scholarly journals A Direct Model for Triangular Neutrosophic Linear Programming

2020 ◽  
pp. 19-28
Author(s):  
S. A. Edalatpanah ◽  
Keyword(s):  
Linear Programming ◽  
Numerical Experiments ◽  
Direct Algorithm ◽  
Right Hand ◽  
Wide Range ◽  
Direct Model ◽  
Triangular Neutrosophic Numbers

This paper aims to propose a new direct algorithm to solve the neutrosophic linear programming where the variables and right-hand side represented with triangular neutrosophic numbers. The effectiveness of the proposed procedure is illustrated through numerical experiments. The extracted results show that the new algorithm is straightforward and could be useful to guide the modeling and design of a wide range of neutrosophic optimization.

scholarly journals A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues

2021 ◽  
Author(s):  
Sven-Erik Ekström ◽  
Paris Vassalos
Keyword(s):  
Distribution Function ◽  
Asymptotic Distribution ◽  
Numerical Experiments ◽  
Toeplitz Matrices ◽  
Future Research ◽  
Research Directions ◽  
Numerical Examples ◽  
Working Hypothesis ◽  
Wide Range ◽  
Future Research Directions

AbstractIt is known that the generating function f of a sequence of Toeplitz matrices {Tn(f)}n may not describe the asymptotic distribution of the eigenvalues of Tn(f) if f is not real. In this paper, we assume as a working hypothesis that, if the eigenvalues of Tn(f) are real for all n, then they admit an asymptotic expansion of the same type as considered in previous works, where the first function, called the eigenvalue symbol $\mathfrak {f}$ f , appearing in this expansion is real and describes the asymptotic distribution of the eigenvalues of Tn(f). This eigenvalue symbol $\mathfrak {f}$ f is in general not known in closed form. After validating this working hypothesis through a number of numerical experiments, we propose a matrix-less algorithm in order to approximate the eigenvalue distribution function $\mathfrak {f}$ f . The proposed algorithm, which opposed to previous versions, does not need any information about neither f nor $\mathfrak {f}$ f is tested on a wide range of numerical examples; in some cases, we are even able to find the analytical expression of $\mathfrak {f}$ f . Future research directions are outlined at the end of the paper.

A method for solving linear programming with interval-valued trapezoidal fuzzy variables

2018 ◽  
Vol 52 (3) ◽  
pp. 955-979 ◽  
Author(s):  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Auxiliary Problem ◽  
Coefficient Matrix ◽  
Uncertain Parameters ◽  
Fuzzy Variables ◽  
Right Hand ◽  
Fuzzy Cost ◽  
The Right ◽  
Interval Valued

An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships between these problems leading to a solution for the primary problem. It is demonstrated that study of LP problems with interval-valued trapezoidal fuzzy variables gives rise to the same expected results as those obtained for LP with trapezoidal fuzzy variables.

scholarly journals Comparative verification in complex topography

2021 ◽  
Author(s):  
Jonas Bhend ◽  
Jean-Christophe Orain ◽  
Vera Schönenberger ◽  
Christoph Spirig ◽  
Lionel Moret ◽  
...  
Keyword(s):  
Weather Forecasting ◽  
Absolute Error ◽  
Time Of Day ◽  
Probabilistic Forecasts ◽  
Wide Range ◽  
Direct Model ◽  
Forecasting System ◽  
The Mean ◽  
Update Frequency ◽  
Core Activity

<p>Verification is a core activity in weather forecasting. Insights from verification are used for monitoring, for reporting, to support and motivate development of the forecasting system, and to allow users to maximize forecast value. Due to the broad range of applications for which verification provides valuable input, the range of questions one would like to answer can be very large. Static analyses and summary verification results are often insufficient to cover this broad range. To this end, we developed an interactive verification platform at MeteoSwiss that allows users to inspect verification results from a wide range of angles to find answers to their specific questions.</p><p>We present the technical setup to achieve a flexible yet performant interactive platform and two prototype applications: monitoring of direct model output from operational NWP systems and understanding of the capabilities and limitations of our pre-operational postprocessing. We present two innovations that illustrate the user-oriented approach to comparative verification adopted as part of the platform. To facilitate the comparison of a broad range of forecasts issued with varying update frequency, we rely on the concept of time of verification to collocate the most recent available forecasts at the time of day at which the forecasts are used. In addition, we offer a matrix selection to more flexibly select forecast sources and scores for comparison. Doing so, we can for example compare the mean absolute error (MAE) for deterministic forecasts to the MAE and continuous ranked probability scores of probabilistic forecasts to illustrate the benefit of using probabilistic forecasts.</p>

scholarly journals Linear programming with interval right hand sides

2010 ◽  
Vol 17 (3) ◽  
pp. 397-408 ◽  
Author(s):  
Virginie Gabrel ◽  
Cécile Murat ◽  
Nabila Remli
Keyword(s):  
Linear Programming ◽  
Right Hand

scholarly journals Deadbeat-Based Model Predictive Voltage Control for a Sensorless Five-Phase Induction Motor Drive

2020 ◽  
Vol 2020 ◽  
pp. 1-30
Author(s):  
Mahmoud A. Mossa ◽  
Nguyen Vu Quynh ◽  
Hamdi Echeikh ◽  
Ton Duc Do
Keyword(s):  
Induction Motor ◽  
Direct Torque Control ◽  
Voltage Control ◽  
Torque Control ◽  
Computational Time ◽  
Motor Drive ◽  
Induction Motor Drive ◽  
Wide Range ◽  
Direct Model ◽  
Rotor Flux

