Optimization is frequently to associate its design, to be a product or system. In mathematics, computational science, or management science, mathematical optimization (alternatively, optimization or mathematical programming) refers to the selection of a best element from some set of available alternatives . Actually, Optimization is deal to finding the maxima and minima of a function that depends on one or more variables. These can be substituted back into the function to compute its optimal values . The methods of finding a local minimum for several independent variables have been devised by NelderMeadMethod and Powell’s Method .
Models can be powerful predictive and interpretive tools to study the geochemistry of natural waters and mineral deposits, solve environmental problems and optimize industrial processes; indeed the Pitzer model is one of the most used ones, which has enjoyed remarkable success. It is especially popular with geochemists, waste chemists, and engineers for prediction of mineral solubility and phase equilibrium. Therefore, Pitzer and his co-workers developed the ion-interaction approach to predict the mean activity coefficients of salts in aqueous electrolyte solutions as a function of the molality as well as the theoretical solubility isotherms [4-6]. Furthermore it’s used for thermodynamic analysis of the experimental mixing solutions solubility data, presented in the literature. Pitzer has determined the ion interaction parameters for a large number of binary and ternary solutions . The specific interaction approach for describing aqueous solutions to high concentration represents a significant advance in physical chemistry that has facilitated the construction of accurate thermodynamic models. However, when the Pitzer parameters are not available from experimental data; they can be theoretically or experimentally determined, as well be seen in the present paper. A several methods have been used for the determination of Pitzer parameters, however some of them are judged expensive in terms of money due to the huge need of materials, energy and equipment; one of the most known processes for Pitzer parameters determination is the isopiestic method  which is an experimental method based on the calculation of the osmotic coefficient and water activity, another method has been used recently, that aims to predict Pitzer parameters through the calculation of thermodynamic properties using the hygrometric method , in a previous work we opted for an iterative method to estimate Pitzer parameters for a ternary system , furthermore to enhance our work, we established an algorithm based essentially on the simplex Nelder-Meadmethod which is an optimization routine with the main object of searching for the Pitzer parameters while minimizing the difference between experimental data and theoretical one.
involved in more than one biological process. Therefore, biclustering algorithms have been preferred to standard clustering techniques to identify local patterns from gene expression data sets. Biclustering is a data mining technique which clustersthe rows and columns of a matrix simultaneously.Finding the biclusters in a large microarray gene expression data is a much more complex problem than clustering. The search space for the biclustering problem is 2 m+n where m represents the number of genes and n represents the number of conditions. Usually m+n is more than 2000. In fact, it has been proven to be a NP-hard problem and hence heuristic search algorithms are used. It solves the problem quickly and finds the approximate solution when classic methods fail to found. It finds the best solution in the current set of conditions.The rest of the paper is organized as follows: Section II describes the literature survey on various biclustering methods. Section III gives the overview about NelderMeadmethod and presents the proposed NelderMead with Levy Flight method. The experimental results are analyzed in section IV. Section V presents conclusion.
This research aims to the efficiency as dependent variable with torque and current as the independent variables of induction motor by using optimization process. The optimal design of induction motor is crucial because of the energy or power consumption. The normal design of induction motor consumes more electricity and energy than the optimal design of induction motor. The application of induction motor is worldwide; therefore minimizing energy consumption of induction motor is one of the important sources for energy savings. Small proportion of the increase in efficiency will be significant energy savings and economic impact. Induction motor efficiency can be raised in various ways. One of them is believed to be optimized for the most economical approach. Therefore, it is very important to choose the best optimization techniques available for three-phase induction motor design. In this research, the optimum efficiency of induction motor will be obtained by using two methods which are Nelder-Meadmethod and Powell‟s method. After the calculation of optimization by these two methods, I will compare the methods in order to determine which one as the best estimation of the optimum efficiency.
