Simplex Procedure Research Articles

Use of a linear function of several variables in simplex optimization as a procedure for assessing analytical versatility in FIA

A linear response function RF=C H R H +C T (1−R T ) (R H =peak height, used as a measure of «sensitivity», and R T =analysis time, 1−R T used as a measure of sampling rate) was used to optimize a FIA system for the determination of nitrite in water with respect to four experimental parameters (two tube lengths and two flow rates) by a Simplex procedure

Optimizing accuracy and precision in spectral data

Parameters derived by computer fitting of Gaussian or Lorentzian curves to spectral data suffer from inaccuracies derived by the data gathering strategy, by instrumental errors and by the inherent statistical fluctuation of the measurements. When measurements of extreme quality are required, minimum uncertainty for peak centroid and linewidth for a given data collection time is obtained by proper choice of the number of ‘channels’ in the peak. The optimum conditions that are derived analytically are supported by results of fitting spectra with Gaussian curves. Fittings were done with the simplex procedure yielding precise values of the centroid and linewidth. Data used were x-ray fluorescence signals and computer-simulated spectral peaks. Results of the theoretical calculations and of computer fittings to both empirical data and simulated spectra indicate that the optimum number of channels in a peak, for the best quality of measurements of the peak centroid and its linewidth, is independent of the peak integral and has full width at half-maximum in the neighborhood of 2.5 channels. Copyright © 2005 John Wiley & Sons, Ltd.

Separation and determination of Vitamins E and A in multivitamin syrup using micellar liquid chromatography and simplex optimization

A rapid method has been described for separation and determination of Vitamins A and E using micellar liquid chromatography (MLC). Influence of temperature of column and addition of organic modifiers on separation efficiency was investigated. A temperature of 30 °C and 1-butanol modifier was selected. Optimization of the parameters affecting the separation including percent of organic modifier, pH of the mobile phase, concentration of surfactant, and flow rate of the mobile phase was performed simultaneously using the super-modified simplex (SMS) procedure. Results showed that 11.7% 1-butanol, 76.9 mM sodium dodecyl sulphate (SDS), pH of 6.73 and a flow rate of 1.35 ml min −1 are the best conditions for separation of these compounds. The analytical parameters including linearity, r > 0.9990; limit of detection 1.71 and 4.52 μg ml −1 for A and E, respectively; precision of the method, R.S.D. < 2.85%; and recovery, more than 90%, show that the method is useful for measuring these compounds in pharmaceutical preparations.

Approach of just-in-time distribution requirements planning for supply chain management

The distribution of finished goods to customers plays an important role in supply chain management. This paper introduces an approach that takes care of multi-warehouse and multi-retailer scenarios. In order to pull material through a supply chain effectively, we proposed a just-in-time distribution requirements planning system under the limited supply capacity. The aim is to establish an optimal distribution requirements planning model to minimize the total cost of manufacturing and transportation as well as the earliness/tardiness penalty in meeting retailer's requirements under limited warehouse capacity. Using mathematical deduction, the model can be translated into a linear programming problem and solved by a simplex procedure. The computational results have shown that the proposed approach can offer more effective distribution requirements plans.

Properties of small- to medium-sized mercury clusters from a combined ab initio, density-functional, and simulated-annealing study.

Relativistic coupled-cluster and second-order many-body perturbation theories were used to construct two- and three-body potentials for the interaction between mercury atoms. A subsequent combined simulated-annealing downhill simplex and conjugate gradient-optimization procedure gave global minima for mercury clusters with up to 30 atoms. The calculations reveal magic cluster numbers of 6, 13, 19, 23, 26, and 29 atoms. At these cluster sizes, the static dipole polarizability obtained from density-functional theory has a minimum. The calculations also reveal a fast convergence of the polarizability towards the bulk limit in contrast to the singlet-triplet gap or the ionization potential.

Optimization of a three-dimensional Simplex procedure for speech in noise

In this study we investigated means to enhance the reliability of a three-dimensional Simplex optimization procedure. The algorithms used to span the three dimensions are noise reduction, spectral tilting, and spectral enhancement, respectively. We considered the influence of an adaptive step size, different starting points, different types of noise, and the effect of an impaired spectral resolution. The subjects were asked to evaluate two consecutive, differently processed sentences on the evaluation criterion listening comfort. Three different noise types were used. We asked the normal-hearing subjects to listen to the stimuli with or without simulated impaired auditory filtering. The impairment was simulated by application of spectral smearing. For the subjects with normal filtering we applied a signal-to-noise ratio (S/N) of 0 dB. For the subjects with simulated impaired frequency resolution we applied S/N=5 dB. Due to several methodological innovations (especially when the step size is adaptive), the reliability of the Simplex procedure increased. Moreover, the reliability depends on the algorithms included and on the type of noise used.

