The use of floating-point calculations limits the accuracy of solutions obtained by standard LP software. We present a simplex-based algorithm that returns exact rational solutions, taking advantage of the speed of fl...
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The use of floating-point calculations limits the accuracy of solutions obtained by standard LP software. We present a simplex-based algorithm that returns exact rational solutions, taking advantage of the speed of floating-point calculation, and attempting to minimize the operations performed in rational arithmetic. Extensive computational results are presented. (C) 2007 Elsevier B.V. All rights reserved.
This letter proposes an optimal subarray design strategy for frequency diverse array (FDA) radar target localization via Cramer-Rao lower bound (CRLB) minimization. To decouple the range and angle response of targets,...
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This letter proposes an optimal subarray design strategy for frequency diverse array (FDA) radar target localization via Cramer-Rao lower bound (CRLB) minimization. To decouple the range and angle response of targets, we divide the FDA transmit array elements into multiple subarrays. For a given number of array elements and subarrays, the optimal array division and frequency increments design strategies are formulated as a constrained CRLB minimization problem. Then it is converted into an unconstrained optimization problem and further resolved by iteratively utilizing the Nelder-Mead algorithm. Numerical results show that, under the same condition, FDA radar localization performance is significantly improved by employing the CRLB minimization strategy.
This paper addresses some pitfalls of some fuzzy data envelopment analysis models which have been provided in recent published papers. This study deals with these papers from both computational and theoretical points ...
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This paper addresses some pitfalls of some fuzzy data envelopment analysis models which have been provided in recent published papers. This study deals with these papers from both computational and theoretical points of view. Moreover, a new approach to deal with fuzzy data in DEA framework is provided, which does not have the mentioned pitfalls. (c) 2006 Elsevier Inc. All rights reserved.
In this paper we develop an equilibrium method for the derivation of critical equilibrium configurations of a non-linearly elastic, discrete rod model, which is supported in a statically indeterminate way, and subject...
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In this paper we develop an equilibrium method for the derivation of critical equilibrium configurations of a non-linearly elastic, discrete rod model, which is supported in a statically indeterminate way, and subjected to general loading. We construct a global computation scheme for the critical equilibrium configurations and demonstrate the effectiveness of the method via a clamped-pinned rod fabricated from linearly elastic, or specially hardening/softening material, loaded by either a horizontal or a follower force. We show some correspondence between the equilibrium states of these two load cases, and different snapping processes are revealed. (C) 2013 Elsevier Ltd. All rights reserved.
In a number of 3D surface topography measurements it is both necessary and of great use to relocate exactly the same area, e.g., in the study of wear processes, in correlation studies of slightly overlapping character...
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In a number of 3D surface topography measurements it is both necessary and of great use to relocate exactly the same area, e.g., in the study of wear processes, in correlation studies of slightly overlapping characterisation techniques, and in the study of replica techniques. The objective of the present paper is to evaluate the performance of an automatic relocation process based on a simplex algorithm. The method is implemented in MATLAB(TM). The cross-correlation coefficient between the topographical data determines the evolution of the relocation process. Two variations of the method are used, i.e., one uses the full range of the input data and the second uses a truncated version of the input data. The truncation is based in selected percentages of the bearing area curve. Four different surfaces and two different techniques are used in this study. (C) 2001 Elsevier Science Ltd. All rights reserved.
A study has been made to optimise the influential parameters of surface lapping process. Lapping time, lapping speed, downward pressure, and charging pressure were chosen from the preliminary studies as parameters to ...
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A study has been made to optimise the influential parameters of surface lapping process. Lapping time, lapping speed, downward pressure, and charging pressure were chosen from the preliminary studies as parameters to determine process performances in terms of material removal, lap width, and clamp force. The desirability functions of the-nominal-the-best were used to compromise multiple responses into the overall desirability function level or D response. The conventional modified simplex or Nelder-Mead simplex method and the interactive desirability function are performed to optimise online the parameter levels in order to maximise the D response. In order to determine the lapping process parameters effectively, this research then applies two powerful artificial intelligence optimisation mechanisms from harmony search and firefly algorithms. The recommended condition of (lapping time, lapping speed, downward pressure, and charging pressure) at (33, 35, 6.0, and 5.0) has been verified by performing confirmation experiments. It showed that the D response level increased to 0.96. When compared with the current operating condition, there is a decrease of the material removal and lap width with the improved process performance indices of 2.01 and 1.14, respectively. Similarly, there is an increase of the clamp force with the improved process performance index of 1.58.
When the simplex algorithm is used to calculate a linear programming (LP) problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will app...
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When the simplex algorithm is used to calculate a linear programming (LP) problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper. The principle of this method is to avoid choosing the row which the value of the element in the right side of constraint expression for LP in this row is zero as the row of the pivot element to make the matrix in LP density and ensure that most subsequent steps will improve the value of the objective function. One step following this principle is inserted in the existing LP algorithm to reselect the pivot element. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of LP problems as examples, the results indicate that this method can effectively improve the efficiency of LP for the sparse matrix.
Column generation is a well-known and widely practiced technique for solving linear programs with too many variables or constraints to include in the initial formulation explicitly. Instead, the required column inform...
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Column generation is a well-known and widely practiced technique for solving linear programs with too many variables or constraints to include in the initial formulation explicitly. Instead, the required column information is generated at each iteration of the simplex algorithm. This paper shows that, even if the number of variables is low enough for explicit inclusion in the model with the available technology, it may still be more efficient to resort to column generation for some class of problems.
Solving linear programming (LP) and nonlinear programming (NLP) problems is momentous because of their wide applications in real-life problems. There is no unified way to find the global optimum for NLPs. But on the o...
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Solving linear programming (LP) and nonlinear programming (NLP) problems is momentous because of their wide applications in real-life problems. There is no unified way to find the global optimum for NLPs. But on the other hand, the simplex algorithm, as the dominating methodology for LPs for several decades moves only on the boundary (vertices) and ignores the vast majority of the feasible region in the process of searching. In this article, we study two gradient-based methodologies that explore the whole feasible region, which guarantee faster convergence rates for both LP and NLP optimization problems including IoT problems such as Software-Defined Internet of Vehicles (SDIoV) and vehicular ad hoc networks (VANETs). The gradient-simplex algorithm (GSA) for LPs, which moves inside the feasible region in the gradient direction at first to reduce the search space and then explores the reduced boundary to find an optimal solution. The evolutionary-gradient algorithm (EGA), on the other hand, is for NLPs and uses an evolutionary population to estimate gradients by evolving to find better solutions in steps. Based on extensive simulations, the obtained numerical results show that both approaches provide efficient solutions and outperform the state-of-the-art methods on optimization problems with large feasible spaces. Comparative results of applying the GSA on SDIoV and VANETs with different sizes are included.
This brief proposes an optimization formulation of the control problem for power electronic converters. A benefit of the approach is a systematic method for the control of high-switch-count static converters. In the c...
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This brief proposes an optimization formulation of the control problem for power electronic converters. A benefit of the approach is a systematic method for the control of high-switch-count static converters. In the case of the three-phase, four-leg, two-level inverter, the framework provides a characterization of all the possible solutions that yield a maximal extension of the inverter linearity range. The method makes it possible to recover well-known modulation strategies as well as to discover some new ones having different properties and distinct advantages. The characteristics resulting from different design choices are evaluated in simulations, with consideration being given to the linearity range, total harmonic distortion, and switching losses. Key principles of extension of the proposed method to multilevel, multileg converters are given, as well as motivations for a field-programmable gate array-based hardware implementation enabling real-time pulsewidth modulation control.
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