Steelmaking industry, one of the most electricity-intensive industrial processes, is seeking for new approaches to improve its competitiveness in terms of energy savings by taking advantage of the volatile electricity prices. This fluctuation in the price is mainly caused by the increasing share of renewable energy sources, the liberalization of energy markets and the growing demand of the energy. Therefore, making the production scheduling of steelmaking processes with knowledge about the cost of the energy may lead to significant cost savings in the electricity bills. With this aim in mind, different models are developed in this project in order to improve the existing monolithic models (continuous-time based scheduling) to find an efficient formulation of accounting for electricity consumption and also to expand them with more detailed scheduling of Electric Arc Furnace stage in the production process. The optimization of the energy cost with multiple electricity sources and contracts and the production planning are usually done as stand-alone optimizers due to their complexity, therefore as a new approach in addition to the monolithic model an iterative framework is developed in this work. The idea to integrate the two models in an iterative manner has potential to be useful in the industry due to low effort for reformulation of existing models. The implemented framework uses multiparametric programming together with bilevel programming in order to direct the schedule to find a compromise between the production constraints and goals, and the energy cost. To ensure applicability heuristic approaches are also examined whenever full sized models are not meeting computational performance requirements. The results show that the monolithic model implemented has a considerable advantage in terms of computational time compared to the models in the literature and in some cases, the solution can be obtained in a few minutes instead of hours. In the contrary, the iterative framework shows a bad performance in terms of computational time when dealing with real world instances. For that matter a heuristic approach, which is easy to implement, is investigated based on coordination theory and the results show that it has a potential since it provides solutions close to the optimal solutions in a reasonable amount of time. Multiparametric programming is the main core of the iterative framework developed in this internship and it is not able to give the solutions for real world instances due to computational time limitations. This computational problem is related to the nature of the algorithm behind mixed integer multiparametric programming and its ability to handle the binary variables. Therefore, further work to this project is to develop new approaches to approximate multiparametric technique or develop some heuristics to approximate the mp-MILP solutions.

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We present a novel bilevel programming formulation that aims to solve a resource allocation problem for request-response systems. Our formulation is motivated by potential inefficiencies in the allocation of computational resources to incoming user requests in such systems. In our experience, systems often operate with a surplus of resources despite potentially incurring unjustifiable cost. Our work attempts to optimize the tradeoff between the financial cost of resources and the opportunity cost of unfulfilled user demand. Our bilevel formulation consists of an \textit{upper} problem which has a constraint value appearing in the \textit{lower} problem. We derive efficient methods for finding global solutions to the upper problem in two settings; first with logarithmic utility functions, and then with a particular type of sigmoidal utility function. A solution to the model we describe (1) determines the optimal number of total resources to allocate and (2) determines the optimal distribution of such resources across the set of user requests.

Large-aspect-ratio wings and composite structures both have been considered for the next-generation civil transport aircraft to achieve improved aerodynamic efficiency and to save aircraft structural weight. The use of the large-aspect-ratio and the light-weight composite wing can lead to an enhanced flexibility of the aircraft wing, which may cause many aeroelastic problems such as large deflections, increased drag, onset of flutter, loss of control authority, etc. Aeroelastic tailoring, internal structural layout design and aerodynamic wing shape morphing are all considered to address these aeroelastic problems through multidisciplinary design, analysis and optimization (MDAO) studies in this work. Performance Adaptive Aeroelastic Wing (PAAW) program was initiated by NASA to leverage the flexibility associated with the use of the large-aspect-ratio wings and light-weight composite structures in a beneficial way for civil transport aircraft wing design. The biologically inspired SpaRibs concept is used for aircraft wing box internal structural layout design to achieve the optimal stiffness distribution to improve the aircraft performance. Along with the use of the active aeroelastic wing concept through morphing wing shape including the wing jig-shape, the control surface rotations and the aeroelastic tailoring scheme using composite laminates with ply-drop for wing skin design, a MDAO framework, which has the capabilities in total structural weight minimization, total drag minimization during cruise, ground roll distance minimization in takeoff and load alleviation in various maneuver loads by morphing its shape, is developed for designing models used in the PAAW program. A bilevel programming (BLP) multidisciplinary design optimization (MDO) architecture is developed for the MDAO framework. The upper-level optimization problem entails minimization of weight, drag and ground roll distance, all subjected to both static constraints and the global dynamic requirements including flutter mode and free vibration modes due to the specified control law design for body freedom flutter suppression and static margin constraint. The lower-level optimization is conducted to minimize the total drag by morphing wing shape, to minimize wing root bending moment by scheduling flap rotations (a surrogate for weight reduction), and to minimize the takeoff ground roll distance. Particle swarm optimization and gradient-based optimization are used, respectively, in the upper-level and the lower-level optimization problems. Optimization results show that the wing box with SpaRibs can further improve the aircraft performances, especially in a large weight saving, as compared to the wing with traditional spars and ribs. Additionally, the nonuniform chord control surface associated with the wing with SpaRibs achieve further reductions in structural weight, total drag and takeoff ground roll distance for an improved aircraft performance. For a further improvement of the global wing skin panel design, an efficient finite element approach is developed in designing stiffened composite panels with arbitrarily shaped stiffeners for buckling and vibration analyses. The developed approach allows the finite element nodes for the stiffeners and panels not to coincide at the panel-stiffeners interfaces. The stiffness, mass and geometric stiffness matrices for the stiffeners can be transformed to those for the panel through the displacement compatibility at their interfaces. The method improves the feasible model used in shape optimizing by avoiding repeated meshing for stiffened plate. Also, it reduces the order of the finite element model, a fine mesh typically associated with the skin panel stiffened by many stiffeners, for an efficient structural analysis. Several benchmark cases have been studied to verify the accuracy of the developed approach for stiffened composite panel structural analyses. Several parametric studies are conducted to show the influence of stiffener shape/placement/depth-ratio on panel's buckling and vibration responses. The developed approach shows a potential benefit of using gradient-based optimization for stiffener shape design. / Ph. D.

