Optimization of Large-Scale Hydrothermal System Operation

This paper presents the development of a mathematical model to optimize the management and operation of the Brazilian hydrothermal system. The system consists of a large set of individual hydropower plants and a set of aggregated thermal plants. The energy generated in the system is interconnected by a transmission network so it can be transmitted to centers of consumption throughout the country. The optimization model offered is capable of handling different types of constraints, such as interbasin water transfers, water supply for various purposes, and environmental requirements. Its overall objective is to produce energy to meet the country's demand at a minimum cost. Called HIDROTERM, the model integrates a database with basic hydrological and technical information to run the optimization model, and provides an interface to manage the input and output data. The optimization model uses the General Algebraic Modeling System (GAMS) package and can invoke different linear as well as nonlinear programming solvers. The optimization model was applied to the Brazilian hydrothermal system, one of the largest in the world. The system is divided into four subsystems with 127 active hydropower plants. Preliminary results under different scenarios of inflow, demand, and installed capacity demonstrate the efficiency and utility of the model. From this and other case studies in Brazil, the results indicate that the methodology developed is suitable to different applications, such as planning operation, capacity expansion, and operational rule studies, and trade-off analysis among multiple water users. DOI: 10.1061/(ASCE)WR.1943-5452.0000149. (C) 2012 American Society of Civil Engineers.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

The Choice of Expedient Regulatory Controls on Housing Market Using Short-Term Equilibria Model

Khutoretsky dealt with the problem of maximising a linear utility function (MUF) over the set of short-term equilibria in a housing market by reducing it to a linear programming problem, and suggested a combinatorial algorithm for this problem. Two approaches to the market adjustment were considered: the funding of housing construction and the granting of housing allowances. In both cases, locally optimal regulatory measures can be developed using the corresponding dual prices. The optimal effects (with the regulation expenditures restricted by an amount K) can be found using specialised models based on MUF: a model M1 for choice of the optimum structure of investment in housing construction, and a model M2 for optimum distribution of housing allowances. The linear integer optimisation problems corresponding to these models are initially difficult but can be solved after slight modifications of the parameters. In particular, the necessary modification of K does not exceed the maximum construction cost of one dwelling (for M1) or the maximum size of one housing allowance (for M2). The result is particularly useful since slight modification of K is not essential in practice.

Shadow Profit Maximization and a Generalized Measure of Inefficiency

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.

Estudio y desarrollo de un preproceso basado en la difusión no lineal para la segmentación en imágenes

En esta Tesis Doctoral se aborda la utilización de filtros de difusión no lineal para obtener imágenes constantes a trozos como paso previo al proceso de segmentación. En una primera parte se propone un formulación intrínseca para la ecuación de difusión no lineal que proporcione las condiciones de diseño necesarias sobre los filtros de difusión. A partir del marco teórico propuesto, se proporciona una nueva familia de difusividades; éstas son obtenidas a partir de técnicas de difusión no lineal relacionadas con los procesos de difusión regresivos. El objetivo es descomponer la imagen en regiones cerradas que sean homogéneas en sus niveles de grises sin contornos difusos. Asimismo, se prueba que la función de difusividad propuesta satisface las condiciones de un correcto planteamiento semi-discreto. Esto muestra que mediante el esquema semi-implícito habitualmente utilizado, realmente se hace un proceso de difusión no lineal directa, en lugar de difusión inversa, conectando con proceso de preservación de bordes. Bajo estas condiciones establecidas, se plantea un criterio de parada para el proceso de difusión, para obtener imágenes constantes a trozos con un bajo coste computacional. Una vez aplicado todo el proceso al caso unidimensional, se extienden los resultados teóricos, al caso de imágenes en 2D y 3D. Para el caso en 3D, se detalla el esquema numérico para el problema evolutivo no lineal, con condiciones de contorno Neumann homogéneas. Finalmente, se prueba el filtro propuesto para imágenes reales en 2D y 3D y se ilustran los resultados de la difusividad propuesta como método para obtener imágenes constantes a trozos. En el caso de imágenes 3D, se aborda la problemática del proceso previo a la segmentación del hígado, mediante imágenes reales provenientes de Tomografías Axiales Computarizadas (TAC). En ese caso, se obtienen resultados sobre la estimación de los parámetros de la función de difusividad propuesta. This Ph.D. Thesis deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. I have first shown an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, I have proposed a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. It has also proved that the proposed filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edgepreserving process. Under the conditions established for the diffusivity and using a stopping criterion I for the diffusion time, I have obtained piecewise constant images with a low computational effort. The whole process in the one-dimensional case is extended to the case where 2D and 3D theoretical results are applied to real images. For 3D, develops in detail the numerical scheme for nonlinear evolutionary problem with homogeneous Neumann boundary conditions. Finally, I have tested the proposed filter with real images for 2D and 3D and I have illustrated the effects of the proposed diffusivity function as a method to get piecewise constant images. For 3D I have developed a preprocess for liver segmentation with real images from CT (Computerized Tomography). In this case, I have obtained results on the estimation of the parameters of the given diffusivity function.

Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Otimização não linear aplicada à operação de sistemas com múltiplos reservatórios para abastecimento de água.

O presente estudo considera a aplicação do modelo SISAGUA de simulação matemática e de otimização para a operação de sistemas de reservatórios integrados em sistemas complexos para o abastecimento de água. O SISAGUA utiliza a programação não linear inteira mista (PNLIM) com os objetivos de evitar ou minimizar racionamentos, equilibrar a distribuição dos armazenamentos em sistemas com múltiplos reservatórios e minimizar os custos de operação. A metodologia de otimização foi aplicada para o sistema produtor de água da Região Metropolitana de São Paulo (RMSP), que enfrenta a crise hídrica diante de um cenário de estiagem em 2013-2015, o pior na série histórica dos últimos 85 anos. Trata-se de uma região com 20,4 milhões de habitantes. O sistema é formado por oito sistemas produtores parcialmente integrados e operados pela Sabesp (Companhia de Saneamento do Estado de São Paulo). A RMSP é uma região com alta densidade demográfica, localizada na Bacia Hidrográfica do Alto Tietê e caracterizada pela baixa disponibilidade hídrica per capita. Foi abordada a possibilidade de considerar a evaporação durante as simulações, e a aplicação de uma regra de racionamento contínua nos reservatórios, que transforma a formulação do problema em programação não linear (PNL). A evaporação se mostrou pouco representativa em relação a vazão de atendimento à demanda, com cerca de 1% da vazão. Se por um lado uma vazão desta magnitude pode contribuir em um cenário crítico, por outro essa ordem de grandeza pode ser comparada às incertezas de medições ou previsões de afluências. O teste de sensibilidade das diferentes taxas de racionamento em função do volume armazenado permite analisar o tempo de resposta de cada sistema. A variação do tempo de recuperação, porém, não se mostrou muito significativo.

Otimização acústica e análise numérica do escoamento ao redor de um conjunto cilindro-placa separadora.

RESUMO Simulações de aeroacústica computacional demandam uma quantidade considerável de tempo, o que torna complicada a realização de estudos paramétricos. O presente trabalho propõe uma metodologia viável para otimização aeroacústica. Através da análise numérica utilizando dinâmica dos fluidos computacional, foi estudada a aplicação de uma placa separadora desacoplada como método de controle passivo da esteira turbulenta de um cilindro e avaliou-se a irradiação de ruído causado pela interação do escoamento com ambos os corpos, empregando ferramentas de aeroacústica computacional baseadas no método de Ffowcs-Williams e Hawkings. Algumas abordagens distintas de metodologias de otimização de projeto foram aplicadas neste problema, com o objetivo de chegar a uma configuração otimizada que permita a redução do nível sonoro ao longe. Assim, utilizando uma ferramenta de otimização multidisciplinar, pode-se avaliar a capacidade de modelos heurísticos e a grande vantagem do emprego de algoritmos baseados em método de superfície de resposta quando aplicados em um problema não linear, pois requerem a avaliação de um menor número de alternativas para se obter um ponto ótimo. Além disso, foi possível identificar e agrupar os resultados em 5 clusters baseados em seus parâmetros geométricos, nível de pressão sonora global e o valor quadrático médio do coeficiente de arrasto, confirmando a eficiência da aplicação de placas separadoras longas desacopladas posicionadas próximas ao cilindro na estabilização da esteira turbulenta, enquanto que o posicionamento de placas acima de um espaçamento crítico aumentou o nível de pressão acústica irradiado devido à formação de vórtices no espaço entre o cilindro e a placa separadora.

Combined simulation-optimization methodology for the design of environmental conscious absorption systems

This work addresses the optimization of ammonia–water absorption cycles for cooling and refrigeration applications with economic and environmental concerns. Our approach combines the capabilities of process simulation, multi-objective optimization (MOO), cost analysis and life cycle assessment (LCA). The optimization task is posed in mathematical terms as a multi-objective mixed-integer nonlinear program (moMINLP) that seeks to minimize the total annualized cost and environmental impact of the cycle. This moMINLP is solved by an outer-approximation strategy that iterates between primal nonlinear programming (NLP) subproblems with fixed binaries and a tailored mixed-integer linear programming (MILP) model. The capabilities of our approach are illustrated through its application to an ammonia–water absorption cycle used in cooling and refrigeration applications.

