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.

Numerical optimization experiments using the hyperbolic smoothing strategy to solve MPCC

In this work we solve Mathematical Programs with Complementarity Constraints using the hyperbolic smoothing strategy. Under this approach, the complementarity condition is relaxed through the use of the hyperbolic smoothing function, involving a positive parameter that can be decreased to zero. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.

Optimization, high availability and redundancy in information communications and technology using networks and systems virtualization architectures

Mestrado em Engenharia Informática

The development and optimization of a modified single-drop microextraction method for organochlorine pesticides determination by gas chromatography-tandem mass spectrometry

We have developed a new method for single-drop microextraction (SDME) for the preconcentration of organochlorine pesticides (OCP) from complex matrices. It is based on the use of a silicone ring at the tip of the syringe. A 5 μL drop of n-hexane is applied to an aqueous extract containing the OCP and found to be adequate to preconcentrate the OCPs prior to analysis by GC in combination with tandem mass spectrometry. Fourteen OCP were determined using this technique in combination with programmable temperature vaporization. It is shown to have many advantages over traditional split/splitless injection. The effects of kind of organic solvent, exposure time, agitation and organic drop volume were optimized. Relative recoveries range from 59 to 117 %, with repeatabilities of <15 % (coefficient of variation) were achieved. The limits of detection range from 0.002 to 0.150 μg kg−1. The method was applied to the preconcentration of OCPs in fresh strawberry, strawberry jam, and soil.

Optimization of QuEChERS method for the analysis of organochlorine pesticides in soils with diverse organic matter

A QuEChERS method has been developed for the determination of 14 organochlorine pesticides in 14 soils from different Portuguese regions with wide range composition. The extracts were analysed by GC-ECD (where GC-ECD is gas chromatography-electron-capture detector) and confirmed by GC-MS/MS (where MS/MS is tandem mass spectrometry). The organic matter content is a key factor in the process efficiency. An optimization was carried out according to soils organic carbon level, divided in two groups: HS (organic carbon>2.3%) and LS (organic carbon<2.3%). Themethod was validated through linearity, recovery, precision and accuracy studies. The quantification was carried out using a matrixmatched calibration to minimize the existence of the matrix effect. Acceptable recoveries were obtained (70–120%) with a relative standard deviation of ≤16% for the three levels of contamination. The ranges of the limits of detection and of the limits of quantification in soils HS were from 3.42 to 23.77 μg kg−1 and from 11.41 to 79.23 μg kg−1, respectively. For LS soils, the limits of detection ranged from 6.11 to 14.78 μg kg−1 and the limits of quantification from 20.37 to 49.27 μg kg−1. In the 14 collected soil samples only one showed a residue of dieldrin (45.36 μg kg−1) above the limit of quantification. This methodology combines the advantages of QuEChERS, GC-ECD detection and GC-MS/MS confirmation producing a very rapid, sensitive and reliable procedure which can be applied in routine analytical laboratories.

Optimization and validation of organochlorine compounds in adipose tissue by SPE-gas chromatography

Scientific evidence has shown an association between organochlorine compounds (OCC) exposure and human health hazards. Concerning this, OCC detection in human adipose samples has to be considered a public health priority. This study evaluated the efficacy of various solid-phase extraction (SPE) and cleanup methods for OCC determination in human adipose tissue. Octadecylsilyl endcapped (C18-E), benzenesulfonic acid modified silica cation exchanger (SA), poly (styrene-divinylbenzene (EN) and EN/RP18 SPE sorbents were evaluated. The relative sample cleanup provided by these SPE columns was evaluated using gas chromatography with electron capture detection (GC–ECD). The C18-E columns with strong homogenization were found to provide the most effective cleanup, removing the greatest amount of interfering substance, and simultaneously ensuring good analyte recoveries higher than 70%. Recoveries>70% with standard deviations (SD)<15% were obtained for all compounds under the selected conditions. Method detection limits were in the 0.003–0.009 mg/kg range. The positive samples were confirmed by gas chromatography coupled with tandem mass spectrometry (GC-MS/MS). The highest percentage found of the OCC in real samples corresponded to HCB, o,p′-DDT and methoxychlor, which were detected in 80 and 95% of samples analyzed respectively. Copyright © 2012 John Wiley & Sons, Ltd.