Optimization of speech in noise with three signal processing algorithms for normal-hearing and hearing-impaired subjects

In this study a three‐dimensional Simplex procedure was applied to optimize speech in noise by a combination of signal processing algorithms for different acoustic conditions and hearing losses. The algorithms used to span the three dimensions are noise reduction, spectral tilting, and spectral enhancement, respectively. Additionally, we studied the algorithms for their main effects and interaction effects within the optimization process. The subjects were asked to evaluate two consecutive, differently processed sentences on listening comfort. Three different noise types and two signal‐to‐noise ratios (S/N) were used. Three groups of subjects participated: normal hearing, normal hearing with simulated impaired auditory filtering (by spectral smearing), and sensorineurally hearing‐impaired subjects. For the normal‐hearing group we applied S/N=0 dB. For the hearing‐impaired and the simulated hearing‐impaired subjects we applied S/N=5 dB. We will discuss the similarities and differences in the response patterns of the three groups. Also, the individual preferences will be related to the hearing capacity, and to the type of interfering noise. Finally, we will discuss differences in the perceptual features that are used to judge listening comfort of the fragments by normal‐hearing and hearing‐impaired subjects.

Optimization of large electrical salient pole synchronous generators

The designs of salient pole generators may differ considerably from one hydroelectric plant to another. Automatic optimization procedure is highly desirable, because the designer may have little experience with a similar machine. The presented approach defines the design space by 12 variables which have the largest influence on the goal function. The design space is constrained by a number of linear and nonlinear constraints. The optimization process is based on successive linearizations of the goal function and the nonlinear constraints followed by a simplex procedure. The process is highly effective because the goal function is heavily constrained, so the optimum is virtually always on the boundary of the feasibility region. The procedure has been tested on a number of earlier designs. The goal function could have been reduced on average by some 8 percent, had this software been available at the time of the design of these machines.

Weighted Simplex Procedures for Determining Boundary Points and Constants for the Univariate and Multivariate Power Methods

The power methods are simple and efficient algorithms used to generate either univariate or multivariate nonnormal distributions with specified values of (marginal) mean, standard deviation, skew, and kurtosis. The power methods are bounded as are other transformation techniques. Given an exogenous value of skew, there is an associated lower bound of kurtosis. Previous approximations of the boundary for the power methods are either incorrect or inadequate. Data sets from education and psychology can be found to lie within, near, or outside tile boundary of the power methods. In view of this, we derived necessary and sufficient conditions using the Lagrange multiplier method to determine the boundary of the power methods. The conditions for locating and classifying modes for distributions on the boundary were also derived. Self-contained interactive Fortran programs using a Weighted Simplex Procedure were employed to generate tabled values of minimum kurtosis for a given value of skew and power constants for various (non)normal distributions.

Computational aspects of linear programming Simplex method

In this paper, the Simplex method is re-examined from the computational view points. Efficient numerical implementation for the Simplex procedure is suggested. Special features of artificial variables, and variables with unrestriction in signs are exploited to reduce the com-putational efforts, and computer memory requirement. The developed Simplex code has been tested on several examples, and its performance has been compared with existing Simplex codes.

An examination of the practicality of the simplex procedure.

