Mixed-integer convex model for VAr expansion planning

This paper presents a mixed-integer convex-optimization-based approach for optimum investment reactive power sources in transmission systems. Unlike some convex-optimization techniques for the reactive power planning solution, in the proposed approach the taps settings of under-load tap-changing of transformers are modeled as a mixed-integer linear set equations. Are also considered the continuous and discrete variables for the existing and new capacitive and reactive power sources. The problem is solved for three significant demand scenarios (low demand, average demand and peak demand). Numerical results are presented for the CIGRE-32 electric power system.

Modelo de programação não-linear para otimização do padrão de cultivo e retorno financeiro em áreas irrigadas

Pós-graduação em Agronomia (Irrigação e Drenagem) - FCA

Reconfiguração de sistemas de distribuição de energia elétrica utilizando uma metodologia multipartida

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Resolução do problema de fluxo de potência ótimo pela meta-heurística algoritmo dos fogos de artifício de busca dinâmica com mutação de covariância

Pós-graduação em Engenharia Elétrica - FEIS

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

A farm-level programming model to compare the atmospheric impact of conventional and organic farming

A model is developed to represent the activity of a farm using the method of linear programming. Two are the main components of the model, the balance of soil fertility and the livestock nutrition. According to the first, the farm is supposed to have a total requirement of nitrogen, which is to be accomplished either through internal sources (manure) or through external sources (fertilisers). The second component describes the animal husbandry as having a nutritional requirement which must be satisfied through the internal production of arable crops or the acquisition of feed from the market. The farmer is supposed to maximise total net income from the agricultural and the zoo-technical activities by choosing one rotation among those available for climate and acclivity. The perspective of the analysis is one of a short period: the structure of the farm is supposed to be fixed without possibility to change the allocation of permanent crops and the amount of animal husbandry. The model is integrated with an environmental module that describes the role of the farm within the carbon-nitrogen cycle. On the one hand the farm allows storing carbon through the photosynthesis of the plants and the accumulation of carbon in the soil; on the other some activities of the farm emit greenhouse gases into the atmosphere. The model is tested for some representative farms of the Emilia-Romagna region, showing to be capable to give different results for conventional and organic farming and providing first results concerning the different atmospheric impact. Relevant data about the representative farms and the feasible rotations are extracted from the FADN database, with an integration of the coefficients from the literature.

Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

Immunologic response to antiretroviral therapy in hepatitis C virus-coinfected adults in a population-based HIV/AIDS treatment program

BACKGROUND: We sought to characterize the impact that hepatitis C virus (HCV) infection has on CD4 cells during the first 48 weeks of antiretroviral therapy (ART) in previously ART-naive human immunodeficiency virus (HIV)-infected patients. METHODS: The HIV/AIDS Drug Treatment Programme at the British Columbia Centre for Excellence in HIV/AIDS distributes all ART in this Canadian province. Eligible individuals were those whose first-ever ART included 2 nucleoside reverse transcriptase inhibitors and either a protease inhibitor or a nonnucleoside reverse transcriptase inhibitor and who had a documented positive result for HCV antibody testing. Outcomes were binary events (time to an increase of > or = 75 CD4 cells/mm3 or an increase of > or = 10% in the percentage of CD4 cells in the total T cell population [CD4 cell fraction]) and continuous repeated measures. Statistical analyses used parametric and nonparametric methods, including multivariate mixed-effects linear regression analysis and Cox proportional hazards analysis. RESULTS: Of 1186 eligible patients, 606 (51%) were positive and 580 (49%) were negative for HCV antibodies. HCV antibody-positive patients were slower to have an absolute (P<.001) and a fraction (P = .02) CD4 cell event. In adjusted Cox proportional hazards analysis (controlling for age, sex, baseline absolute CD4 cell count, baseline pVL, type of ART initiated, AIDS diagnosis at baseline, adherence to ART regimen, and number of CD4 cell measurements), HCV antibody-positive patients were less likely to have an absolute CD4 cell event (adjusted hazard ratio [AHR], 0.84 [95% confidence interval [CI], 0.72-0.98]) and somewhat less likely to have a CD4 cell fraction event (AHR, 0.89 [95% CI, 0.70-1.14]) than HCV antibody-negative patients. In multivariate mixed-effects linear regression analysis, HCV antibody-negative patients had increases of an average of 75 cells in the absolute CD4 cell count and 4.4% in the CD4 cell fraction, compared with 20 cells and 1.1% in HCV antibody-positive patients, during the first 48 weeks of ART, after adjustment for time-updated pVL, number of CD4 cell measurements, and other factors. CONCLUSION: HCV antibody-positive HIV-infected patients may have an altered immunologic response to ART.

