenomenon. All the obtained approximate results are compared to see the goodness of the new schemes. Different step-size analysis and sensitivity tests are also investigated to obtain more accurate and stable predictions of time-series results for a better service in the real-world application areas. The presented time-continuous and time-discrete dynamical models are identified based on given data, and studied by means of an analytical theory and stability theories of rarefication, regularization and robustification.

<p>This thesis consists of four independent papers concerningdifferent aspects of interior methods for optimization. Threeof the papers focus on theoretical aspects while the fourth oneconcerns some computational experiments.</p><p>The systems of equations solved within an interior methodapplied to a convex quadratic program can be viewed as weightedlinear least-squares problems. In the first paper, it is shownthat the sequence of solutions to such problems is uniformlybounded. Further, boundedness of the solution to weightedlinear least-squares problems for more general classes ofweight matrices than the one in the convex quadraticprogramming application are obtained as a byproduct.</p><p>In many linesearch interior methods for nonconvex nonlinearprogramming, the iterates can "falsely" converge to theboundary of the region defined by the inequality constraints insuch a way that the search directions do not converge to zero,but the step lengths do. In the sec ond paper, it is shown thatthe multiplier search directions then diverge. Furthermore, thedirection of divergence is characterized in terms of thegradients of the equality constraints along with theasymptotically active inequality constraints.</p><p>The third paper gives a modification of the analytic centerproblem for the set of optimal solutions in linear semidefiniteprogramming. Unlike the normal analytic center problem, thesolution of the modified problem is the limit point of thecentral path, without any strict complementarity assumption.For the strict complementarity case, the modified problem isshown to coincide with the normal analytic center problem,which is known to give a correct characterization of the limitpoint of the central path in that case.</p><p>The final paper describes of some computational experimentsconcerning possibilities of reusing previous information whensolving system of equations arising in interior methods forlinear programming.</p><p><b>Keywords:</b>Interior method, primal-dual interior method,linear programming, quadratic programming, nonlinearprogramming, semidefinite programming, weighted least-squaresproblems, central path.</p><p><b>Mathematics Subject Classification (2000):</b>Primary90C51, 90C22, 65F20, 90C26, 90C05; Secondary 65K05, 90C20,90C25, 90C30.</p>

Solid oxide fuel cells are a promising option for distributed stationary power generation that offers efficiencies ranging from 50% in stand-alone applications to greater than 80% in cogeneration. To advance SOFC technology for widespread market penetration, the SOFC should demonstrate improved cell lifetime and load-following capability. This work seeks to improve lifetime through dynamic analysis of critical lifetime variables and advanced control algorithms that permit load-following while remaining in a safe operating zone based on stress analysis. Control algorithms typically have addressed SOFC lifetime operability objectives using unconstrained, single-input-single-output control algorithms that minimize thermal transients. Existing SOFC controls research has not considered maximum radial thermal gradients or limits on absolute temperatures in the SOFC. In particular, as stress analysis demonstrates, the minimum cell temperature is the primary thermal stress driver in tubular SOFCs. This dissertation presents a dynamic, quasi-two-dimensional model for a high-temperature tubular SOFC combined with ejector and prereformer models. The model captures dynamics of critical thermal stress drivers and is used as the physical plant for closed-loop control simulations. A constrained, MIMO model predictive control algorithm is developed and applied to control the SOFC. Closed-loop control simulation results demonstrate effective load-following, constraint satisfaction for critical lifetime variables, and disturbance rejection. Nonlinear programming is applied to find the optimal SOFC size and steady-state operating conditions to minimize total system costs. / text