Optimization and Distance Function Proce-dures in Aberration Criteria of Efficient Frac-tional Factorial Design

2021 ◽  
Vol 12 (5) ◽  
pp. 667-673
Author(s):  
Salawu I.S.
Keyword(s):  
Factorial Design ◽  
Distance Function ◽  
Orthogonal Array ◽  
Optimization Procedure ◽  
Optimality Criteria ◽  
Minimum Aberration ◽  
Minimum Moment Aberration ◽  
Orthogonal Property ◽  
Minimum Moment

An efficient orthogonal array was constructed with near balance and near the orthogonal property for the lowest common multiples of runs, using the balance coefficient criteria for determining near balance and J2 optimality criteria for orthogonal properties. The optimization and distance function forms of balance coefficient criteria were used for the classification of the designs. The Minimum Moment Aberration (MMA) and Minimum Aberration Projection (MAP) are compared using the optimization and distance function to determine the near balance criteria. The result indicated that, the MMA and MAP criteria was efficient using the optimization procedure of the balance coefficient.

Setting Attribute Weights for Nearest Neighbor Learning Algorithms Using C4.5

1997 ◽  
Vol 11 (03) ◽  
pp. 405-415 ◽  
Author(s):  
Charles X. Ling ◽  
John J. Parry ◽  
Handong Wang
Keyword(s):  
Machine Learning ◽  
Decision Trees ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Learning Algorithms ◽  
Simple Approach ◽  
Nearest Neighbour ◽  
Attribute Weights ◽  
New Methods

Nearest Neighbour (NN) learning algorithms utilize a distance function to determine the classification of testing examples. The attribute weights in the distance function should be set appropriately. We study situations where a simple approach of setting attribute weights using decision trees does not work well, and design three improvements. We test these new methods thoroughly using artificially generated datasets and datasets from the machine learning repository.

scholarly journals Consumer Preferences for Geranium Flower Color, Leaf Variegation, and Price in Five U.S. Markets

HortScience ◽  
1997 ◽  
Vol 32 (3) ◽  
pp. 510C-510
Author(s):  
Bridget Behe ◽  
Robert Nelson ◽  
Susan Barton ◽  
Charles Hall ◽  
Steve Turner ◽  
...  
Keyword(s):  
Factorial Design ◽  
Orthogonal Array ◽  
Consumer Preferences ◽  
Flower Color ◽  
Demographic Characteristics ◽  
Marketing Strategies ◽  
Purchase Behavior ◽  
Photographic Images ◽  
Leaf Variegation ◽  
Purchase Likelihood

Consumers in five U.S. markets evaluated photographs of geranium plants with regard to purchase likelihood. Photographic images were colored electronically to produce uniform geranium plants with five flower colors (pink, white, red, lavender, and blue) and three leaf variegation patterns (dark zone, white zone, and no zonal pattern). Photographs were mounted on cards with five selected price points ranging from ($1.39 to $2.79). We randomly generated an orthogonal array, partial-factorial design for consumers to rate a reduced number of choices. Consumers shopping in cooperating garden centers located in Dallas, Texas; Montgomery, Ala.; Athens, Ga.; Charlotte, N.C.; and Wilmington, Dela., rated 25 photographs on the basis of their likelihood to purchase the plants shown. Conjoint analysis revealed that customers in the Georgia garden center placed the highest proportion of their decision to buy on leaf variegation (29%), while customers in the Alabama outlet placed the most emphasis on price (46% of the decision). Shoppers in Texas valued flower color most highly (58% of their decision to buy). Demographic characteristics and past purchase behavior also varied widely, suggesting diverse marketing strategies for geraniums.

scholarly journals Optimization of Split-Plot Design in the Context of Mixture Process Variable Settings

2021 ◽  
pp. 1-36
Author(s):  
Samson W. Wanyonyi ◽  
Ayubu A. Okango ◽  
Julius K. Koech ◽  
Betty C. Korir
Keyword(s):  
Factorial Design ◽  
Process Variable ◽  
Optimality Criteria ◽  
Mixture Design ◽  
Parameter Estimates ◽  
Process Variables ◽  
Split Plot ◽  
Set Up ◽  
Plot Structure ◽  
Plot Design

In the presence of process variables, a mixture design has become well-known in statistical modeling due to its utility in modeling the blending surface, which empirically predicts any mixture's response and serves as the foundation for optimizing the expected response blends of different components.  In the most common practical situation involving a mixture-process variable, restricted randomization occurs frequently. This problem is solved when the split-plot layout arrangement is used within the constraints. This study's primary goal was to find the best split-plot design (SPD) for the settings mixture-process variables. The SPD was made up of a simplex centroid design (SCD) of four mixture blends and a factorial design with a central composite design (CCD) of the process variable and compared six different context split-plot structure arrangement.  We used JMP software version 15 to create D-optimal split-plot designs. The study compared the constructed designs' relative efficiency using A-, D-, I-, and G- optimality criteria. Furthermore, a graphical technique (fraction of design space plot) was used to display, explain, and evaluate experimental designs' performance in terms of precision of the six designs' variance prediction properties. We discovered that arranging subplots with more SCD points than pure mixture design points within SPD with two high process variables is more helpful and provides more precise parameter estimates. We recommend using SPDs in experiments involving mixture process settings developments to measure the mixture components' interaction effects and the processing conditions. Also, the investigation should be set up at each of the points of a factorial design.