Mass spectrometry parameters optimization for the 46 multiclass pesticides determination in strawberries with gas chromatography ion-trap tandem mass spectrometry

Multiclass analysis method was optimized in order to analyze pesticides traces by gas chromatography with ion-trap and tandem mass spectrometry (GC-MS/MS). The influence of some analytical parameters on pesticide signal response was explored. Five ion trap mass spectrometry (IT-MS) operating parameters, including isolation time (IT), excitation voltage (EV), excitation time (ET),maximum excitation energy or “q” value (q), and isolationmass window (IMW) were numerically tested in order to maximize the instrument analytical signal response. For this, multiple linear regression was used in data analysis to evaluate the influence of the five parameters on the analytical response in the ion trap mass spectrometer and to predict its response. The assessment of the five parameters based on the regression equations substantially increased the sensitivity of IT-MS/MS in the MS/MS mode. The results obtained show that for most of the pesticides, these parameters have a strong influence on both signal response and detection limit.Using the optimized method, a multiclass pesticide analysis was performed for 46 pesticides in a strawberry matrix. Levels higher than the limit established for strawberries by the European Union were found in some samples.

Aspectos de aprendizagem em optimização

A optimização e a aprendizagem em Sistemas Multi-Agente são consideradas duas áreas promissoras mas relativamente pouco exploradas. A optimização nestes ambientes deve ser capaz de lidar com o dinamismo. Os agentes podem alterar o seu comportamento baseando-se em aprendizagem recente ou em objectivos de optimização. As estratégias de aprendizagem podem melhorar o desempenho do sistema, dotando os agentes da capacidade de aprender, por exemplo, qual a técnica de optimização é mais adequada para a resolução de uma classe particular de problemas, ou qual a parametrização é mais adequada em determinado cenário. Nesta dissertação são estudadas algumas técnicas de resolução de problemas de Optimização Combinatória, sobretudo as Meta-heurísticas, e é efectuada uma revisão do estado da arte de Aprendizagem em Sistemas Multi-Agente. É também proposto um módulo de aprendizagem para a resolução de novos problemas de escalonamento, com base em experiência anterior. O módulo de Auto-Optimização desenvolvido, inspirado na Computação Autónoma, permite ao sistema a selecção automática da Meta-heurística a usar no processo de optimização, assim como a respectiva parametrização. Para tal, recorreu-se à utilização de Raciocínio baseado em Casos de modo que o sistema resultante seja capaz de aprender com a experiência adquirida na resolução de problemas similares. Dos resultados obtidos é possível concluir da vantagem da sua utilização e respectiva capacidade de adaptação a novos e eventuais cenários.

Balanceamento de linhas de produção usando algoritmos genéticos

Aquando da definição de um layout por fluxo de produto, ou linha de produção, é necessário proceder-se à melhor selecção de combinações de tarefas a serem executadas em cada estação / posto de trabalho para que o trabalho seja executado numa sequência exequível e sejam necessárias quantidades de tempo aproximadamente iguais em cada estação / posto de trabalho. Este processo é chamado de balanceamento da linha de produção. Verifica-se que as estações de trabalho e equipamentos podem ser combinados de muitas maneiras diferentes; daí que a necessidade de efectuar o balanceamento das linhas de produção implique a distribuição de actividades sequenciais por postos de trabalho de modo a permitir uma elevada utilização de trabalho e de equipamentos e a minimizar o tempo de vazio. Os problemas de balanceamento de linhas são tipicamente problemas complexos de tratar, devido ao elevado número de combinações possíveis. Entre os métodos utilizados para resolver estes problemas encontram-se métodos de tentativa e erro, métodos heurísticos, métodos computacionais de avaliação de diferentes opções até se encontrar uma boa solução e métodos de optimização. O objectivo deste trabalho passou pelo desenvolvimento de uma ferramenta computacional para efectuar o balanceamento de linhas de produção recorrendo a algoritmos genéticos. Foi desenvolvida uma aplicação que implementa dois algoritmos genéticos, um primeiro que obtém soluções para o problema e um segundo que optimiza essas soluções, associada a uma interface gráfica em C# que permite a inserção do problema e a visualização de resultados. Obtiveram-se resultados exequíveis demonstrando vantagens em relação aos métodos heurísticos, pois é possível obter-se mais do que uma solução. Além disso, para problemas complexos torna-se mais prático o uso da aplicação desenvolvida. No entanto, esta aplicação permite no máximo seis precedências por cada operação e resultados com o máximo de nove estações de trabalho.

