Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Determination of total petroleum hydrocarbons in soil from different locations using infrared spectrophotometry and gas chromatography

Total petroleum hydrocarbons (TPH) are important environmental contaminants which are toxic to human and environmental receptors. Several analytical methods have been used to quantify TPH levels in contaminated soils, specifically through infrared spectrometry (IR) and gas chromatography (GC). Despite being two of the most used techniques, some issues remain that have been inadequately studied: a) applicability of both techniques to soils contaminated with two distinct types of fuel (petrol and diesel), b) influence of the soil natural organic matter content on the results achieved by various analytical methods, and c) evaluation of the performance of both techniques in analyses of soils with different levels of contamination (presumably non-contaminated and potentially contaminated). The main objectives of this work were to answer these questions and to provide more complete information about the potentials and limitations of GC and IR techniques. The results led us to the following conclusions: a) IR analysis of soils contaminated with petrol is not suitable due to volatilisation losses, b) there is a significant influence of organic matter in IR analysis, and c) both techniques demonstrated the capacity to accurately quantify TPH in soils, irrespective of their contamination levels.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Improvement of a filters method in a derivative free optimization

Constraints nonlinear optimization problems can be solved using penalty or barrier functions. This strategy, based on solving the problems without constraints obtained from the original problem, have shown to be e ective, particularly when used with direct search methods. An alternative to solve the previous problems is the lters method. The lters method introduced by Fletcher and Ley er in 2002, , has been widely used to solve problems of the type mentioned above. These methods use a strategy di erent from the barrier or penalty functions. The previous functions de ne a new one that combine the objective function and the constraints, while the lters method treat optimization problems as a bi-objective problems that minimize the objective function and a function that aggregates the constraints. Motivated by the work of Audet and Dennis in 2004, using lters method with derivative-free algorithms, the authors developed works where other direct search meth- ods were used, combining their potential with the lters method. More recently. In a new variant of these methods was presented, where it some alternative aggregation restrictions for the construction of lters were proposed. This paper presents a variant of the lters method, more robust than the previous ones, that has been implemented with a safeguard procedure where values of the function and constraints are interlinked and not treated completely independently.

Quantificação de polifosfatos no bacalhau. Validação de um método de análise

O bacalhau (Gadus morhua) faz parte da dieta alimentar dos portugueses há vários séculos, sendo atualmente, um dos maiores consumidores deste peixe a nível mundial. Após o processo de salga, esta espécie possui características únicas como a consistência, cheiro, paladar e cor amarela. É precisamente devido à coloração do peixe que alguns produtores da Islândia, Noruega e Dinamarca requisitaram às autoridades da União Europeia (UE) a aprovação da utilização de polifosfatos no processo de salga húmida do bacalhau. Os polifosfatos são aditivos alimentares bastante usados no processamento do pescado pois previnem a oxidação dos lípidos e proteínas do músculo do bacalhau, evitando assim a indesejada mudança de cor do peixe. Apesar dos esforços da Associação dos Industriais do Bacalhau (AIB) e do governo português para a rejeição da proposta nórdica, tal não se verificou. Deste modo, no início do próximo ano já será possível a venda na UE de bacalhau com fosfatos. A quantificação do teor de fosfatos no bacalhau é geralmente efetuada por Espetrofotometria de absorção molecular no ultravioleta-visível (UV-Visível). Esta quantificação é baseada no método de determinação do fósforo total, através da hidrólise dos fosfatos a ortofosfatos com posterior medição da cor amarela, gerada pela reação destes com uma solução de molibdato-vanadato. O objetivo desta dissertação foi a validação de um método de análise para a quantificação dos polifosfatos no bacalhau. O método validado foi o descrito na norma NP 4495 para produtos de pesca e aquicultura. O desenvolvimento deste trabalho foi realizado em laboratório acreditado para águas e produtos alimentares (Equilibrium - Laboratório de Controlo de Qualidade e de Processos Lda, L0312). Foi ainda determinada a influência do teor de cloreto de sódio na quantificação dos polifosfatos e o teor de humidade, uma vez que este pode afetar o produto durante a sua comercialização. No processo de validação do método foram estudados diversos parâmetros, tais como a seletividade, linearidade, sensibilidade, limite de quantificação e precisão. Pela análise dos resultados obtidos conclui-se que o método para determinação de fosfatos no bacalhau se encontra validado, uma vez que satisfaz todas as especificações determinadas para cada parâmetro de validação avaliado.

