scholarly journals Dual Modelling of Permutation and Injection Problems

2004 ◽  
Vol 21 ◽  
pp. 357-391 ◽  
Author(s):  
B. Hnich ◽  
B. M. Smith ◽  
T. Walsh
Keyword(s):  
Dual Variable ◽  
Combined Model ◽  
Multiple Viewpoints ◽  
Constraint Program ◽  
Decision Variables ◽  
Primal Dual ◽  
Combined Models ◽  
Dual Variables ◽  
Primal And Dual ◽  
Permutation Problems

When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general methodology for comparing different constraint models.

scholarly journals Combined Tomography and Epithelial Thickness Mapping for Diagnosis of Keratoconus

2016 ◽  
Vol 27 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Ronald H. Silverman ◽  
Raksha Urs ◽  
Arindam RoyChoudhury ◽  
Timothy J. Archer ◽  
Marine Gobbe ◽  
...  
Keyword(s):  
Discriminant Analysis ◽  
Corneal Thickness ◽  
High Frequency Ultrasound ◽  
Combined Model ◽  
Variable Model ◽  
Linear Discriminant ◽  
Combined Models ◽  
Combining Information ◽  
Variance Explained ◽  
Frequency Ultrasound

Purpose Scanning Scheimpflug provides information regarding corneal thickness and 2-surface topography while arc-scanned high-frequency ultrasound allows depiction of the epithelial and stromal thickness distributions. Both techniques are useful in detection of keratoconus. Our aim was to develop and test a keratoconus classifier combining information from both methods. Methods We scanned 111 normal and 30 clinical keratoconus subjects with Artemis-1 and Pentacam data. After selecting one random eye per subject, we performed stepwise linear discriminant analysis on a dataset combining parameters generated by each method to obtain classification models based on each technique alone and in combination. Results Discriminant analysis resulted in a 4-variable model (R2 = 0.740) based on Artemis data alone and a 4-variable model (R2 = 0.734) using Pentacam data alone. The combined model (R2 = 0.828) consisted of 3 Artemis- and 4 Pentacam-derived variables. The combined model R value was significantly higher than either model alone (p = 0.031, one-tailed). In cross-validation, Artemis had 100% sensitivity and 99.2% specificity, Pentacam had 97.3% sensitivity and 98.0% specificity, and the combined model had 97.3% sensitivity and 100% specificity. Conclusions Pentacam, Artemis, and combined models were all effective in distinguishing normal from clinical keratoconus subjects. From the standpoint of variance explained by the model (R2 values), the combined model was most effective. Application of the model to early and subclinical keratoconus will ultimately be required to assess the effectiveness of the combined approach.

scholarly journals An Improved Decomposition Approach and its Computational Technique for Analyzing Primal-Dual Relationship in LP & LFP Problems

2014 ◽  
Vol 33 ◽  
pp. 65-75
Author(s):  
HK Das ◽  
M Babul Hasan
Keyword(s):  
Computational Technique ◽  
Dual Decomposition ◽  
Linear Fractional Programming ◽  
Decomposition Approach ◽  
Dual Approach ◽  
Numerical Examples ◽  
Primal Dual ◽  
Primal And Dual ◽  
Relationship Of ◽  
The Relationship

In this paper, we study the methodology of primal dual solutions in Linear Programming (LP) & Linear Fractional Programming (LFP) problems. A comparative study is also made on different duals of LP & LFP. We then develop an improved decomposition approach for showing the relationship of primal and dual approach of LP & LFP problems by giving algorithm. Numerical examples are given to demonstrate our method. A computer programming code is also developed for showing primal and dual decomposition approach of LP & LFP with proper instructions using AMPL. Finally, we have drawn a conclusion stating the privilege of our method of computation. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 65-75 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17660

scholarly journals Multiscale Combined Model Based on Run-Length-Judgment Method and Its Application in Oil Price Forecasting