A literature review on the optimization of legged robots

Over the last two decades the research and development of legged locomotion robots has grown steadily. Legged systems present major advantages when compared with ‘traditional’ vehicles, because they allow locomotion in inaccessible terrain to vehicles with wheels and tracks. However, the robustness of legged robots, and especially their energy consumption, among other aspects, still lag behind mechanisms that use wheels and tracks. Therefore, in the present state of development, there are several aspects that need to be improved and optimized. Keeping these ideas in mind, this paper presents the review of the literature of different methods adopted for the optimization of the structure and locomotion gaits of walking robots. Among the distinct possible strategies often used for these tasks are referred approaches such as the mimicking of biological animals, the use of evolutionary schemes to find the optimal parameters and structures, the adoption of sound mechanical design rules, and the optimization of power-based indexes.

Optimization of Cu(II) biosorption onto ascophyllum nodosum by factorial design methodology

A Box–Behnken factorial design coupled with surface response methodology was used to evaluate the effects of temperature, pH and initial concentration in the Cu(II) sorption process onto the marine macroalgae Ascophyllum nodosum. The effect of the operating variables on metal uptake capacitywas studied in a batch system and a mathematical model showing the influence of each variable and their interactions was obtained. Study ranges were 10–40ºC for temperature, 3.0–5.0 for pH and 50–150mgL−1 for initial Cu(II) concentration. Within these ranges, the biosorption capacity is slightly dependent on temperature but markedly increases with pH and initial concentration of Cu(II). The uptake capacities predicted by the model are in good agreement with the experimental values. Maximum biosorption capacity of Cu(II) by A. nodosum is 70mgg−1 and corresponds to the following values of those variables: temperature = 40ºC, pH= 5.0 and initial Cu(II) concentration = 150mgL−1.

Multi-criteria design optimization study of solvent extraction in mixer–settler units

Solvent extraction is considered as a multi-criteria optimization problem, since several chemical species with similar extraction kinetic properties are frequently present in the aqueous phase and the selective extraction is not practicable. This optimization, applied to mixer–settler units, considers the best parameters and operating conditions, as well as the best structure or process flow-sheet. Global process optimization is performed for a specific flow-sheet and a comparison of Pareto curves for different flow-sheets is made. The positive weight sum approach linked to the sequential quadratic programming method is used to obtain the Pareto set. In all investigated structures, recovery increases with hold-up, residence time and agitation speed, while the purity has an opposite behaviour. For the same treatment capacity, counter-current arrangements are shown to promote recovery without significant impairment in purity. Recycling the aqueous phase is shown to be irrelevant, but organic recycling with as many stages as economically feasible clearly improves the design criteria and reduces the most efficient organic flow-rate.

Entropy diversity in multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyzethe MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.

Optimization of QuEChERS procedure coupled to GC-ECD for organochlorine pesticide determination in carrot samples

An optimised version of the Quick, Easy, Cheap, Effective, Rugged and Safe (QuEChERS) method for simultaneous determination of 14 organochlorine pesticides in carrots was developed using gas chromatography coupled with electron-capture detector (GC-ECD) and confirmation by gas chromatography tandem mass spectrometry (GC-MS/MS). A citrate-buffered version of QuEChERS was applied for the extraction of the organochlorine pesticides, and for the extract clean-up, primary secondary amine, octadecyl-bonded silica (C18), magnesium sulphate (MgSO4) and graphitized carbon black were used as sorbents. The GC-ECD determination of the target compounds was achieved in less than 20 min. The limits of detection were below the EUmaximum residue limits (MRLs) for carrots, 10–50 μg kg−1, while the limit of quantification did exceed 10 μg kg−1 for hexachlorobenzene (HCB). The introduction of a sonication step was shown to improve the recoveries. The overall average recoveries in carrots, at the four tested levels (60, 80, 100 and 140 μg kg−1), ranged from 66 to 111% with relative standard deviations in the range of 2– 15 % (n03) for all analytes, with the exception of HCB. The method has been applied to the analysis of 21 carrot samples from different Portuguese regions, and β-HCH was the pesticide most frequently found, with concentrations oscillating between less than the limit of quantification to 14.6 μg kg−1. Only one sample had a pesticide residue (β-HCH) above the MRL, 14.6 μg kg−1. This methodology combines the advantages of both QuEChERS and GC-ECD, producing a very rapid, sensitive and reliable procedure which can be applied in routine analytical laboratories.