Optimización de operaciones unitarias utilizando líquidos iónicos como agentes materiales de separación

En este trabajo se estudia la modelización y optimización de procesos industriales de separación mediante el empleo de mezclas de líquidos iónicos como disolventes. Los disolventes habitualmente empleados en procesos de absorción o extracción suelen ser componentes orgánicos muy volátiles y dañinos para la salud humana. Las innovadoras propiedades que presentan los líquidos iónicos, los convierten en alternativas adecuadas para solucionar estos problemas. La presión de vapor de estos compuestos es muy baja y apenas varía con la temperatura. Por tanto, estos compuestos apenas se evaporan incluso a temperaturas altas. Esto supone una gran ventaja en cuanto al empleo de estos compuestos como disolventes industriales ya que permite el reciclaje continuo del disolvente al final del proceso sin necesidad de introducir disolvente fresco debido a la evaporación del mismo. Además, al no evaporarse, estos compuestos no suponen un peligro para la salud humana por inhalación; al contrario que otros disolventes como el benceno. El único peligro para la salud que tienen estos compuestos es por tanto el de contacto directo o ingesta, aunque de hecho muchos Líquidos Iónicos son inocuos con lo cual no existe peligro para la salud ni siquiera a través de estas vías. Los procesos de separación estudiados en este trabajo, se rigen por la termodinámica de fases, concretamente el equilibrio líquido-vapor. Para la predicción de los equilibrios se ha optado por el empleo de modelos COSMO (COnductor-like Screening MOdel). Estos modelos tienen su origen en el empleo de la termodinámica de solvatación y en la mecánica cuántica. En el desarrollo de procesos y productos, químicos e ingenieros frecuentemente precisan de la realización de cálculos de predicción de equilibrios de fase. Previamente al desarrollo de los modelos COSMO, se usaban métodos de contribución de grupos como UNIFAC o modelos de coeficientes de actividad como NRTL.La desventaja de estos métodos, es que requieren parámetros de interacción binaria que únicamente pueden obtenerse mediante ajustes por regresión a partir de resultados experimentales. Debido a esto, estos métodos apenas tienen aplicabilidad para compuestos con grupos funcionales novedosos debido a que no se dispone de datos experimentales para llevar a cabo los ajustes por regresión correspondientes. Una alternativa a estos métodos, es el empleo de modelos de solvatación basados en la química cuántica para caracterizar las interacciones moleculares y tener en cuenta la no idealidad de la fase líquida. Los modelos COSMO, permiten la predicción de equilibrios sin la necesidad de ajustes por regresión a partir de resultados experimentales. Debido a la falta de resultados experimentales de equilibrios líquido-vapor de mezclas en las que se ven involucrados los líquidos iónicos, el empleo de modelos COSMO es una buena alternativa para la predicción de equilibrios de mezclas con este tipo de materiales. Los modelos COSMO emplean las distribuciones superficiales de carga polarizada (sigma profiles) de los compuestos involucrados en la mezcla estudiada para la predicción de los coeficientes de actividad de la misma, definiéndose el sigma profile de una molécula como la distribución de probabilidad de densidad de carga superficial de dicha molécula. Dos de estos modelos son COSMO-RS (Realistic Solvation) y COSMO-SAC (Segment Activity Coefficient). El modelo COSMO-RS fue la primera extensión de los modelos de solvatación basados en continuos dieléctricos a la termodinámica de fases líquidas mientras que el modelo COSMO-SAC es una variación de este modelo, tal y como se explicará posteriormente. Concretamente en este trabajo se ha empleado el modelo COSMO-SAC para el cálculo de los coeficientes de actividad de las mezclas estudiadas. Los sigma profiles de los líquidos iónicos se han obtenido mediante el empleo del software de química computacional Turbomole y el paquete químico-cuántico COSMOtherm. El software Turbomole permite optimizar la geometría de la molécula para hallar la configuración más estable mientras que el paquete COSMOtherm permite la obtención del perfil sigma del compuesto mediante el empleo de los datos proporcionados por Turbomole. Por otra parte, los sigma profiles del resto de componentes se han obtenido de la base de datos Virginia Tech-2005 Sigma Profile Database. Para la predicción del equilibrio a partir de los coeficientes de actividad se ha empleado