This paper introduces a direct model predictive voltage control (DMP VC) for a sensorless five-phase induction motor drive. The operation of the proposed sensorless DMP VC is based on the direct control of the applied stator voltages instead of controlling the torque and flux as in model predictive direct torque control (MP DTC). Thus, the simplicity of the control system is enhanced, which saves the computational time and reduces the commutation losses as well. The methodology based on which the proposed sensorless DMP VC performs its operation depends on minimizing a cost function that calculates the error between the reference and actual values of the direct and quadrature (d-q) axes components of stator voltages. The reference values of d-q components of stator voltages are obtained through incorporating the deadbeat control within the proposed model predictive system. A robust back-stepping observer is proposed for estimating the speed, stator currents, rotor flux, and rotor resistance. The validity of the proposed sensorless DMP VC is confirmed through performing detailed and extensive comparisons between the proposed DMP VC and MP DTC approach. The obtained results state that the drive is exhibiting better performance under the proposed DMP VC with less ripples content and reduced computational burden. Moreover, the proposed back-stepping observer has confirmed its effectiveness in estimating the speed and other variables for a wide range of speed operation.

scholarly journals Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials

2009 ◽  
Vol 24 (12) ◽  
pp. 3653-3663 ◽  
Author(s):  
Taihua Zhang ◽  
Peng Jiang ◽  
Yihui Feng ◽  
Rong Yang
Keyword(s):  
Numerical Experiments ◽  
Spherical Indentation ◽  
Numerical Verification ◽  
Instrumented Indentation ◽  
Plastic Properties ◽  
Wide Range ◽  
Validity Range ◽  
Indentation Tests ◽  
Properties Of Materials ◽  
Indentation Methods

Instrumented indentation tests have been widely adopted for elastic modulus determination. Recently, a number of indentation-based methods for plastic properties characterization have been proposed, and rigorous verification is absolutely necessary for their wide application. In view of the advantages of spherical indentation compared with conical indentation in determining plastic properties, this study mainly concerns verification of spherical indentation methods. Five convenient and simple models were selected for this purpose, and numerical experiments for a wide range of materials are carried out to identify their accuracy and sensitivity characteristics. The verification results show that four of these five methods can give relatively accurate and stable results within a certain material domain, which is defined as their validity range and has been summarized for each method.

scholarly journals Postoptimization of the model of water supply for urban and industrial agglomeration

2018 ◽  
Vol 23 ◽  
pp. 00035
Author(s):  
Jacek Wawrzosek ◽  
Szymon Ignaciuk
Keyword(s):  
Linear Programming ◽  
Water Supply ◽  
Programming Models ◽  
Industrial Agglomeration ◽  
Infinitely Many Solutions ◽  
Nodal Solutions ◽  
Parametric Linear Programming ◽  
Right Hand ◽  
The Right

A case study of the tools used by an analyst of the economic aspects of the operation of the water supply network has been undertaken in this paper. All issues discussed here are formulated by using degenerated linear programming models ( PL ). Below, it is noted that the linear dependence of binding constraints ( CO ) distorts standard postoptimization procedures in PL. This observed fact makes postoptimization analysis mostly unhelpful for an average analyst due to problems with the int erpretation of ambiguous sensitivity reports which are obtained from popular computer packages. In standard postoptimization methods, changes to single parameters of the right-hand vector CO are analyzed or referred to parametric linear programming that unfortunately requires prior knowledge of mathematically and economically justified vectors of changes of right-hand sides CO. Therefore, it is suggested that modifications are introduced to some of the postoptimization procedures in this work. For issues in the field of hydrology, the following were presented: interpretation and methods of generating justified vectors of changes of right-hand sides of limiting conditions. And so, the procedure of generating infinitely many solutions of the dual issue based on certain vectors orthogonal to the vector of right-hand sides of constraint conditions was demonstrated. Furthermore, the same orthogonal vectors were used to obtain nodal solutions of the dua0l model and the corresponding vectors of changes of the entire right-hand sides of the constraint conditions. Then, managerial interpretation was applied to this way of proceeding. The methods presented in the work serve to improve the functioning of the system of water supply.

Tangent bundle RRT: A randomized algorithm for constrained motion planning

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 202-225 ◽  
Author(s):  
Beobkyoon Kim ◽  
Terry Taewoong Um ◽  
Chansu Suh ◽  
F. C. Park
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Tangent Bundle ◽  
Numerical Experiments ◽  
Randomized Algorithm ◽  
Random Trees ◽  
Constrained Motion ◽  
Wide Range ◽  
Random Node ◽  
Planning Problems

SUMMARYThe Tangent Bundle Rapidly Exploring Random Tree (TB-RRT) is an algorithm for planning robot motions on curved configuration space manifolds, in which the key idea is to construct random trees not on the manifold itself, but on tangent bundle approximations to the manifold. Curvature-based methods are developed for constructing tangent bundle approximations, and procedures for random node generation and bidirectional tree extension are developed that significantly reduce the number of projections to the manifold. Extensive numerical experiments for a wide range of planning problems demonstrate the computational advantages of the TB-RRT algorithm over existing constrained path planning algorithms.

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