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wang Shu-ping ◽  
Hu Ai-mei ◽  
Wu Zhen-xin ◽  
Liu Ya-qing ◽  
Bai Xiao-wei
Keyword(s):  
Low Frequency ◽  
Oil Price ◽  
Support Vector ◽  
Combined Model ◽  
Run Length ◽  
Price Series ◽  
Mode Decomposition ◽  
Combined Models ◽  
Artificial Neural Network Ann ◽  
Combined Forecasting

Forecasting of oil price is an important area of energy market research. Based on the idea of decomposition-reconstruction-integration, this paper built a new multiscale combined forecasting model with the methods of empirical mode decomposition (EMD), artificial neural network (ANN), support vector machine (SVM), and time series methods. While building the model, we proposed a new idea to use run length judgment method to reconstruct the component sequences. Then this model was applied to analyze the fluctuation and trend of international oil price. Oil price series was decomposed and reconstructed into high frequency, medium frequency, low frequency, and trend sequences. Different features of fluctuation can be explained by irregular factors, season factors, major events, and long-term trend. Empirical analysis showed that the multiscale combined model obtained the best forecasting result compared with single models including ARIMA, Elman, SVM, and GARCH and combined models including ARIMA-SVM model and EMD-SVM-SVM method.

scholarly journals Current Techniques for Diabetes Prediction: Review and Case Study

2019 ◽  
Vol 9 (21) ◽  
pp. 4604 ◽  
Author(s):  
Larabi-Marie-Sainte ◽  
Aburahmah ◽  
Almohaini ◽  
Saba
Keyword(s):  
Machine Learning ◽  
Deep Learning ◽  
Recent Survey ◽  
Combined Model ◽  
Common Diseases ◽  
Combined Models ◽  
Diabetes Prediction

Diabetes is one of the most common diseases worldwide. Many Machine Learning (ML) techniques have been utilized in predicting diabetes in the last couple of years. The increasing complexity of this problem has inspired researchers to explore the robust set of Deep Learning (DL) algorithms. The highest accuracy achieved so far was 95.1% by a combined model CNN-LSTM. Even though numerous ML algorithms were used in solving this problem, there are a set of classifiers that are rarely used or even not used at all in this problem, so it is of interest to determine the performance of these classifiers in predicting diabetes. Moreover, there is no recent survey that has reviewed and compared the performance of all the proposed ML and DL techniques in addition to combined models. This article surveyed all the ML and DL techniques-based diabetes predictions published in the last six years. In addition, one study was developed that aimed to implement those rarely and not used ML classifiers on the Pima Indian Dataset to analyze their performance. The classifiers obtained an accuracy of 68%–74%. The recommendation is to use these classifiers in diabetes prediction and enhance them by developing combined models.

Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem

2007 ◽  
Vol 19 (4) ◽  
pp. 552-564 ◽  
Author(s):  
Pierre Hansen ◽  
Jack Brimberg ◽  
Dragan Urošević ◽  
Nenad Mladenović
Keyword(s):  
Variable Neighborhood Search ◽  
Location Problem ◽  
Plant Location ◽  
Neighborhood Search ◽  
Dual Variable ◽  
Primal Dual

Resizing: Predicting a New Geometric Programming Optimum as Coefficients Vary

1984 ◽  
Vol 106 (1) ◽  
pp. 11-16
Author(s):  
D. J. Wilde
Keyword(s):  
Design Problem ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Matrix Equations ◽  
Dual Variable ◽  
Method Of Least Squares ◽  
Satisfactory Solution ◽  
Geometric Program ◽  
The Matrix ◽  
Dual Variables

Imagine that an optimal solution is available for a constrained geometric program, and suppose one wishes a satisfactory solution for greatly different values of some of the coefficients. An estimate can be constructed by using the values of the dual variables for the old optimum in the invariance conditions for the new problem. Although these are inconsistent except at the precise optimum, a unique primal solution can easily be generated from them by the method of least squares with individual equations weighted by the value of the corresponding dual variable. The matrix equations for these linear operations are derived and applied to a well-known merchant fleet design problem. The predictions are remarkably accurate—1.4 percent error for a 100 percent coefficient change.

