An Expository Paper on Optimal Design

Johnson, Rachel T.; Montgomery, Douglas C.; Jones, Bradley

doi:10.1080/08982112.2011.576203

Cited by 33 publications

(15 citation statements)

References 19 publications

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“…Even for linear polynomial models with a few factors, recent papers acknowledge the difficulty of finding minimax optimal designs; see Rodriguez et al (2010) and Johnson et al (2011), who considered finding a Goptimal design to minimize the maximal variance of the fitted response across the design space. Optimal minimax designs for nonlinear models can be challenging even when there are just two parameters in the model; earlier attempts to solve such minimax problems have to impose constraints to simplify the optimization problem.…”

Section: Pso-generated Minimax Optimal Designsmentioning

confidence: 99%

Minimax optimal designs via particle swarm optimization methods

et al. 2014

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Particle swarm optimization (PSO) techniques are widely used in applied fields to solve challenging optimization problems but they do not seem to have made an impact in mainstream statistical applications hitherto. PSO methods are popular because they are easy to implement and use, and seem increasingly capable of solving complicated problems without requiring any assumption on the objective function to be optimized. We modify PSO techniques to find minimax optimal designs, which have been notoriously challenging to find to date even for linear models, and show that the PSO methods can readily generate a variety of minimax optimal designs in a novel and interesting way, including adapting the algorithm to generate standardized maximin optimal designs.

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Section: Pso-generated Minimax Optimal Designsmentioning

confidence: 99%

Minimax optimal designs via particle swarm optimization methods

et al. 2014

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“…The choice was based on the suitability of this optimality criterion to build prediction models. This fact is caused by its relatively smaller prediction variance over the experimental domain than those shown by other optimality criteria usually implemented in commercial software like D‐optimality . This is probably the first study which utilizes I‐optimal design for modelling and optimizing enzyme production through solid‐state fermentation.…”

Section: Resultsmentioning

confidence: 99%

Artificial intelligence approach for high level production of amylase usingRhizopus microsporusvar. oligosporusand different agro-industrial wastes

Núñez

Barchi

Ito

et al. 2016

J. Chem. Technol. Biotechnol

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BACKGROUND Culture medium is a key element to be defined when biotechnologies are chosen for agro‐industrial wastes reutilization. This work aimed at definition of culture medium composition using four agro‐industrial wastes (wheat bran, type II wheat flour, soybean meal and sugarcane bagasse) in solid‐state fermentation (SSF) of Rhizopus oligosporus, for high‐level production of amylases through approaches based on artificial intelligence (AI) or response surface methodologies (RSM). First, substrates were individually assessed. Then, I‐optimal mixture experimental designs were performed to determine the influence of two sets of ternary agro‐industrial waste mixtures on amylase and specific amylase activities. RESULTS The best individual substrate for amylases production was wheat bran (392.5 U g−1). As a rule, no significant interactions among substrates affecting amylase activities were observed for ternary systems and the approaches under consideration. A significant exception was the amylolytic activity for mixtures composed of wheat bran (91% w/w) and soybean meal (9% w/w). This finding was confirmed analytically by a combination of artificial neural network (ANN) and genetic algorithm (GA). The AI approach improved modelling quality with respect to RSM for production of fungal amylases in SSF. CONCLUSION The I‐optimal design in conjunction with ANN‐GA is suggested to optimize accurately culture medium to maximize amylase production by SSF. © 2016 Society of Chemical Industry

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“…As the goals of the present work concern the identification of the key factors contributing to the HS-SPME performance and the maximization of response value, the accuracy of the model to be estimated from the experimental points is a key aspect, which justifies the choice of the D-optimality criterion [26,49].…”

Section: Hs-spme Optimizationmentioning

confidence: 99%

Optimal design of experiments applied to headspace solid phase microextraction for the quantification of vicinal diketones in beer through gas chromatography-mass spectrometric detection

Leça

Pereira

Vieira

et al. 2015

Analytica Chimica Acta

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Vicinal diketones, namely diacetyl (DC) and pentanedione (PN), are compounds naturally found in beer that play a key role in the definition of its aroma. In lager beer, they are responsible for off-flavors (buttery flavor) and therefore their presence and quantification is of paramount importance to beer producers. Aiming at developing an accurate quantitative monitoring scheme to follow these off-flavor compounds during beer production and in the final product, the head space solid-phase microextraction (HS-SPME) analytical procedure was tuned through experiments planned in an optimal way and the final settings were fully validated. Optimal design of experiments (O-DOE) is a computational, statistically-oriented approach for designing experiences that are most informative according to a well-defined criterion. This methodology was applied for HS-SPME optimization, leading to the following optimal extraction conditions for the quantification of VDK: use a CAR/PDMS fiber, 5 ml of samples in 20 ml vial, 5 min of pre-incubation time followed by 25 min of extraction at 30 °C, with agitation. The validation of the final analytical methodology was performed using a matrix-matched calibration, in order to minimize matrix effects. The following key features were obtained: linearity (R(2) > 0.999, both for diacetyl and 2,3-pentanedione), high sensitivity (LOD of 0.92 μg L(-1) and 2.80 μg L(-1), and LOQ of 3.30 μg L(-1) and 10.01 μg L(-1), for diacetyl and 2,3-pentanedione, respectively), recoveries of approximately 100% and suitable precision (repeatability and reproducibility lower than 3% and 7.5%, respectively). The applicability of the methodology was fully confirmed through an independent analysis of several beer samples, with analyte concentrations ranging from 4 to 200 g L(-1).

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An Expository Paper on Optimal Design

Cited by 33 publications

References 19 publications

Minimax optimal designs via particle swarm optimization methods

Minimax optimal designs via particle swarm optimization methods

Artificial intelligence approach for high level production of amylase usingRhizopus microsporusvar. oligosporusand different agro-industrial wastes

Optimal design of experiments applied to headspace solid phase microextraction for the quantification of vicinal diketones in beer through gas chromatography-mass spectrometric detection

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