A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Ar...A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.展开更多
Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurren...Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been obtained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. The complex number computation is completely avoided. A restart technique is used to enable the reduction algorithm to have iterative characteristics. It has been found that the restart technique is not only effective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with a technique to check and compute missed eigenvalues. By combining it with the restart technique, the algorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are given to demonstrate the effectiveness of the method proposed.展开更多
To guarantee the optimal reduct set, a heuristic reduction algorithm is proposed, which considers the distinguishing information between the members of each pair decision classes. Firstly the pairwise positive region ...To guarantee the optimal reduct set, a heuristic reduction algorithm is proposed, which considers the distinguishing information between the members of each pair decision classes. Firstly the pairwise positive region is defined, based on which the pairwise significance measure is calculated between the members of each pair classes. Finally the weighted pairwise significance of attribute is used as the attribute reduction criterion, which indicates the necessity of attributes very well. By introducing the noise tolerance factor, the new algorithm can tolerate noise to some extent. Experimental results show the advantages of our novel heuristic reduction algorithm over the traditional attribute dependency based algorithm.展开更多
By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field ...By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field F. Its computational complexity is O(N2) operations in F where N is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomi-als is given. The set and exact number of all minimal polynomials are also described when F is a finite field.展开更多
In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an alg...In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.展开更多
In this paper, we analyze the features and distinctions of 6 classical algorithms： greedy algorithm （G）, greedy evolution algorithm （GE）, heuristics algorithm （H）, greedy heuristic G （GRE）, integer linear pro...In this paper, we analyze the features and distinctions of 6 classical algorithms： greedy algorithm （G）, greedy evolution algorithm （GE）, heuristics algorithm （H）, greedy heuristic G （GRE）, integer linear programming algorithm （ILP） and genetic algorithm （GA） to ensure the main influencing factors-the performance of algorithms and the running time of algorithms. What＇s more, we would not only present a research design that aims at gaining deeper understanding about the algorithm classification and its function as well as their distinction, but also make an empirical study in order to obtain a practical range standard that can guide the selection of reduction algorithms. When the size of a test object （product of test requirements and test cases） is smaller than 2000×2000, G algorithm is the commonly recommended algorithm. With the growth of test size, the usage of GE and GRE becomes more general.展开更多
The general corrosion and local corrosion of Q235 steel were tested by acoustic emission （AE） detecting system under 6% FeCl3.6H2O solution to effectively detect the corrosion acoustic emission signal from complex b...The general corrosion and local corrosion of Q235 steel were tested by acoustic emission （AE） detecting system under 6% FeCl3.6H2O solution to effectively detect the corrosion acoustic emission signal from complex background noise. The short-time fractal dimension and discrete fractional cosine transform methods are combined to reduce noise. The input SNR is 0-15 dB while corrosion acoustic emission signals being added with white noise, color noise and pink noise respectively. The results show that the output signal-to-noise ratio is improved by up to 8 dB compared with discrete cosine transform and discrete fractional cosine transform. The above-mentioned noise reduction method is of significance for the identification of corrosion induced acoustic emission signals and the evaluation of the metal remaining life.展开更多
Feature selection （FS） is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that not all features are important. Some of the features ma...Feature selection （FS） is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that not all features are important. Some of the features may be redundant, and others may be irrelevant and noisy. The conventional supervised FS methods evaluate various feature subsets using an evaluation function or metric to select only those features which are related to the decision classes of the data under consideration. However, for many data mining applications, decision class labels are often unknown or incomplete, thus indicating the significance of unsupervised feature selection. However, in unsupervised learning, decision class labels are not provided. In this paper, we propose a new unsupervised quick reduct （QR） algorithm using rough set theory. The quality of the reduced data is measured by the classification performance and it is evaluated using WEKA classifier tool. The method is compared with existing supervised methods and the result demonstrates the efficiency of the proposed algorithm.展开更多