I declare that this report entitle “Analyzing AC Induction Motor variables(Voltage, Angular Velocity, And Efficiency) To Compare Between Nelder-MeadMethod And Powell‟s Method of Optimization” is the result of my own research except as cited in the references. The report has not been accepted for any degree and is not concurrently submitted in candidature of any
The Nelder-Meadmethod [14, 15] (Algorithm 4, Fig. 3) is an optimization method that uses a simplex proposed by Nelder and Mead. Gilles et al. applied this method for the hyperparameter tuning problem in support vector machine modeling. They demonstrated that the method can find very good hyperparameter settings reliably for support vector machines . Currently, the Nelder-Meadmethod is not considered in DNN research; however, it has a long history and many achievements in other research areas . Thus, we think it is worth considering
One can easily realize that it is difficult to detect the valleys precisely, because valleys are flat and broad and the peaks are unequal in height, making valleys untraceable. One of the peak and valley based segmented image is displayed in Figure 9(a) but for entire brain volume this derivative based peak valley method fails as all slices within a volume needs different value for peak detection. So Unconstrained Nonlinear Optimization method is used which is commonly known as NelderMeadmethod or downhill simplex method . Figure 9(b) shows the segmented image where thresholds are obtained from NelderMeadmethod; the result is thus an improved version in comparison to Figure 9(a). Possible optimization steps of the downhill simplex algorithm in in search of best possible thresholds that separates the four classes in brain MR images with three thresholds namely , and are illustrated in Figure 10. The steps allow the tetrahedron to move in space at every iteration via reflection, expansion, inside contraction, outside contraction and shrink operations. We have used different colors to show
The optimization approach used for tuning the plants is shown in Fig. 3. The NelderMeadmethod was used for the simulation  for optimizing the parameters of the fractional PID controller. This method finds out minimum of a function from more than one independent variables without using derivatives. A simplex has n+1 points in n dimensional space, which represents the number of independent variables. For tuning of fractional PID controller, the integrated square error (ISE) was chosen as the performance index. This measure is more useful because the range of error was large in most cases and was thus more appropriate for designing the controller. ., and it is given for unity feedback system considering unit step input,
function about y (see ), and then the problems (1)-(3) essentially belong to the convex programming problem. Obviously the recourse function is not diffe- rential, so the Newton method proposed in  is no longer applicable. In order to solve this problem, we design a solution based on the improved Nelder-Meadmethod. The experimental results show that the method is effective.
For optimization purpose Nelder-Mead Simplex method for nonlinear unconstrained minimization is used as Nelder-Mead Simplex method is a direct search method which does not require any derivative information, so it can optimize non- stationary functions, as needed for the problems under study [9, 10, 11]. Nelder-Mead Simplex method is also widely used for solving parameter estimation and similar statistical problems, where the function values are uncertain, noisy or even discontinuous [12, 13]. The Nelder-Mead simplex method gained popularity very quickly. At earlier time, due to its simplicity and low storage requirements, it was ideally suited for use on minicomputers especially in laboratories i.e. it is effective and computationally compact. Although the method is relatively old and considering recent advances in direct search methods, the Nelder-Meadmethod is still among the most popular direct search methods in practice [14, 15].
Abstract— This paper describes the design of a patch antenna on FR4 substrate. It deals with the determination of conditions for the simulation and subsequent optimization of the dimensions using the Nelder-Meadmethod according to two parameters - antenna gain and S11 parameter. It uses the Comsol Multiphysics program. Operating frequency of the patch antenna is 5,6GHz.
The Nelder-Mead  is a direct search method that attempts to minimize a non-linear unconstrained optimization and does not use the gradient information. This derivative free optimization technique can handle discontinuous or non-smooth functions. The Nelder-Meadmethod (NM) attempts to minimize nonlinear function of real variables using only function values, without any derivative information (explicit or implicit). The NM thus falls in the general class of direct search methods.
Abstract—In this paper, a new measurement method is proposed to estimate the complex permittivity for each layer in a bi-layer dielectric material using a Ku-band rectangular waveguide WR62. The S ij - parameters at the reference planes in the rectangular waveguide loaded by a bi-layer material sample are measured as a function of frequency using the E8634A Network Analyzer. Also, by applying the transmission lines theory, the expressions for these parameters as a function of complex permittivity of each layer are calculated. The Nelder-Mead algorithm is then used to estimate the complex permittivity of each layer by matching the measured and calculated the S ij -parameters. This method has been
Abstract. The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from nonsmooth analysis, and our framework is based on recent results for the MADS sampling algorithms.