THE PARAMETER-DEPENDENT FERMION STATES FOR MOLECULES WITH SYMPLECTIC SYMMETRY

2006 ◽  
Vol 05 (04) ◽  
pp. 779-799
Author(s):  
C. C. SUN ◽  
B. F. LI ◽  
Z. S. LI ◽  
H. X. ZHANG ◽  
X. R. HUANG
Keyword(s):  
Quantum Chemistry ◽  
Explicit Form ◽  
Symplectic Group ◽  
Similarity Transformation ◽  
Optimization Procedure ◽  
Complete Classification ◽  
Branching Rule ◽  
Parameter Dependent

Under a certain kind of similarity transformation, a parameter-dependent (abbreviated as PD) symplectic group chain Sp(2M) ⊃ Sp(2M - 2) ⊃ ⋯ ⊃ Sp(2) that is characterized by a set of pairing parameters is introduced to build up the PD antisymmetrized fermion states for molecules with symplectic symmetry, and these states will be useful in carrying out the optimization procedure in quantum chemistry. In order to make a complete classification of the states, a generalized branching rule associated with the symplectic group chain is proposed. Further, we are led to the result that the explicit form of the PD antisymmetrized fermion states is obtained in terms of M one-particle operators and M geminal operators.

Structural Optimization of Building Materials Using Optimality Criteria Approach and its Realization in ANSYS

2011 ◽  
Vol 321 ◽  
pp. 55-58 ◽  
Author(s):  
Ruo Hong Zhao
Keyword(s):  
Structural Optimization ◽  
Optimization Algorithm ◽  
Design Variable ◽  
Building Materials ◽  
Iteration Process ◽  
Optimization Procedure ◽  
Optimality Criteria ◽  
Iteration Algorithm ◽  
Explicit Formulation ◽  
Key Points

In this paper, the structural optimization of building materials is discussed focusing on the explicit formulation of the constraints and the optimal iteration algorithm. The whole optimization procedure was realized by programming using the APDL provided by the commercial software ANSYS. Some key points in programming are discussed such as how to determine a design variable is active or inactive during optimization iteration process. Finally an example was illustrated to demonstrate the validation of the optimization algorithm and the programming method using APDL.

A Bound on Modeling Error in Observable Operator Models and an Associated Learning Algorithm

2009 ◽  
Vol 21 (9) ◽  
pp. 2687-2712 ◽  
Author(s):  
Ming-Jie Zhao ◽  
Herbert Jaeger ◽  
Michael Thon
Keyword(s):  
Markov Models ◽  
Learning Algorithm ◽  
Expectation Maximization Algorithm ◽  
Optimization Procedure ◽  
Optimality Criteria ◽  
Matrix Formalism ◽  
Statistical Efficiency ◽  
Modeling Error ◽  
Transformation Matrices ◽  
Optimization Task

Observable operator models (OOMs) generalize hidden Markov models (HMMs) and can be represented in a structurally similar matrix formalism. The mathematical theory of OOMs gives rise to a family of constructive, fast, and asymptotically correct learning algorithms, whose statistical efficiency, however, depends crucially on the optimization of two auxiliary transformation matrices. This optimization task is nontrivial; indeed, even formulating computationally accessible optimality criteria is not easy. Here we derive how a bound on the modeling error of an OOM can be expressed in terms of these auxiliary matrices, which in turn yields an optimization procedure for them and finally affords us with a complete learning algorithm: the error-controlling algorithm. Models learned by this algorithm have an assured error bound on their parameters. The performance of this algorithm is illuminated by comparisons with two types of HMMs trained by the expectation-maximization algorithm, with the efficiency-sharpening algorithm, another recently found learning algorithm for OOMs, and with predictive state representations (Littman & Sutton, 2001 ) trained by methods representing the state of the art in that field.

scholarly journals Size of samples and homogenizers during classification of damaged soybeans

2019 ◽  
Vol 23 (5) ◽  
pp. 378-382
Author(s):  
José R. Quirino ◽  
Osvaldo Resende ◽  
Natalia N. Fonseca ◽  
Daniel E. C. de Oliveira ◽  
Fatima C. Parizzi ◽  
...  
Keyword(s):  
Factorial Design ◽  
Representative Sample ◽  
Grain Quality ◽  
Sample Sizes ◽  
Tukey Test ◽  
Student’S T ◽  
Sample Homogenization ◽  
Different Levels ◽  
Student’S T Test

