Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.

Use of soybean oil fry waste for economical biosurfactant production by isolated Pseudomonas aeruginosa using response surface methodology

The present study sought biotensoactive production from soybean oil fry waste using Pseudomonas aeruginosa ATCC 10145 and Pseudomonas aeruginosa isolated from the soil of a petroleum station having undergone gasoline and diesel oil spills. The results of the experiments were analyzed using a complete factorial experimental design, investigating the concentration of soybean oil waste, ammonia sulfate and residual brewery yeast. Assays were performed in 250-mL Erlenmeyer beakers containing 50 mL of production medium, maintained on a rotary shaker at 200 rpm and a temperature of 30±1 °C for a 48-hour fermentation period. Biosurfactant production was monitored through the determination of rhamnose, surface tension and emulsification activity. The Pseudomonas aeruginosa ATCC 10145 strain and isolated Pseudomonas aeruginosa were able to reduce the surface tension of the initial mexlium from 61 mN/m to 32.5 mN/m and 30.0 mN/m as well as produce rhamnose at concentrations of 1.96 and 2.89 g/L with emulsification indices of 96% and 100%, respectively.

Optimization of a synbiotic formulation of soy yoghurt containing yacon extract by response surface methodology

A synbiotic yoghurt based on a combination of soymilk and yacon water extract (from yacon root tubers) was developed as a novel food product fermented with a probiotic culture of Enterococcus faecium CRL 183 and Lactobacillus helveticus ssp jugurti 4l6. Response surface methodology (RSM) was used to optimize the independent variables soymilk protein concentration and percentage of yacon extract in the formulation through a Central Composite Rotatable Design (CCRD), consisting of a 22 factorial design with two levels (-1, +1), two central points (0) and four axial points (± a, 0) (0, ± α). The responses were assessed by consumer acceptance tests. The optimization indicated that a formulation with a soymilk protein concentration of 1.74g/L and 25.86% of yacon extract gave the best average values, 5.91 for the taste and 6.00 for the overall impression responses. The formulation with 40% of yacon extract and the same concentration of soymilk protein achieved similar acceptance values: taste (5.94) and overall impression (5.87), however, with the extra yacon, it probably had a greater content of prebiotic fructooligosaccharides. Consequently, both formulations may give useful functional foods, with sensory properties comparable with those of soy yoghurt (control formulation). Copyright © 2010 by New Century Health Publishers.

Optimization of integrated chemical-biological degradation of a reactive azo dye using response surface methodology

The integrated chemical-biological degradation combining advanced oxidation by UV/H2O2 followed by aerobic biodegradation was used to degrade C.I. Reactive Azo Red 195A, commonly used in the textile industry in Australia. An experimental design based on the response surface method was applied to evaluate the interactive effects of influencing factors (UV irradiation time, initial hydrogen peroxide dosage and recirculation ratio of the system) on decolourisation efficiency and optimizing the operating conditions of the treatment process. The effects were determined by the measurement of dye concentration and soluble chemical oxygen demand (S-COD). The results showed that the dye and S-COD removal were affected by all factors individually and interactively. Maximal colour degradation performance was predicted, and experimentally validated, with no recirculation, 30 min UV irradiation and 500 mg H2O2/L. The model predictions for colour removal, based on a three-factor/five-level Box-Wilson central composite design and the response surface method analysis, were found to be very close to additional experimental results obtained under near optimal conditions. This demonstrates the benefits of this approach in achieving good predictions while minimising the number of experiments required. (c) 2006 Elsevier B.V. All rights reserved.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

Biodiesel production from non-edible beauty leaf (Calophyllum Inophyllum) oil : process optimization using response surface methodology (RSM)