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

What is a fractional derivative?

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Macrociclos tetrapirrólicos e produtos de contraste iodados: uma nova abordagem

O trabalho descrito no presente documento reporta a preparação de derivados tetrapirrólicos iodados de tipo porfirina tornando-os potenciais veículos a meio de contraste iodado, usado em radiodiagnóstico. Com os resultados deste trabalho irá ser realizado um pedido de patente das moléculas e portanto, o acesso a este trabalho será restrito nos termos do Código da Propriedade Industrial, aprovado pelo Decreto de Lei nº 36/2003 de 5 de Março. Na primeira fase do trabalho, foi sintetizado o derivado porfirínico simétrico, meso-substituído, contendo um total de 8 iodos. Este foi preparado por condensação do pirrol e do aldeído iodado em meio ácido e na presença de nitrobenzeno. Foram ainda preparados as respetivas metaloporfirinas contendo os iões metálicos de manganês e gadolínio. Posteriormente foi avaliada a capacidade destes derivados atenuarem o feixe de raio-X, através da mediação das Unidades de Hounsfield, após serem adquiridas imagens por Tomografia Computorizada. Na segunda fase do trabalho procedeu-se ao estudo da influência destes compostos na diferenciação celular, usando como modelo as células de pré-adipócitos 3T3-L1. Foi avaliada a diferenciação celular, através da quantificação de lípidos das células maduras, marcados com Red Oil O, por espectrofotometria de Visível 3 e 10 dias após a administração dos derivados em estudo.

Iron oxide/gold core/shell nanomagnetic probes and CdS biolabels for amplified electrochemical immunosensing of Salmonella typhimurium

There is an imminent need for rapid methods to detect and determine pathogenic bacteria in food products as alternatives to the laborious and time-consuming culture procedures. In this work, an electrochemical immunoassay using iron/gold core/shell nanoparticles (Fe@Au) conjugated with anti-Salmonella antibodies was developed. The chemical synthesis and functionalization of magnetic and gold-coated magnetic nanoparticles is reported. Fe@Au nanoparticles were functionalized with different self-assembled monolayers and characterized using ultraviolet-visible spectrometry, transmission electron microscopy, and voltammetric techniques. The determination of Salmonella typhimurium, on screen-printed carbon electrodes, was performed by square-wave anodic stripping voltammetry through the use of CdS nanocrystals. The calibration curve was established between 1×101 and 1×106 cells/mL and the limit of detection was 13 cells/mL. The developed method showed that it is possible to determine the bacteria in milk at low concentrations and is suitable for the rapid (less than 1 h) and sensitive detection of S. typhimurium in real samples. Therefore, the developed methodology could contribute to the improvement of the quality control of food samples.

Natural organic matter fractionation along the treatment of water for human consumption

The main objective of this study was to characterize the organic matter present in raw water and along the treatment process, as well as its seasonal variation. A natural organic matter fractionation approach has been applied to Lever water treatment plant located in Douro River, in Oporto (Portugal). The process used was based on the sorption of dissolved organic matter in different types of ion exchange resins, DAX-8, DAX-4 and IRA-958, allowing its separation into four fractions: very hydrophobic acids (VHA), slightly hydrophobic acids (SHA), charged hydrophilic (CHA) and hydrophilic neutral (NEU). The dissolved organic carbon (DOC) determination was used to quantify dissolved organic matter. Samples were collected monthly, during approximately one year, from raw water captured at the surface and under the bed of the river, and after each step of the treatment: pre-filtration in sand/anthracite filters, ozonation, coagulation/flocculation, counter current dissolved air flotation and filtration (CoCoDAFF) and chlorination. The NEU fraction showed a seasonal variation, with maximum values in autumn for the sampling points corresponding to raw water captured at the surface and under the bed of the river. It was usually the predominating fraction and did not show a significant decrease throughout the treatment. Nevertheless their low concentration, the same occurred for the CHA and VHA fractions. There was an overall decrease in the SHA fraction throughout the water treatment (especially after CoCoDAFF and ozonation) as well as in the DOC. The TSUVA254 values obtained for raw water generally varied between 2.0 and 4.0 L mgC-1 m-1 and between 0.75 and 1.78 L mgC-1 m-1 for treated water. It was observed a decrease of TSUVA values along the treatment, especially after ozonation. These results may contribute to a further optimization in the process of treating water for human consumption.