The practical importance of the simplex procedure, a subjective technique used to refine the frequency gain characteristic (FGC) of a hearing aid according to listener preference, was determined for individual listeners by measuring hearing aid benefit using both laboratory studies and field studies. A digital research hearing aid with two memories was used as the test hearing aid. The modified simplex procedure was used to select the FGC judged to yield the best speech clarity in the presence of low-level vent noise and again in higher-level cafeteria noise by 10 experienced hearing aid users. The FGCs assessed by the listeners varied systematically from The National Acoustic Laboratories Revised (NAL-R) response in the amount of low-frequency or high-frequency amplification. The benefit obtained with these two simplex-selected settings was compared with that obtained using the NAL-R FGC. Measures of benefit included speech recognition testing in the laboratory and ratings of speech intelligibility in the field. In the first field study, the two simplex settings were compared. In the second field study, the simplex-selected setting for higher level noise and the NAL-R setting were compared. In the laboratory, the majority of listeners selected an increase in the low-frequency channel gain compared with the NAL-R. Desired high-frequency channel gain was correlated with degree of hearing loss and type of background noise. The benefit as measured using nonsense syllables did not differ significantly among the three fittings, but differences in benefit were measurable with the rating procedure. Five of eight participants noticed a significant difference in their speech understanding in the real world for the FGCs selected in different background noises. Two of seven participants reported significantly better speech intelligibility with a simplex-selected FGC compared with the NAL-R FGC in the real world. The remaining subjects reported similar speech understanding capabilities with both hearing aid settings. The majority of subjects included in this study selected an FGC with real ear insertion gain different than the NAL-R prescription to improve subjective speech understanding in the laboratory. A small number of these listeners rated the selected FGC as providing improved speech intelligibility over the NAL-R FGC in the real world. This finding indicates that the simplex procedure should be used selectively to modify the NAL-R prescription. A screening technique would be useful in selecting those who might benefit from a modified fitting. The simplex procedure may also prove to be useful in selecting listeners who would benefit from multiple memory hearing aids.

Investigation of mathematical methods for efficient optimisation of aqueous two-phase extraction

Mathematical strategies were applied to optimise the extraction of recombinant leucine dehydrogenase from E. coli homogenates and endoglucanase 1 from culture filtrates of Trichoderma reesei in polyethylene glycol–phosphate systems. The goal was to test mathematical tools which could facilitate the optimisation procedure in aqueous two-phase systems. A modified simplex approach, the method of steepest ascent and a genetic algorithm were successfully applied and compared. The methods differ in the height of the optimum found, the number of experiments and the time required. The genetic algorithm proved to be an optimisation procedure which can be used well in aqueous two-phase systems. The simplex procedure has to be further improved.

Weighted Simplex Procedures for Determining Boundary Points and Constants for the Univariate and Multivariate Power Methods

Weighted Simplex Procedures for Determining Boundary Points and Constants for the Univariate and Multivariate Power Methods

Synthesis and characterization of long chain alkyl stationary phases on a silica hydride surface

C22 and C30 alkyl chains were attached to a silica hydride surface by a hydrosolation reaction. In each case both moieties were successfully bonded by either metal complex catalysis or free radical initiation. Carbon analysis, DRIFT spectra and13C CP-MAS NMR spectra confirm the bonding of the olefin to silica hydride. Conditions for maximum coverage were determined by a simplex procedure. Chromatographic evaluation of these long chain bonded phases was accomplished by separations of several types of mixtures: alkyl substituted benzenes; polycyclic aromatic hydrocarbons; carotenoids, tocopherols; tricyclic antidepressants; and peptides. The C30 column proved significantly better for separating the carotenoid and antidepressant mixtures and somewhat better for the peptide sample.

A robust superlinearly convergent algorithm for linearly constrained optimization problems under degeneracy

In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex procedure with lexicographic scheme is proposed to deal with the degenerative case in the sense that the gradients of active constraints at the iteration point are dependent. Unlike other methods, the new algorithm possesses the following important property that, at any iteration point generated by the algorithm, one can choose a set of the most suitable basis and from it one can drop all constraints which can be relaxed, not only one constraint once. This property will be helpful in decreasing the computation amount of the algorithm. The global convergence and superlinear convergence of this algorithm are proved, without any assumption of linear independence of the gradients of active constraints.

Flow injection chemiluminescence determination of medazepam

A new flow injection chemiluminescence method for the assay of medazepam is explored. The method involves the use of permanganate in sulfuric acid for the oxidation of medazepam with the emission of chemiluminescence detected by a photomultiplier tube. A simplex procedure was employed for optimising the conditions for high sensitivity detection, which were found to be 1.03 × 10–3 mol L–1 permanganate, 0.153 mol L–1 sulfuric acid and 3.43 mL min–1 flow rate. The linear calibration range was 3.7 × 10–5 to 1.7 × 10–3 mol L–1. The detection limit (3σ) and the sample throughput were 1.85 × 10–5 mol L–1 and 100 per hour, respectively. The relative standard deviation for 5 replicate determinations of 1.9 × 10–4 mol L–1 medazepam was 0.15%. Common excipients (starch, glucose, maltose, lactose) used in pharmaceutical preparations had no effect.