The computation burden in the model-based predictive control algorithm is heavy when solving QR optimization with a limited sampling step, especially for a complicated system with large dimension. A fast algorithm is ...The computation burden in the model-based predictive control algorithm is heavy when solving QR optimization with a limited sampling step, especially for a complicated system with large dimension. A fast algorithm is proposed in this paper to solve this problem, in which real-time values are modulated to bit streams to simplify the multiplication. In addition, manipulated variables in the prediction horizon are deduced to the current control horizon approximately by a recursive relation to decrease the dimension of QR optimization. The simulation results demonstrate the feasibility of this fast algorithm for MIMO systems.展开更多
Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to enumeration.The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwa...Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to enumeration.The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in 2017.Although they extended the sampling space compared to Schnorr's work through the natural number representation,they did not show how to sample specifically in practice and what vectors should be sampled,in order to find short enough lattice vectors.In this paper,the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors efficiently.Then,as an application of this new random sampling algorithm,the authors show that it can improve the performance of progressive BKZ algorithm in practice.Finally,the authors solve the Darmstadt's Lattice Challenge and get a series of new records in the dimension from 500 to 825,using the improved progressive BKZ algorithm.展开更多
An integrated method based on optical and digital image processing is presented to suppress speckle in digital holography. A spatial light modulator is adopted to introduce random phases to the illuminating beam. Mult...An integrated method based on optical and digital image processing is presented to suppress speckle in digital holography. A spatial light modulator is adopted to introduce random phases to the illuminating beam. Multiple holograms are reconstructed and superimposed, and the intensity is averaged to smooth the noise. The adaptive algorithm based on the nonlocal means is designed to further suppress the speckle. The presented method is compared with other methods reduction is improved, and the proposed method is effective The experimental results show that speckle and feasible.展开更多
Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis ...Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis of the algorithm; Analysis of the complexity bound on obtaining an approximate solution.展开更多
Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task ow...Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.展开更多
We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly...We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly within the Maple package DifferentialAlgebra—in order to automate the handling of the arising highly complex linear systems of PDE’s.Before treating these new examples which prolong previous works of Beloshapka,of Shananina and of Mamai,we provide general formulas for the explicitation of the concerned PDE systems that are valid in arbitrary codimension k 1 and in any CR dimension n 1.Also,we show how Ritt’s reduction algorithm can be adapted to the case under interest,where the concerned PDE systems admit so-called complex conjugations.展开更多
Based on improved multi-objective particle swarm optimization（MOPSO） algorithm with principal component analysis（PCA） methodology, an efficient high-dimension multiobjective optimization method is proposed, which,...Based on improved multi-objective particle swarm optimization（MOPSO） algorithm with principal component analysis（PCA） methodology, an efficient high-dimension multiobjective optimization method is proposed, which, as the purpose of this paper, aims to improve the convergence of Pareto front in multi-objective optimization design. The mathematical efficiency,the physical reasonableness and the reliability in dealing with redundant objectives of PCA are verified by typical DTLZ5 test function and multi-objective correlation analysis of supercritical airfoil,and the proposed method is integrated into aircraft multi-disciplinary design（AMDEsign） platform, which contains aerodynamics, stealth and structure weight analysis and optimization module.Then the proposed method is used for the multi-point integrated aerodynamic optimization of a wide-body passenger aircraft, in which the redundant objectives identified by PCA are transformed to optimization constraints, and several design methods are compared. The design results illustrate that the strategy used in this paper is sufficient and multi-point design requirements of the passenger aircraft are reached. The visualization level of non-dominant Pareto set is improved by effectively reducing the dimension without losing the primary feature of the problem.展开更多
文摘A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.
基金This research is supported by The National Science FoundationThe Doctoral Training Foundation
文摘Based on Arnoldi's method, a version of generalized Arnoldi algorithm has been developed for the reduction of gyroscopic eigenvalue problems. By utilizing the skew symmetry of system matrix, a very simple recurrence scheme, named gyroscopic Arnoldi reduction algorithm has been obtained, which is even simpler than the Lanczos algorithm for symmetric eigenvalue problems. The complex number computation is completely avoided. A restart technique is used to enable the reduction algorithm to have iterative characteristics. It has been found that the restart technique is not only effective for the convergence of multiple eigenvalues but it also furnishes the reduction algorithm with a technique to check and compute missed eigenvalues. By combining it with the restart technique, the algorithm is made practical for large-scale gyroscopic eigenvalue problems. Numerical examples are given to demonstrate the effectiveness of the method proposed.
