The present article presents the optimization of electric stress distribution over the live electrode of an axisymmetric electrode-spacer arrangement that is used in a Gas insulated substation (GIS) typically for 12-4...
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The present article presents the optimization of electric stress distribution over the live electrode of an axisymmetric electrode-spacer arrangement that is used in a Gas insulated substation (GIS) typically for 12-420 kV operations. The technique is based on a classical approach employing simplex algorithm which is used to solve constrained linear programming problems (LPPs). For this purpose, the objective function is obtained by applying multiple linear regression analysis by which a mathematical relationship between the maximum resultant electric stress (ERmax) over the surface of the live electrode and the critical dimensions affecting this stress. For this purpose, a set of 71 data is used for building the regression model, which is prepared by varying the critical dimensions within the constraints of the overall dimension of the system and calculating the value of ER max over the surface of the live electrode by employing the indirect boundary element method (BEM).
In the first part of the paper we survey some far-reaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments ...
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In the first part of the paper we survey some far-reaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concerning the simplex algorithm. We describe subexponential randomized pivot rules and upper bounds on the diameter of graphs of polytopes. (C) 1997 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
Parameter identification algorithms are very fundamental techniques in system engineering practices. For example, estimating the parameters of the AutoRegresive model with an eXternal input or AutoRegresive Moving-Ave...
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Parameter identification algorithms are very fundamental techniques in system engineering practices. For example, estimating the parameters of the AutoRegresive model with an eXternal input or AutoRegresive Moving-Average model with an eXternal input by using the least squares (LS) method has become a standard approach. However, the estimated parameters may generate extremely erroneous results when the signal is disturbed by large noise, which cannot be effectively filtered. If a frequency response method that scatters the power of a broadband noise over different frequencies is adopted, the effect of noise on the estimated parameters would be relatively reduced. Moreover, estimating whether the plant is a high-order system or is perturbed by a large noise is difficult. The estimated accuracy decreases even after applying the generalized LS method or other modified approaches. To overcome this problem, this study proposed a new technique combining a simplex algorithm and frequency response method for improving the accuracy of the parameter estimation of a dynamic system with a large noise (i.e., an extremely low signal-to-noise ratio) of the system. The algorithm is simple and easy to implement. Moreover, the precision of parameter identification can be increased even when estimated systems suffer from large measurement noises.
The use of a special-purpose VLSI chip for solving a linear programming problem is presented. The chip is structured as a mesh of trees and is designed to implement the well-known simplex algorithm. A high degree of p...
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The use of a special-purpose VLSI chip for solving a linear programming problem is presented. The chip is structured as a mesh of trees and is designed to implement the well-known simplex algorithm. A high degree of parallelism is introduced in each pivot step, which can be carried out in O (log n) time using an m × n mesh of trees having an O(mn log m log3 n) area where m − 1 and n − 1 are the number of constraints and variables, respectively. Two variants of the simplex algorithm are also considered: the two-phase method and the revised one. The proposed chip is intended as being a possible basic block for a VLSI operations research machine.
作者：
Mallach, SvenUniv Bonn
High Performance Comp & Analyt Lab Friedrich Hirzebruch Allee 8 D-53115 Bonn Germany
A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non -deteriorating s...
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A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non -deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the quadratic objective function. The algorithm so generalizes over local improvement methods for according applications, including in particular quadratic optimization problems whose feasible solutions correspond to vertices of a 0-1 polytope. Computational experiments for unconstrained binary quadratic programs, maximum cut, and the quadratic assignment problem serve as a proof of concept and underline the importance of a pivoting rule that is able to accept at least a restricted class of degenerate steps. (c) 2024 Elsevier B.V. All rights reserved.
This study describes a data-driven algorithm as a rapid alternative to conventional Design of Experiments (DoE) approaches for identifying feasible operating conditions during early bioprocess development. In general,...