la Ley de Raoult modificada. Se ha supuesto por tanto que la fracción de cada componente en el vapor es proporcional a la fracción del mismo componente en el líquido, dónde la constante de proporcionalidad es el coeficiente de actividad del componente en la mezcla multiplicado por la presión de vapor del componente y dividido por la presión del sistema. Las presiones de vapor de los componentes se han obtenido aplicando la Ley de Antoine. Esta ecuación describe la relación entre la temperatura y la presión de vapor y se deduce a partir de la ecuación de Clausius-Clapeyron. Todos estos datos se han empleado para la modelización de una separación flash usando el algoritmo de Rachford-Rice. El valor de este modelo reside en la deducción de una función que relaciona las constantes de equilibrio, composición total y fracción de vapor. Para llevar a cabo la implementación del modelado matemático descrito, se ha programado un código empleando el software MATLAB de análisis numérico. Para comprobar la fiabilidad del código programado, se compararon los resultados obtenidos en la predicción de equilibrios de mezclas mediante el código con los resultados obtenidos mediante el simulador ASPEN PLUS de procesos químicos. Debido a la falta de datos relativos a líquidos iónicos en la base de datos de ASPEN PLUS, se han introducido estos componentes como pseudocomponentes, de manera que se han introducido únicamente los datos necesarios de estos componentes para realizar las simulaciones. El modelo COSMO-SAC se encuentra implementado en ASPEN PLUS, de manera que introduciendo los sigma profiles, los volúmenes de la cavidad y las presiones de vapor de los líquidos iónicos, es posible predecir equilibrios líquido-vapor en los que se ven implicados este tipo de materiales. De esta manera pueden compararse los resultados obtenidos con ASPEN PLUS y como el código programado en MATLAB y comprobar la fiabilidad del mismo. El objetivo principal del presente Trabajo Fin de Máster es la optimización de mezclas multicomponente de líquidos iónicos para maximizar la eficiencia de procesos de separación y minimizar los costes de los mismos. La estructura de este problema es la de un problema de optimización no lineal con variables discretas y continuas, es decir, un problema de optimización MINLP (Mixed Integer Non-Linear Programming). Tal y como se verá posteriormente, el modelo matemático de este problema es no lineal. Por otra parte, las variables del mismo son tanto continuas como binarias. Las variables continuas se corresponden con las fracciones molares de los líquidos iónicos presentes en las mezclas y con el caudal de la mezcla de líquidos iónicos. Por otra parte, también se ha introducido un número de variables binarias igual al número de líquidos iónicos presentes en la mezcla. Cada una de estas variables multiplican a las fracciones molares de sus correspondientes líquidos iónicos, de manera que cuando dicha variable es igual a 1, el líquido se encuentra en la mezcla mientras que cuando dicha variable es igual a 0, el líquido iónico no se encuentra presente en dicha mezcla. El empleo de este tipo de variables obliga por tanto a emplear algoritmos para la resolución de problemas de optimización MINLP ya que si todas las variables fueran continuas, bastaría con el empleo de algoritmos para la resolución de problemas de optimización NLP (Non-Linear Programming). Se han probado por tanto diversos algoritmos presentes en el paquete OPTI Toolbox de MATLAB para comprobar cuál es el más adecuado para abordar este problema. Finalmente, una vez validado el código programado, se han optimizado diversas mezclas de líquidos iónicos para lograr la máxima recuperación de compuestos aromáticos en un proceso de absorción de mezclas orgánicas. También se ha usado este código para la minimización del coste correspondiente a la compra de los líquidos iónicos de la mezcla de disolventes empleada en la operación de absorción. En este caso ha sido necesaria la introducción de restricciones relativas a la recuperación de aromáticos en la fase líquida o a la pureza de la mezcla obtenida una vez separada la mezcla de líquidos iónicos. Se han modelizado los dos problemas descritos previamente (maximización de la recuperación de Benceno y minimización del coste de operación) empleando tanto únicamente variables continuas (correspondientes a las fracciones o cantidades molares de los líquidos iónicos) como variables continuas y binarias (correspondientes a cada uno de los líquidos iónicos implicados en las mezclas).