基金Sponsored by the Ministerial Level Advanced Research Foundation(11415133)
文摘To guarantee the optimal reduct set, a heuristic reduction algorithm is proposed, which considers the distinguishing information between the members of each pair decision classes. Firstly the pairwise positive region is defined, based on which the pairwise significance measure is calculated between the members of each pair classes. Finally the weighted pairwise significance of attribute is used as the attribute reduction criterion, which indicates the necessity of attributes very well. By introducing the noise tolerance factor, the new algorithm can tolerate noise to some extent. Experimental results show the advantages of our novel heuristic reduction algorithm over the traditional attribute dependency based algorithm.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 19931010, G1999035804).
文摘By means of F[x]-lattice basis reduction algorithm, a new algorithm is presented for synthesizing minimum length linear feedback shift registers (or minimal polynomials) for the given mul-tiple sequences over a field F. Its computational complexity is O(N2) operations in F where N is the length of each sequence. A necessary and sufficient condition for the uniqueness of minimal polynomi-als is given. The set and exact number of all minimal polynomials are also described when F is a finite field.
基金This research was partially supported by a fund from Chinese Academy of Science,and a fund from the Personal Department of the State Council.It is also sponsored by scientific research foundation for returned overseas Chinese Scholars,State Education
文摘In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.
基金Supported by the National Natural Science Foundation of China(10904080)
文摘In this paper, we analyze the features and distinctions of 6 classical algorithms： greedy algorithm （G）, greedy evolution algorithm （GE）, heuristics algorithm （H）, greedy heuristic G （GRE）, integer linear programming algorithm （ILP） and genetic algorithm （GA） to ensure the main influencing factors-the performance of algorithms and the running time of algorithms. What＇s more, we would not only present a research design that aims at gaining deeper understanding about the algorithm classification and its function as well as their distinction, but also make an empirical study in order to obtain a practical range standard that can guide the selection of reduction algorithms. When the size of a test object （product of test requirements and test cases） is smaller than 2000×2000, G algorithm is the commonly recommended algorithm. With the growth of test size, the usage of GE and GRE becomes more general.
文摘The general corrosion and local corrosion of Q235 steel were tested by acoustic emission （AE） detecting system under 6% FeCl3.6H2O solution to effectively detect the corrosion acoustic emission signal from complex background noise. The short-time fractal dimension and discrete fractional cosine transform methods are combined to reduce noise. The input SNR is 0-15 dB while corrosion acoustic emission signals being added with white noise, color noise and pink noise respectively. The results show that the output signal-to-noise ratio is improved by up to 8 dB compared with discrete cosine transform and discrete fractional cosine transform. The above-mentioned noise reduction method is of significance for the identification of corrosion induced acoustic emission signals and the evaluation of the metal remaining life.
基金supported by the UGC, SERO, Hyderabad under FDP during XI plan periodthe UGC, New Delhi for financial assistance under major research project Grant No. F-34-105/2008
文摘Feature selection （FS） is a process to select features which are more informative. It is one of the important steps in knowledge discovery. The problem is that not all features are important. Some of the features may be redundant, and others may be irrelevant and noisy. The conventional supervised FS methods evaluate various feature subsets using an evaluation function or metric to select only those features which are related to the decision classes of the data under consideration. However, for many data mining applications, decision class labels are often unknown or incomplete, thus indicating the significance of unsupervised feature selection. However, in unsupervised learning, decision class labels are not provided. In this paper, we propose a new unsupervised quick reduct （QR） algorithm using rough set theory. The quality of the reduced data is measured by the classification performance and it is evaluated using WEKA classifier tool. The method is compared with existing supervised methods and the result demonstrates the efficiency of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(61333010,61203157)the Fundamental Research Funds for the Central Universities+2 种基金the National High-Tech Research and Development Program of China(2013AA040701)Shanghai Natural Science Foundation Project(15ZR1408900)Shanghai Key Technologies R&D Program Project(13111103800)
文摘The computation burden in the model-based predictive control algorithm is heavy when solving QR optimization with a limited sampling step, especially for a complicated system with large dimension. A fast algorithm is proposed in this paper to solve this problem, in which real-time values are modulated to bit streams to simplify the multiplication. In addition, manipulated variables in the prediction horizon are deduced to the current control horizon approximately by a recursive relation to decrease the dimension of QR optimization. The simulation results demonstrate the feasibility of this fast algorithm for MIMO systems.
