Today, in most cases, such as transportation, management, artificial intelligence, industries, decision-making, and in many real-life situations, we deal with uncertainty, imprecise boundaries, and qualitative informa...
详细信息
Today, in most cases, such as transportation, management, artificial intelligence, industries, decision-making, and in many real-life situations, we deal with uncertainty, imprecise boundaries, and qualitative information. In order to deal with these kinds of critical circumstances, we need to solve an optimization problem with interval-valued Fermatean fuzzy (IVFF) information. A few works have been done on transportation problems with Interval-valued Fermatean fuzzy sets (IVFFSs). In this paper, we first introduce a few new arithmetic operations on the set of IVFFSs. Second, we propose a linear programming problem (LPP) model under an interval-valued Fermatean fuzzy environment and study its Mathematical properties by establishing various theorems. Third, we propose a new simplex algorithm to solve a fully interval-valued Fermatean fuzzy Linear programming (IVFFLPP) problem and solve a few numerical problems to show the applicability of our proposed algorithm. Fourth, we discuss the formulation of the interval-valued Fermatean fuzzy assignment problem (IVFFAP) as a particular case of IVFFLPP and study its properties. Fifth, we establish a new algorithm for solving IVFFAP and solve two numerical problems to discuss the applicability, importance of the proposed algorithms.
A comparative analysis of the computational complexity of exact algorithms for estimating linear regression equations has been carried out using the least absolute deviations method. The aim of this study is to compar...
详细信息
A comparative analysis of the computational complexity of exact algorithms for estimating linear regression equations has been carried out using the least absolute deviations method. The aim of this study is to compare the computational efficiency of exact algorithms for descent along nodal straight lines and algorithms based on solving linear programming problems. To do that, the algorithm of gradient descent along nodal straight lines and algorithms for solving the equivalent primal and dual linear programming problems using the simplex method have been discussed. The computational complexity of the algorithms for implementing the least absolute deviation method in solving the primal and dual linear programming problems has been estimated. The average time for determining regression coefficients using the primal and dual linear programming problems and the average time for gradient descent along nodal straight lines have been compared in Monte Carlo statistical experiments. It is shown that both options are significantly inferior to the gradient descent along nodal straight lines in both the computational complexity of the algorithms and the computation time. The advantage of the algorithm for descent along nodal straight lines increases by two orders of magnitude or more with an increase in the sample size.
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...
详细信息
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.
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...
详细信息
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).
The simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the ...
详细信息
ISBN:
(纸本)9781450394314
The simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the algorithm relies on intuitive geometric ideas, the computationally-involved mechanics of the algorithm can obfuscate a geometric understanding. In this paper, we present gilp, an easy-to-use simplex algorithm visualization tool designed to connect the mechanical steps of the algorithm with their geometric interpretation. We provide an extensive library of example visualizations, and our tool allows instructors to quickly produce custom interactive HTML files for students to experiment with the algorithm (without requiring students to install anything!). The tool can also be used for interactive assignments in Jupyter notebooks, and has been incorporated into a forthcoming Data Science and Decision Making interactive textbook. In this paper, we first describe how the tool fits into the existing algorithm visualization literature: how it was designed to facilitate student engagement and instructor adoption, and how it substantially extends existing algorithm visualization tools for simplex. We then describe the development and usage of the tool, and report feedback from its use in a course with roughly 100 students. Student feedback was overwhelmingly positive, with students finding the tool easy to use: it effectively helped them link the algebraic and geometrical views of the simplex algorithm and understand its nuances. Finally, gilp is open-source, includes an extension to visualizing linear programming-based branch and bound, and is readily amenable to further extensions.
This work explored the epoxidation of high oleic palm oil (HOPO) extracted from recently developed palm tree hybrids. The process was carried out by reaction with 50 % wt.H2O2 using peracetic acid generated in-situ as...
详细信息
This work explored the epoxidation of high oleic palm oil (HOPO) extracted from recently developed palm tree hybrids. The process was carried out by reaction with 50 % wt.H2O2 using peracetic acid generated in-situ as oxygen carrier, and H2SO4 as catalyst. The study focused on the optimization of the operating conditions to maximize the productivity of oxirane groups in the epoxidized oil, considering the conversion of unsaturated groups and the selectivity to oxirane ring. The optimization was done by experimental application of a simplex algorithm varying reaction temperature (55-70 degrees C), catalyst loading (1-5 % wt.), mol ratio of H2O2 to HOPO unsaturations (1-10), acetic acid loading with respect to HOPO (2-10 % wt.), and reaction time (1-6 h). Optimal conditions were obtained after eight experimental steps, reaching a conversion of oil's unsaturations of nearly 90 %, with a selectivity towards oxirane groups of 88.6 %. The obtained oil had an oxygen oxirane content of 3.48 % wt., which corresponded to similar to 80 % of theoretical yield. The optimal conditions were tested in a subsequent kinetic experiment, and the results were reproduced obtaining an epoxy number of 3.5 and a yield of 79.7 %. This methodology can also be used to assess novel epoxidation catalysts.
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...
详细信息
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.
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...
详细信息
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 multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the pr...
详细信息
The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson's outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered.
The paper proposes an optimization formulation of the control problem for modular multilevel converter (MMC). The main control stage computes arm voltages on average over a fixed switching period by minimizing control...
详细信息
ISBN:
(纸本)9781538663769
The paper proposes an optimization formulation of the control problem for modular multilevel converter (MMC). The main control stage computes arm voltages on average over a fixed switching period by minimizing control errors in order to satisfy as best as possible the desired references of input, circulating and output currents, while taking into account arm voltage limits. Then, mean-values of required arm voltages are achieved by phase shift pulse-width modulation (PSPWM) by computing duty cycles for each submodule while taking into account the issue of active balancing of the capacitor voltages in a secondary control stage. The proposed optimization problems are solved by using a numerical method based on the simplex algorithm and simulation results are shown in order to support the validity of the approach.
暂无评论