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This study describes a data-driven algorithm as a rapid alternative to conventional Design of Experiments (DoE) approaches for identifying feasible operating conditions during early bioprocess development. In general, DoE methods involve fitting regression models to experimental data, but if model fitness is inadequate then further experimentation is required to gain more confidence in the location of an optimum. This can be undesirable during very early process development when feedstock is in limited supply and especially if a significant percentage of the tested conditions are ultimately found to be sub-optimal. An alternative approach involves focusing solely upon the feasible regions by using the knowledge gained from each condition to direct the choice of subsequent test locations that lead towards an optimum. To illustrate the principle, this study describes the application of the simplex algorithm which uses accumulated knowledge from previous test points to direct the choice of successive conditions towards better regions. The method is illustrated by two case studies;a two variable precipitation example investigating how salt concentration and pH affect FAb' recovery from E. coli homogenate and a three-variable chromatography example identifying the optimal pH and concentrations of two salts in an elution buffer used to recover ovine antibody bound to a multimodal cation exchange matrix. Two-level and face-centered central composite regression models were constructed for each study and statistical analysis showed that they provided a poor fit to the data, necessitating additional experimentation to confirm the robust regions of the search space. By comparison, the simplex algorithm identified a good operating point using 50% and 70% fewer conditions for the precipitation and chromatography studies, respectively. Hence, data-driven approaches have significant potential for early process development when material supply is at a premium. Biotechnol. Bioeng. 2
We propose a new pivot rule for the simplex algorithm, which is demonstrative in the dual space intuitively. Although it is based on normalized reduced costs, like the steepest-edge rule and its variants, the rule is ...
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We propose a new pivot rule for the simplex algorithm, which is demonstrative in the dual space intuitively. Although it is based on normalized reduced costs, like the steepest-edge rule and its variants, the rule is much simpler and cheaper than the latter. We report computational results obtained with the 47 largest Netlib problems in terms of the number of rows and columns, all of the 16 Kennington problems, and the 17 largest BPMPD problems. Over the total 80 problems, a variant of the rule outperformed the Devex rule with iterations and time ratio 1.43 and 3.24, respectively. (c) 2007 Elsevier B.V. All rights reserved.
作者：
Calvete, HIUniv Zaragoza
Fac Ciencias Dept Metodos Estadist Edificio Math Zaragoza 50009 Spain
In this paper the general equal flow problem is considered. This is a minimum cost network flow problem with additional side constraints requiring the flow of arcs in some given sets of arcs to take on the same value....
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In this paper the general equal flow problem is considered. This is a minimum cost network flow problem with additional side constraints requiring the flow of arcs in some given sets of arcs to take on the same value. This model can be applied to approach water resource system management problems or multiperiod logistic problems in general involving policy restrictions which require some arcs to carry the same amount of flow through the given study period. Although the bases of the general equal flow problem are no longer spanning trees, it is possible to recognize a similar structure that allows us to take advantage of the practical computational capabilities of network models. After characterizing the bases of the problem as good (r +1)-forests, a simplex primal algorithm is developed that exploits the network structure of the problem and requires only slight modifications of the well-known network simplex algorithm. (C) 2002 Elsevier B.V. All rights reserved.
We show that the simplex Method, the Network simplex Method-both with Dantzig's original pivot rule- and the Successive Shortest Path algorithm are NP-mighty. That is, each of these algorithms can be used to solve...
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We show that the simplex Method, the Network simplex Method-both with Dantzig's original pivot rule- and the Successive Shortest Path algorithm are NP-mighty. That is, each of these algorithms can be used to solve, with polynomial overhead, any problem in NP implicitly during the algorithm's execution. This result casts a more favorable light on these algorithms' exponential worst-case running times. Furthermore, as a consequence of our approach, we obtain several novel hardness results. For example, for a given input to the simplex algorithm, deciding whether a given variable ever enters the basis during the algorithm's execution and determining the number of iterations needed are both NP-hard problems. Finally, we close a long-standing open problem in the area of network flows over time by showing that earliest arrival flows are NP-hard to obtain.
The Semi-Infinite simplex algorithm (SISA) with applications to so called Semi-Infinite Linear Programs (SILP) with capacity constraints as a direct analog to column generating techniques in linear programming methods...
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The Semi-Infinite simplex algorithm (SISA) with applications to so called Semi-Infinite Linear Programs (SILP) with capacity constraints as a direct analog to column generating techniques in linear programming methods of was presented by the author in 1978. Later in 1981, the SISA for SILP in partially ordered spaces was described with more algebraic framework in terms of feasible basic solutions, extreme points and so on. Now this paper has two aims: to reflect the history of one branch of the so-called Leipzig-Optimization-Tree with roots J. Focke/A. Gopfert / R. Klotzler and to demonstrate some applications of the simplex algorithm.
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