Aplicação de algoritmos genéticos para sintonia de controladores

Mestrado em Engenharia Electrotécnica e de Computadores

Produção de bioetanol a partir de um resíduo orgânico proveniente da central de compostagem da LIPOR

Mestrado em Engenharia Química

Autoxidação de ácidos gordos na presença de antioxidantes naturais e sintéticos

Nas últimas décadas, devido ao desenvolvimento económico, e a uma necessidade constante de gerir os recursos energéticos, existe uma necessidade de procurar novas fontes de energia, em particular fontes de energia renováveis. O biodiesel surge assim como uma energia alternativa ao combustível fóssil. Este biocombustível tem ganho uma importância significativa na sociedade moderna. Quimicamente o biodiesel é constituído por ésteres metílicos de ácidos gordos de cadeia longa, derivados de óleos vegetais ou gorduras animais. O principal problema que este enfrenta é a sua susceptibilidade à oxidação, devido ao seu conteúdo de ácidos gordos insaturados, logo existe uma procura constante de soluções que possam solucionar este problema. É necessária a identificação de técnicas e métodos para retardar a seu envelhecimento ao longo do tempo. O objectivo deste trabalho consiste no estudo da estabilidade do biodiesel ao longo do tempo, quando armazenado a diferentes condições de temperatura, superiores às normalmente suportadas pelo biodiesel durante o armazenamento, de modo a acelerar o processo de degradação. As amostras de biodiesel foram sujeitas a duas temperaturas. Uma amostra de biodiesel não estabilizado foi colocada a uma temperatura entre 40 e 50ºC ao longo de 203 dias, e uma outra amostra foi colocada a uma temperatura entre 95º e 105ºC ao longo de 146 dias. Realizaram-se ensaios semanais de modo registar a evolução do envelhecimento do biodiesel. As análises foram efectuadas por espectrofotometria de ultravioleta e visível (UV-VIS) e por espectroscopia de absorção na região do infravermelho (FTIR). No UV-VIS foi possível observar que o aumento de temperatura foi responsável pela aceleração da oxidação do biodiesel que resulta num aumento generalizado da absorvância do biodiesel. Através das análises efectuadas no FTIR verificou-se a formação e aumento da banda dos hidroperóxidos (grupo ROOH) localizada entre 3000 e 3600 cm-1 nos espectros, e igualmente um alargamento na banda dos carbonilos (grupo C=O) entre 1500 e 1900 cm-1. Numa fase posterior testaram-se antioxidantes para retardar o envelhecimento do biodiesel. Os ensaios foram efectuados a uma temperatura entre 95º e 105ºC. Os antioxidantes utilizados foram o galhato de propilo (PG), o galhato de etilo (EG) e o ácido gálhico (AG). Recorreu-se a técnicas como o UV-VIS e o FTIR para o registo dos espectros do biodiesel ao longo do tempo. Através destas técnicas foi possível verificar a influência de antioxidantes na estabilidade oxidativa do biodiesel. O PG foi o antioxidante que melhor desempenho mostrou no retardamento da oxidação do biodiesel e a técnica que melhor permitiu analisar a acção dos antioxidantes foi o UVVIS. Os resultados obtidos por FTIR não se mostraram tão conclusivos. Para caracterizar o envelhecimento do biodiesel não estabilizado e estabilizado utilizou-se também a cromatografia gasosa (CG) para quantificar a percentagem de ésteres metílicos presentes nas diferentes amostras no inicio e no fim do processo de oxidação. O biodiesel envelheceu mais rapidamente para temperaturas mais elevadas e comprovou-se que o antioxidante que melhor estabiliza o biodiesel é o PG.