基金supported by the National Natural Science Foundation of China under Grant Nos.62032009 and 62102440。
文摘Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to enumeration.The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in 2017.Although they extended the sampling space compared to Schnorr's work through the natural number representation,they did not show how to sample specifically in practice and what vectors should be sampled,in order to find short enough lattice vectors.In this paper,the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors efficiently.Then,as an application of this new random sampling algorithm,the authors show that it can improve the performance of progressive BKZ algorithm in practice.Finally,the authors solve the Darmstadt's Lattice Challenge and get a series of new records in the dimension from 500 to 825,using the improved progressive BKZ algorithm.
基金supported by the National Natural Science Foundation of China(No.61177018)the Program for New Century Excellent Talents in University(No.NECT-11-0596)+1 种基金the Key Program of Beijing Sci-ence and Technology Plan(No.D121100004812001)Beijing Nova Program(No.2011066)
文摘An integrated method based on optical and digital image processing is presented to suppress speckle in digital holography. A spatial light modulator is adopted to introduce random phases to the illuminating beam. Multiple holograms are reconstructed and superimposed, and the intensity is averaged to smooth the noise. The adaptive algorithm based on the nonlocal means is designed to further suppress the speckle. The presented method is compared with other methods reduction is improved, and the proposed method is effective The experimental results show that speckle and feasible.
基金This research supported partially by The National Natural Science Foundation of China-19771079 and 19601035State Key Laboratory of Scientific and Engineering Computing.
文摘Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis of the algorithm; Analysis of the complexity bound on obtaining an approximate solution.
文摘Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity （LF） model provides physics-based approximation of the high-fidelity （HF） model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.
基金supported by the Center for International Scientific Studies and Collaboration(CISSC)and French Embassy in TehranThe resend of the first and second authors was in part supported by grants from IPM(Grant Nos.91530040 and 92550420)
文摘We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C9by employing differential algebra computer tools—mostly within the Maple package DifferentialAlgebra—in order to automate the handling of the arising highly complex linear systems of PDE’s.Before treating these new examples which prolong previous works of Beloshapka,of Shananina and of Mamai,we provide general formulas for the explicitation of the concerned PDE systems that are valid in arbitrary codimension k 1 and in any CR dimension n 1.Also,we show how Ritt’s reduction algorithm can be adapted to the case under interest,where the concerned PDE systems admit so-called complex conjugations.
基金supported by the National Natural Science Foundation of China (No.11402288)
文摘Based on improved multi-objective particle swarm optimization（MOPSO） algorithm with principal component analysis（PCA） methodology, an efficient high-dimension multiobjective optimization method is proposed, which, as the purpose of this paper, aims to improve the convergence of Pareto front in multi-objective optimization design. The mathematical efficiency,the physical reasonableness and the reliability in dealing with redundant objectives of PCA are verified by typical DTLZ5 test function and multi-objective correlation analysis of supercritical airfoil,and the proposed method is integrated into aircraft multi-disciplinary design（AMDEsign） platform, which contains aerodynamics, stealth and structure weight analysis and optimization module.Then the proposed method is used for the multi-point integrated aerodynamic optimization of a wide-body passenger aircraft, in which the redundant objectives identified by PCA are transformed to optimization constraints, and several design methods are compared. The design results illustrate that the strategy used in this paper is sufficient and multi-point design requirements of the passenger aircraft are reached. The visualization level of non-dominant Pareto set is improved by effectively reducing the dimension without losing the primary feature of the problem.