In recent years, the beauty leaf plant (Calophyllum Inophyllum) is being considered as a potential 2nd generation biodiesel source due to high seed oil content, high fruit production rate, simple cultivation and ability to grow in a wide range of climate conditions. However, however, due to the high free fatty acid (FFA) content in this oil, the potential of this biodiesel feedstock is still unrealized, and little research has been undertaken on it. In this study, transesterification of beauty leaf oil to produce biodiesel has been investigated. A two-step biodiesel conversion method consisting of acid catalysed pre-esterification and alkali catalysed transesterification has been utilized. The three main factors that drive the biodiesel (fatty acid methyl ester (FAME)) conversion from vegetable oil (triglycerides) were studied using response surface methodology (RSM) based on a Box-Behnken experimental design. The factors considered in this study were catalyst concentration, methanol to oil molar ratio and reaction temperature. Linear and full quadratic regression models were developed to predict FFA and FAME concentration and to optimize the reaction conditions. The significance of these factors and their interaction in both stages was determined using analysis of variance (ANOVA). The reaction conditions for the largest reduction in FFA concentration for acid catalysed pre-esterification was 30:1 methanol to oil molar ratio, 10% (w/w) sulfuric acid catalyst loading and 75 °C reaction temperature. In the alkali catalysed transesterification process 7.5:1 methanol to oil molar ratio, 1% (w/w) sodium methoxide catalyst loading and 55 °C reaction temperature were found to result in the highest FAME conversion. The good agreement between model outputs and experimental results demonstrated that this methodology may be useful for industrial process optimization for biodiesel production from beauty leaf oil and possibly other industrial processes as well.

Optimisation of high shear granulation of multicomponent fertiliser using response surface methodology

This work describes a novel method of producing multicomponent fertiliser granules using high shear granulation. The granulation process was optimised using the response surface methodology technique. The variables used in the optimisation process include granulation time, batch size, impeller speed and binder concentration. Granulation time, binder concentration and interaction between the batch size and granulation time were found to be the main factors affecting the granule median size. The product yield is mainly influenced by granulation time and binder concentration. The interaction between the impeller speed and batch size also have a significant influence on the product yield. Product yield (2-4 mm) of approximately 60% could be obtained with high sphericity and granule strength (> 0.5 MPa). A low product recycle ratio of about 2:3 can be obtained at the optimised process conditions, compared to typical recycle rations of 6:1 which are obtained in typical fertiliser plants. © 2012 Elsevier B.V. All rights reserved.

Determination of ochratoxin A in bread: evaluation of microwave-assisted extraction using an orthogonal composite design coupled with response surface methodology

An analytical method using microwave-assisted extraction (MAE) and liquid chromatography (LC) with fluorescence detection (FD) for the determination of ochratoxin A (OTA) in bread samples is described. A 24 orthogonal composite design coupled with response surface methodology was used to study the influence of MAE parameters (extraction time, temperature, solvent volume, and stirring speed) in order to maximize OTA recovery. The optimized MAE conditions were the following: 25 mL of acetonitrile, 10 min of extraction, at 80 °C, and maximum stirring speed. Validation of the overall methodology was performed by spiking assays at five levels (0.1–3.00 ng/g). The quantification limit was 0.005 ng/g. The established method was then applied to 64 bread samples (wheat, maize, and wheat/maize bread) collected in Oporto region (Northern Portugal). OTAwas detected in 84 % of the samples with a maximum value of 2.87 ng/g below the European maximum limit established for OTA in cereal products of 3 ng/g.

Response surface analysis of extract yield and flavour intensity of Brazilian cherry (Eugenia uniflora L.) obtained by supercritical carbon dioxide extraction

