A Usable Selection Range Standard Based on Test Suite Reduction Algorithms

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.

ARNOLDI REDUCTION ALGORITHM FOR LARGE SCALE GYROSCOPIC EIGENVALUE PROBLEM

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.

Heuristic Reduction Algorithm Based on 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.

A POTENTIAL REDUCTION ALGORITHM FOR LINEARLY CONSTRAINED CONVEX PROGRAMMING

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.

Unsupervised Quick Reduct Algorithm Using Rough Set Theory

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.

UNIFYING REPRESENTATION OF BZIER CURVE AND GENERALIZED BALL CURVES

This paper presents two new families of the generalized Ball curves which include the Be ′zier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves. The relative degree elevation and reduction schemes, recursive algorithms and the Bernstein\|Be ′zier representation are also given.

THE PRIMAL-DUAL POTENTIAL REDUCTION ALGORITHM FOR POSITIVE SEMI-DEFINITE PROGRAMMING

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.

F[x]-lattice basis reduction algorithm and multisequence synthesis

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.

Variable-fidelity optimization with design space reduction

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.

Speckle noise reduction in digital holography with spatial light modulator and nonlocal means algorithm

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.

Noise reduction algorithm of corrosion acoustic emission signal based on short-time fractal dimension enhancement

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.

Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints

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.

Aerodynamic multi-objective integrated optimization based on principal component analysis

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.