Simultaneous synthesis of heat exchanger networks with pressure recovery: optimal integration between heat and work

The optimal integration between heat and work may significantly reduce the energy demand and consequently the process cost. This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs) in which the pressure levels of the process streams can be adjusted to enhance the heat integration. A superstructure is proposed for the HEN design with pressure recovery, developed via generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation. The process conditions (stream temperature and pressure) must be optimized. Furthermore, the approach allows for coupling of the turbines and compressors and selection of the turbines and valves to minimize the total annualized cost, which consists of the operational and capital expenses. The model is tested for its applicability in three case studies, including a cryogenic application. The results indicate that the energy integration reduces the quantity of utilities required, thus decreasing the overall cost.

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

Simultaneous environmental and economic process synthesis of Isobutane Alkylation

This multidisciplinary study concerns the optimal design of processes with a view to both maximizing profit and minimizing environmental impacts. This can be achieved by a combination of traditional chemical process design methods, measurements of environmental impacts and advanced mathematical optimization techniques. More to the point, this paper presents a hybrid simulation-multiobjective optimization approach that at once optimizes the production cost and minimizes the associated environmental impacts of isobutane alkylation. This approach has also made it possible to obtain the flowsheet configurations and process variables that are needed to manufacture isooctane in a way that satisfies the above-stated double aim. The problem is formulated as a Generalized Disjunctive Programming problem and solved using state-of-the-art logic-based algorithms. It is shown, starting from existing alternatives for the process, that it is possible to systematically generate a superstructure that includes alternatives not previously considered. The optimal solution, in the form a Pareto curve, includes different structural alternatives from which the most suitable design can be selected. To evaluate the environmental impact, Life Cycle Assessment based on two different indicators is employed: Ecoindicator 99 and Global Warming Potential.

MINLP Optimization Algorithm for the Synthesis of Heat and Work Exchange Networks

This paper introduces a new optimization model for the simultaneous synthesis of heat and work exchange networks. The work integration is performed in the work exchange network (WEN), while the heat integration is carried out in the heat exchanger network (HEN). In the WEN synthesis, streams at high-pressure (HP) and low-pressure (LP) are subjected to pressure manipulation stages, via turbines and compressors running on common shafts and stand-alone equipment. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as helper motors and generators to respond to any shortage and/or excess of energy, respectively, in the SSTC axes. The heat integration of the streams occurs in the HEN between each WEN stage. Thus, as the inlet and outlet streams temperatures in the HEN are dependent of the WEN design, they must be considered as optimization variables. The proposed multi-stage superstructure is formulated in mixed-integer nonlinear programming (MINLP), in order to minimize the total annualized cost composed by capital and operational expenses. A case study is conducted to verify the accuracy of the proposed approach. The results indicate that the heat integration between the WEN stages is essential to enhance the work integration, and to reduce the total cost of process due the need of a smaller amount of hot and cold utilities.

Enseñando a programar: un camino directo para desarrollar el pensamiento computacional

Está ampliamente aceptado que es fundamental desarrollar la habilidad de resolver problemas. El pensamiento computacional se basa en resolver problemas haciendo uso de conceptos fundamentales de la informática. Nada mejor para desarrollar la habilidad de resolver problemas usando conceptos informáticos que una asignatura de introducción a la programación. Este trabajo presenta nuestras reflexiones acerca de cómo iniciar a un estudiante en el campo de la programación de computadores. El trabajo no detalla los contenidos a impartir, sino que se centra en aspectos metodológicos, con la inclusión de experiencias y ejemplos concretos, a la vez que generales, extensibles a cualquier enseñanza de programación. En general, aunque se van desarrollado lenguajes cada vez más cercanos al lenguaje humano, la programación de ordenadores utilizando lenguajes formales no es una materia intuitiva y de fácil comprensión por parte de los estudiantes. A la persona que ya sabe programar le parece una tarea sencilla, pero al neófito no. Es más, dominar el arte de la programación es complejo. Por esta razón es indispensable utilizar todas las técnicas y herramientas posibles que faciliten dicha labor.

Retrofit of heat exchanger networks with pressure recovery of process streams at sub-ambient conditions

This paper presents a new mathematical programming model for the retrofit of heat exchanger networks (HENs), wherein the pressure recovery of process streams is conducted to enhance heat integration. Particularly applied to cryogenic processes, HENs retrofit with combined heat and work integration is mainly aimed at reducing the use of expensive cold services. The proposed multi-stage superstructure allows the increment of the existing heat transfer area, as well as the use of new equipment for both heat exchange and pressure manipulation. The pressure recovery of streams is carried out simultaneously with the HEN design, such that the process conditions (streams pressure and temperature) are variables of optimization. The mathematical model is formulated using generalized disjunctive programming (GDP) and is optimized via mixed-integer nonlinear programming (MINLP), through the minimization of the retrofit total annualized cost, considering the turbine and compressor coupling with a helper motor. Three case studies are performed to assess the accuracy of the developed approach, including a real industrial example related to liquefied natural gas (LNG) production. The results show that the pressure recovery of streams is efficient for energy savings and, consequently, for decreasing the HEN retrofit total cost especially in sub-ambient processes.