A basis-deficiency-allowing variation of the simplex method for linear programming

As one of the most important and fundamental concepts in the simplex methodology, basis is restricted to being a square matrix of the order exactly equal to the number of rows of the coefficient matrix. Such inflexibility might have been the source of too many zero steps taken by the simplex method in solving real-world linear programming problems, which are usually highly degenerate. To dodge this difficulty, we first generalize the basis to allow the deficient case, characterized as one that has columns fewer than rows of the coefficient matrix. Variations of the primal and dual simplex procedures are then made, and used to form a two-phase method based on such a basis, the number of whose columns varies dynamically in the solution process. Generally speaking, the more degenerate a problem to be handled is, the fewer columns the basis will have; so, this renders the possibility of efficiently solving highly degenerate problems. We also provide a valuable insight into the distinctive and favorable behavior of the proposed method by reporting our computational experiments.

Quantitative correlation between molecular similarity and receptor-binding activity of neonicotinoid insecticides

Quantitative correlation between molecular similarity and receptor-binding activity of neonicotinoid insecticides such as imidacloprid and acetamiprid was studied by using a method of similarity index and semi-empirical molecular orbital calculations. A series of compounds having an aromatic ring and a cyclic or acyclic amine moiety with an electron-withdrawing group were subjected to the similarity-activity analysis. Energy-minimum structures and electrostatic properties of the molecules were obtained by MNDO-PM3. The electrostatic similarity of each molecule compared with the most active compounds was found to correlate significantly with the binding activity to nicotinic acetylcholine receptor (nAChR) in honey bee when the two molecules were superimposed to maximize the molecular shape similarity by simplex procedure. This indicates that molecular similarity in terms of electrostatic properties is important for activity, as well as superimposability in terms of molecular shape. A schematic model of interaction between neonicotinoids and nAChR is proposed according to the results of similarity-activity analyses.

Data Smoothing in Stripping Voltammetry by Simplex Function Fitting

Stripping voltammetry (SV), in common with all trace voltammetric analytical techniques, suffers from poor signal-to-noise (S/N) ratios due to external interference pick up and inherent generation of noise in the electrochemical system. In addition to other methods developed to smooth noisy data (such as time and frequency domain filtering), optimisation methods can also be used to reject the noise present in electrochemical measurements. In this paper, an optimisation method, based on a modified Simplex procedure, is presented. The method is based on minimising the deviation (in terms of the mean square error) between the recorded data and a theoretical model of the data. In this case, the model was a response surface consisting of one or more peak-shaped functions of one of the following types: Gaussian (G), exponentially modified Gaussian (EMG), Lorentzian (L), combined Gaussian-Lorentzian (GL) and theoretical voltammetric peak (TVP). The method was successfully applied to stripping signals obtained for the trace quantification of riboflavin and for the simultaneous determination of zinc, cadmium lead and copper by SV. *Present address: Laboratory of Analytical Chemistry, Chemistry Department, University of Athens, Panepistimiopolis, Athens 157 71, GREECE

Application of tertiary amines for arsenic and selenium signal enhancement and polyatomic interference reduction in ICP-MS analysis of biological samples

Water soluble tertiary amines enhance signals and decrease polyatomic chloride interferences in the direct inductively coupled plasma – mass spectrometric (ICP-MS) determination of As and Se in biological samples. Preliminary experiments with amine concentrations and nebulizer flow rates produced element and interference signal intensity changes. Arsenic and Se ICP-MS determination parameters have been optimized by a simplex procedure with amines in an argon plasma or without amines but with addition of N2 to the Ar. Variables include RF (radio frequency) power, nebulizer gas flow rate, intermediate gas flow rate, and amine concentration or nitrogen gas flow rate. Detection limit, minimization of polyatomic ion intensities, and reproducibility have been evaluated as reponse factors. The signal enhancement and element-to-molecular interference ratios differ to some extent with analyte intensity optimum operating conditions. The detection limits with addition of nitrogen (16 pg mL–1 for As and 180 pg mL–1 for Se) or of amines (8 pg mL–1 for As and 120 pg mL–1 for Se) and the extent of chloride interference minimization were compared. Amines addition was more beneficial. Biological standard reference materials and food and fecal samples were analyzed following different sample dissolution procedures.