This work evaluated the effect of pressure and temperature on yield and characteristic flavour intensity of Brazilian cherry (Eugenia uniflora L) extracts obtained by supercritical CO(2) using response surface analysis, which is a simple and efficient method for first inquiries. A complete central composite 2(2) factorial experimental design was applied using temperature (ranging from 40 to 60 degrees C) and pressure (from 150 to 250 bar) as independent variables. A second order model proved to be predictive (p <= 0.05) for the extract yield as affected by pressure and temperature, with better results being achieved at the central point (200 bar and 50 degrees C). For the flavour intensity, a first order model proved to be predictive (p <= 0.05) showing the influence of temperature. Greater characteristic flavour intensity in extracts was obtained for relatively high temperature (> 50 degrees C), Therefore, as far as Brazilian cherry is concerned, optimum conditions for achieving higher extract yield do not necessarily coincide to those for obtaining richer flavour intensity. Industrial relevance: Supercritical fluid extraction (SFE) is an emerging clean technology through which one may obtain extracts free from organic solvents. Extract yields from natural products for applications in food, pharmaceutical and cosmetic industries have been widely disseminated in the literature. Accordingly, two lines of research have industrial relevance, namely, (i) operational optimization studies for high SFE yields and (ii) investigation on important properties extracts are expected to present (so as to define their prospective industrial application). Specifically, this work studied the optimization of SFE process to obtain extracts from a tropical fruit showing high intensity of its characteristic flavour, aiming at promoting its application in natural aroma enrichment of processed foods. (C) 2008 Elsevier Ltd. All rights reserved.

Development of a spectrophotometric Sequential Injection Analysis (SIA) procedure for determination of ammonium: A Response Surface Methodology (RSM) approach

This paper describes the optimization and use of a Sequential Injection Analysis (SIA) procedure for ammonium determination in waters. Response Surface Methodology (RSM) was used as a tool for optimization of a procedure based on the modified Berthelot reaction. The SIA system was designed to (i) prepare the reaction media by injecting an air-segmented zone containing the reagents in a mixing chamber, (ii) to aspirate the mixture back to the holding coil after homogenization, (iii) drive it to a thermostated reaction coil, where the flow is stopped for a previously established time, and (iv) to pump the mixture toward the detector flow cell for the spectrophotometric measurements. Using a 100 mu mol L(-1) ammonium solution, the following factors were considered for optimization: reaction temperature (25 - 45 degrees C), reaction time (30 - 90 s), hypochlorite concentration (20 - 40 mmol L(-1)) nitroprusside concentration (10 - 40 mmol L(-1)) and salicylate concentration (0.1 - 0.3 mol L(-1)). The proposed system fed the statistical program with absorbance data for fast construction of response surface plots. After optimization of the method, figures of merit were evaluated, as well as the ammonium concentration in some water samples. No evidence of statistical difference was observed in the results obtained by the proposed method in comparison to those obtained by a reference method based on the phenol reaction. (C) 2010 Elsevier B.V. All rights reserved.

Response surface models to predict broiler performance and applications for economic analysis

A study was carried out to elaborate response surface models using broiler performance data recovered from literature in order to predict performance and elaborate economic analyses. Nineteen studies published between 1995 and 2005 were retrieved using the systematic literature review method. Weight gain and feed conversion data were collected from eight studies that fulfilled the pre-established inclusion criteria, and a response surface model was adjusted using crude protein, environmental temperature, and age as independent variables. The models produced for weight gain (r² = 0.93) and feed conversion (r² = 0.85) were accurate, precise, and not biased. Protein levels, environmental temperature and age showed linear and quadratic effects on weight gain and feed conversion. There was no interaction between protein level and environmental temperature. Age and crude protein showed interaction for weight gain and feed conversion, whereas interaction between age and temperature was detected only for weight gain. It was possible to perform economic analyses to determine maximum profit as a function of the variables that were included in the model. It was concluded that the response surface models are effective to predict the performance of broiler chickens and allow the elaboration of economic analyses to optimize profit.

Multistratum response surface designs

Response surface designs are usually described as if the treatments have been completely randomized to the experimental units. However, in practice there is often a structure to the units, implying the need for blocking. If, in addition, some factors are more difficult to vary between units than others, a multistratum structure arises naturally. We present a general strategy for constructing response surface designs in multistratum unit structures. Designs are constructed stratum by stratum, starting in the highest stratum. In each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata, allowing-for all the effects that have to be estimated. Three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set. Finally, some practical considerations in randomization are discussed.