Análise do aproveitamento múltiplo do reservatório de Barra Bonita - SP, através da aplicação de técnica de programação linear associada a modelo de rede de fluxo

O objeto deste trabalho é a análise do aproveitamento múltiplo do reservatório de Barra Bonita, localizado na confluência entre os rios Piracicaba e Tietê, no estado de São Paulo e pertencente ao chamado sistema Tietê-Paraná. Será realizada a otimização da operação do reservatório, através de programação linear, com o objetivo de aumentar a geração de energia elétrica, através da maximização da vazão turbinada. Em seguida, a partir dos resultados da otimização da geração de energia, serão utilizadas técnicas de simulação computacional, para se obter índices de desempenho conhecidos como confiabilidade, resiliência e vulnerabilidade, além de outros fornecidos pelo próprio modelo de simulação a ser utilizado. Estes índices auxiliam a avaliação da freqüência, magnitude e duração dos possíveis conflitos existentes. Serão analisados os possíveis conflitos entre a navegação, o armazenamento no reservatório, a geração de energia e a ocorrência de enchentes na cidade de Barra Bonita, localizada a jusante da barragem.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Linear low-density polyethylene colored with a nanoclay-based pigment: Morphology and mechanical, thermal, and colorimetric properties

In this study, a novel kind of hybrid pigment based on nanoclays and dyes was synthesized and characterized. These nanoclay-based pigments (NCPs) were prepared at the laboratory with sodium montmorillonite nanoclay (NC) and methylene blue (MB). The cation-exchange capacity of NC exchanged with MB was varied to obtain a wide color gamut. The synthesized nanopigments were thoroughly characterized. The NCPs were melt-mixed with linear low-density polyethylene (PE) with an internal mixer. Furthermore, samples with conventional colorants were prepared in the same way. Then, the properties (mechanical, thermal, and colorimetric) of the mixtures were assessed. The PE–NCP samples developed better color properties than those containing conventional colorants and used as references, and their other properties were maintained or improved, even at lower contents of dye compared to that with the conventional colorants.

Isobutane Alkylation Process Synthesis by means of Hybrid Simulation-Multiobjective Optimization

Multiobjective Generalized Disjunctive Programming (MO-GDP) optimization has been used for the synthesis of an important industrial process, isobutane alkylation. The two objective functions to be simultaneously optimized are the environmental impact, determined by means of LCA (Life Cycle Assessment), and the economic potential of the process. The main reason for including the minimization of the environmental impact in the optimization process is the widespread environmental concern by the general public. For the resolution of the problem we employed a hybrid simulation- optimization methodology, i.e., the superstructure of the process was developed directly in a chemical process simulator connected to a state of the art optimizer. The model was formulated as a GDP and solved using a logic algorithm that avoids the reformulation as MINLP -Mixed Integer Non Linear Programming-. Our research gave us Pareto curves compounded by three different configurations where the LCA has been assessed by two different parameters: global warming potential and ecoindicator-99.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.