The “digital image inpainting” was firstly put forward on the international conference in 2000 in Singapore. There are many typical image inpainting algorithms proposed by researchers during the past decade. The BSCB  model was presented by Sapiro, Caselles, Bertalmio and Ballester. The TV (total variation) model  was proposed by Chan and his team. The CDD (curvature driven diffusions) model  was introduced by Shen J and Chan T. and. An isotropic diffusion of fast image inpainting was proposed by Oliverira. There have been a very few algorithms that utilize the advantages of both the image inpainting methods i.e. the structure recreation and texture synthesis algorithms. One such work was proposed in the paper by Criminisi et al. . Exemplar based image inpainting is a very simpler and faster method compare to other which is not suffer from any blurry effect. First the object is removing and then it is filled by some special
The Nelder-Mead simplex method (NM) is a derivative free optimization method. Since NM does not need to calculate derivatives, it can be performed at much lower computational cost than optimization methods that require derivative information. This reduction in computational cost is one of the main reasons it was chosen for study in this thesis. NM starts by constructing a simplex with n+1 points, where n is the number of parameters. Thus, for a two parameter problem there will be three points that form a triangle. Then a weighted sum of squares is computed at each point. The point with the highest value, assuming minimization, is reflected through the centroid of the simplex. Following this a weighted sum of squares is computed for the new point. If the value of the new point is the lowest of them the process continues by reflecting the point with the highest value. However, if the value of the new point is higher than the other points the simplex is compressed and the new point is reflected closer. If the value of the new point is neither the lowest nor the highest then start at the top and reflect again. These are repeated until the simplex converges. A visualization of the Nelder-Mead simplex method can be seen in Figure 2.2.
in 1971. The material is readily available, although with one major drawback. There are approximately 1,000 boxes of filed correspondence which include contract documents, bills of sale, contractors’, sub-contractors’ and nominated suppliers’ letters; most of which have little bearing on design decisions and factors which strike at the heart of architectural history. In addition to this research material there are hundreds of rolls of drawings and photographs. These consist of working drawings, rather than original design drawings and only com municate the ideas of architecture to the practical-minded builder and his workmen. The McKim, Mead and White collection is also a hodge-podge of projects, a few dating from the l$90’s, but many after 1910. A huge structure may be represented by a small file containing two letters—one to and another from Lawrence Grant White when the material was disposed of. A small residence, on the other hand, may consist of a dozen boxes. Some of the material is invaluable for a specific pro
DOI: 10.4236/fns.2018.912103 1430 Food and Nutrition Sciences resistance to high concentrations of ethanol and the osmotic stress of honey  . These strains, quite similar to those used in oenology, are responsible for the biotransformation of glucose and fructose, in ethanol and carbon dioxide . The volatile acidities established in Bessoudioury beverages, lower than ac- ceptable limits in oenology , corroborate the hypothesis of a single alcoholic fermentation. This further confirms its sanitary and organoleptic quality. The acid pH (pH = 3) of both wines and finished mead is incompatible with the growth of most microorganisms. To this is added the bactericidal and antifungal effect of ethanol.
Drawing on the temporal continuity of past, present and future as articulated by Mead (1932), the linguistic pragmatics of Austin (1962) and Searle (1969), and a conception of agency as inherently social and dynamic (Emirbayer & Mische, 1998), we understand talk as the ongoing gesture and response of conversation, where it is the intentional and contextual aspects of this talk that actually perform, rather than merely describe, the actions of change (Taylor, et al., 1996). This approach reflects recent developments in the organizational literature on practice (e.g. Miettinen, Samra-Fredericks, & Yanow, 2009), where what people actually do is understood as a temporal unfolding of agentic action (Simpson, 2009; 2013). Thus temporality and agency are key constructs for understanding organizational change.