ABSTRACT Grain quality determination involves important stages such as collection of the representative sample, homogenization, and dilution. The interrelation among sampling, homogenization, and working sample size is essential to the reliability of the information generated. Therefore, this work aimed to analyse the performance of mechanical homogenizers used in the commercialization of grains in Brazil, as a function of the size of the working sample masses during grain classification. The samples were homogenized and diluted in Boerner, 16:1 multichannel splitter, and 4:1 multichannel splitter until reaching masses of 0.025, 0.050, 0.075, 0.100 and 0.125 kg to determine the level of damaged grains. A 3 x 4 x 5 factorial design was used, meaning three treatments relative to homogenizers (Boerner, 16:1 multichannel splitter, and 4:1 multichannel splitter), four dilutions (4, 8, 12 and 16% damaged grains), and five grain sample sizes (0.025, 0.050, 0.075, 0.100 and 0.125 kg) with nine repetitions. The means were compared by Tukey test and to the original means of prepared samples (4, 8, 12, and 16%) by Student’s t-test. Working samples can be utilized with masses between 0.025 and 0.125 kg to classify damaged soybeans grains. The devices Boerner, 16:1 multichannel splitter, and 4:1 multichannel splitter are similar in the reduction and homogenization of soybean samples for different levels of damaged grains and sample sizes.

Surface Shape Optimization of Tire Pattern by Optimality Criteria

2003 ◽  
Vol 31 (1) ◽  
pp. 2-18 ◽  
Author(s):  
Y. Nakajima ◽  
F. Takahashi ◽  
A. Abe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Friction Coefficient ◽  
Flat Surface ◽  
Optimization Procedure ◽  
Optimality Criteria ◽  
Surface Shape ◽  
Contact Pressure Distribution ◽  
Vehicle Handling ◽  
Rubber Block

Abstract A new optimization procedure to design the surface shape of tire patterns is proposed in which the optimality criteria is combined with finite element method. The effectiveness of this new procedure to control tread-element contact pressure distribution was verified by building and testing the rubber block samples. The objective function was the pressure uniformity on the block and the constraint was to keep the contact area in the optimization process. The shape of the optimized surface was round at the edges and concave at the center where the pressure was large in the flat surface block. The pressure of the block with the optimized surface became uniform and the friction coefficient increased 10% on dry compared with the flat surface block. Furthermore, this procedure was applied to complicated block shapes such as tire patterns and it was verified that the optimized surface effectively improved vehicle handling, riding comfort and irregular wear.

Connection between uniformity and minimum moment aberration

Metrika ◽  
2008 ◽  
Vol 70 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Hong Qin ◽  
Na Zou ◽  
Kashinath Chatterjee
Keyword(s):  
Minimum Moment Aberration ◽  
Minimum Moment

scholarly journals Energy and Environment Performance of Resource-Based Cities in China: A Non-Parametric Approach for Estimating Hyperbolic Distance Function

2020 ◽  
Vol 17 (13) ◽  
pp. 4795
Author(s):  
Yao Hu ◽  
Tai-Hua Yan ◽  
Feng-Wen Chen
Keyword(s):  
Distance Function ◽  
Resource Dependence ◽  
Environmental Efficiency ◽  
Hyperbolic Distance ◽  
Annual Growth Rate ◽  
Undesirable Output ◽  
Green Development ◽  
Technological Efficiency ◽  
Efficiency And Productivity

Scientific determination of energy and environmental efficiency and productivity is the key foundation of green development policy-making. The hyperbolic distance function (HDF) model can deal with both desirable output and undesirable output asymmetrically, and measure efficiency from the perspective of “increasing production and reducing pollution”. In this paper, a nonparametric linear estimation method of an HDF model including uncontrollable index and undesirable output is proposed. Under the framework of global reference, the changes of energy environmental efficiency and productivity and their factorization of 107 resource-based cities in China from 2003 to 2018 are calculated and analyzed. With the classification of resource-based cities by resource dependence (RD) and region, we discuss the feature in green development quality of those cities. The results show that: (1) On the whole, the average annual growth rate of energy and environmental productivity of resource-based cities in China is 2.6%, which is mainly due to technological changes. The backward of relative technological efficiency hinders the further growth of productivity, while the scale diseconomy is the main reason for the backward of relative technological efficiency. (2) For the classification of RD, the energy and environmental efficiency of the high-dependent group are significantly lower than the other two, and the growth of productivity of the medium-dependent group is the highest. (3) In terms of classification by region, the energy and environmental efficiency of the eastern region is the highest, and that of the middle and western regions is not as good as that of the eastern and northeastern regions. The middle region shows the situation of “middle collapse” in both static efficiency and dynamic productivity change, and the main reason for its low productivity growth is the retreat of relatively pure technical efficiency. This conclusion provides practical reference for the classification and implementation of regional energy and environmental policies.

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