scholarly journals Improved Lagrangian-PPA based prediction correction method for linearly constrained convex optimization

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanfei You ◽  
Suhong Jiang
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Correction Method ◽  
Lagrangian Function ◽  
Convex Optimization Problem ◽  
Constrained Convex Optimization ◽  
Linearly Constrained ◽  
Dual Variables ◽  
Primal And Dual ◽  
Linearly Constrained Convex Optimization

<p style='text-indent:20px;'>This paper presents an improved Lagrangian-PPA based prediction correction method to solve linearly constrained convex optimization problem. At each iteration, the predictor is achieved by minimizing the proximal Lagrangian function with respect to the primal and dual variables. These optimization subproblems involved either admit analytical solutions or can be solved by a fast algorithm. The new update is generated by using the information of the current iterate and the predictor, as well as an appropriately chosen stepsize. Compared with the existing PPA based method, the parameters are relaxed. We also establish the convergence and convergence rate of the proposed method. Finally, numerical experiments are conducted to show the efficiency of our Lagrangian-PPA based prediction correction method.</p>

scholarly journals A primal-dual exterior point algorithm for linear programming problems

2009 ◽  
Vol 19 (1) ◽  
pp. 123-132 ◽  
Author(s):  
Nikolaos Samaras ◽  
Angelo Sifelaras ◽  
Charalampos Triantafyllidis
Keyword(s):  
Linear Programming ◽  
Computational Study ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Dual Algorithm ◽  
Optimal Linear ◽  
Primal Dual ◽  
Primal And Dual ◽  
Two Phases ◽  
Feasible Solutions

The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

scholarly journals CT-based Radiomics Combined with Signs: A Valuable Tool to help Physician Discriminate COVID-19 and Other Viral Pneumonia

2020 ◽  
Author(s):  
Yilong Huang ◽  
Zhenguang Zhang ◽  
Xiang Li ◽  
Yunhui Yang ◽  
Zhipeng Li ◽  
...  
Keyword(s):  
Roc Analysis ◽  
Operating Characteristic ◽  
Discrimination Performance ◽  
Predictive Performance ◽  
Potential Method ◽  
Classification Performance ◽  
Viral Pneumonia ◽  
Combined Model ◽  
Training Cohort ◽  
Combined Models

Abstract Background: In this COVID-19 pandemic, the differential diagnosis of different viral types of pneumonia is still challenging. We aimed to assess the classification performance of computed tomography (CT)-based CT signs and radiomics features for discriminating COVID-19 pneumonia and other viral pneumonia.Methods: A total of 181 patients with confirmed viral pneumonia (COVID-19: 89 cases, Non-COVID-19: 92 cases; training cohort: 126 cases; test cohort: 55 cases) were collected retrospectively in this study. Pneumonia signs and radiomics features were extracted from the initial unenhanced chest CT images to build independent and combined models. The predictive performance of the radiomics model and the combined model were evaluated using an intra-cross validation cohort. Diagnostic performance of two models was assessed via receiver operating characteristic (ROC) analysis.Results: The combined models consisted of 3 significant CT signs and 14 selected features and demonstrated better discrimination performance between COVID-19 and Non-COVID-19 pneumonia than the single radiomics model. For the radiomics model along, the area under the ROC curve (AUC) were 0.904 (sensitivity, 85.5%; specificity, 84.4%; accuracy, 84.9%) in the training cohort and 0.866 (sensitivity, 77.8%; specificity, 78.6%; accuracy, 78.2%) in the test cohort. After combining CT signs and radiomics features, AUC of the combined model for the training cohort was 0.956 (sensitivity, 91.9%; specificity, 85.9%; accuracy, 88.9%), while that for the test cohort was 0.943 (sensitivity, 88.9%; specificity, 85.7%; accuracy, 87.3%).Conclusion: CT-based radiomics combined with signs might be a potential method for distinguishing COVID-19 and other viral pneumonia with satisfactory performance.

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