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.

O objetivo deste trabalho é propor uma metodologia para a priorização de obras do sistema de distribuição de média tensão - até 36 kV - voltada ao cumprimento do índice de continuidade DEC e FEC imposto pela ANEEL, visando reduzir a quantidade de conjuntos que estão fora dos limites e que geram multas para a empresa frente ao órgão regulador e aos consumidores. Inicialmente, os diversos tipos de obras têm seu benefício calculado com o uso do Método do Payoff Simplificado, baseado no Método do Payoff COPEL, que consiste na extração somente da parcela relativa a interrupção, no DEC ou FEC, que determinada obra trará ao sistema. De posse deste benefício estimado, as obras foram analisadas de duas maneiras: geral e por conjunto. A análise Geral consiste em observar as obras propostas de maneira independente, preocupando-se com o benefício que elas trarão para a empresa como um todo. Na análise por conjunto, as obras são agrupadas por conjunto ANEEL, e o objetivo é a colocação da maior quantidade de conjuntos dentro dos limites de continuidade impostos pelo órgão regulador. A definição do objetivo apropriado é que irá orientar todo o processo de seleção das obras. Para isso são propostos modelos matemáticos, e para trabalhar com eles, foi utilizada como ferramenta a programação matemática. Foram realizadas simulações divididas em dois grupos: no primeiro, análise geral, a otimização é executada diretamente. Já no segundo, na análise por conjunto, é aplicada a programação multi-nível, mais especificamente, a programação em dois níveis (\"Bilevel Programming Problem\"), utilizando a programação inteira ou por metas (\"goal programming\"). Os resultados das simulações mostraram que o objetivo principal, que é tirar a maior quantidade de conjuntos da transgressão, foi atingido com menor orçamento com o uso da metodologia e dos modelos matemáticos empregados neste trabalho. A metodologia proposta pretende ser uma ferramenta adicional para as concessionárias de distribuição de energia elétrica que normalmente elaboram programas de obras específicos para redução de índices de continuidade ou quando pressionados pelo órgão regulador elaboram programas alternativos que competem pelo mesmo orçamento frente aos programas de obras tradicionais. / The purpose of this paper is to propose a methodology to prioritize planned works in the medium-voltage distribution system - up to 36 kV - aiming to adequate the DEC and FEC continuity index to the limits defined by the Brazilian regulatory agency (ANEEL) through the reduction of the number of sets out of target and consequently the reduction of monetary penalties to the utility imposed by the regulatory agency and consumers. At first every planned work has its benefit calculated by the Simplified Payoff Method which is based on COPEL Payoff Method and which consists in extracting just the interruption event from the DEC or FEC which a given work will bring to the system. Once you have got the estimated benefit, the planned works are analyzed in two different ways - general analysis and set analysis. General analysis consists in checking up proposed works independently, focusing on the benefit they will bring to the company as a whole. In the set analysis, works are grouped by \"ANEEL sets\" and the main aim is to gather the greatest number of sets into the continuity limits defined by the regulatory agency. The aims definition will lead the whole work selection process. To achieve that mathematical models are proposed and mathematical programming tools are used. Two groups of simulations were done - in the first one which is also called general analysis, optimization is executed directly. The second one called set analysis, is applied the bilevel programming using the integer programming or goal programming. The simulation results showed that the main aim which was to eliminate the greatest number of sets from the transgression was reached with a lower budget using the methodology and mathematical models. The proposed methodology intends to be an additional tool to the electricity distribution companies (utilities). These companies usually plan specific works to reduce the continuity index or when they are pressed by regulatory agencies, they plan alternative programs which compete by the same budget facing traditional work programs.