Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.

Immune algorithm for discretization of decision systems in rough set theory

Rough set theory plays an important role in knowledge discovery, but cannot deal with continuous attributes, thus discretization is a problem which we cannot neglect. And discretization of decision systems in rough set theory has some particular characteristics. Consistency must be satisfied and cuts for discretization is expected to be as small as possible. Consistent and minimal discretization problem is NP-complete. In this paper, an immune algorithm for the problem is proposed. The correctness and effectiveness were shown in experiments. The discretization method presented in this paper can also be used as a data pre- treating step for other symbolic knowledge discovery or machine learning methods other than rough set theory.

Prediction method of rock burst proneness based on rough set and genetic algorithm

A new method based on rough set theory and genetic algorithm was proposedto predict the rock burst proneness. Nine influencing factors were first selected, and then,the decision table was set up. Attributes were reduced by genetic algorithm. Rough setwas used to extract the simplified decision rules of rock burst proneness. Taking the practical engineering for example, the rock burst proneness was evaluated and predicted bydecision rules. Comparing the prediction results with the actual results, it shows that theproposed method is feasible and effective.

Heuristic Genetic Algorithm for Discretization of Continuous Attributes in Rough Set Theory

Discretization based on rough set theory aims to seek the possible minimum number of the cut set without weakening the indiscernibility of the original decision system. Optimization of discretization is an NP-complete prob- lem and the genetic algorithm is an appropriate method to solve it. In order to achieve optimal discretization, first the choice of the initial set of cut set is discussed, because a good initial cut set can enhance the efficiency and quality of the follow-up algorithm. Second, an effective heuristic genetic algorithm for discretization of continuous attributes of the decision table is proposed, which takes the significance of cut dots as heuristic information and introduces a novel op- erator to maintain the indiscernibility of the original decision system and enhance the local research ability of the algo- rithm. So the algorithm converges quickly and has global optimizing ability. Finally, the effectiveness of the algo- rithm is validated through experiment.

A Hybrid Genetic Algorithm for Reduct of Attributes in Decision System Based on Rough Set Theory

Knowledge reduction is an important issue when dealing with huge amounts of data. And it has been proved that computing the minimal reduct of decision system is NP-complete. By introducing heuristic information into genetic algorithm, we proposed a heuristic genetic algorithm. In the genetic algorithm, we constructed a new operator to maintaining the classification ability. The experiment shows that our algorithm is efficient and effective for minimal reduct, even for the special example that the simple heuristic algorithm can’t get the right result.

A neurofuzzy system based on rough set theory and genetic algorithm

This paper presents a hybrid soft computing modeling approach for a neurofuzzy system based on rough set theory and the genetic algorithms (NFRSGA). The fundamental problem of a neurofuzzy system is that when the input dimension increases, the fuzzy rule base increases exponentially. This leads to a huge infrastructure network which results in slow convergence. To solve this problem, rough set theory is used to obtain the reductive rules, which are used as fuzzy rules of the fuzzy system. The number of rules decrease, and each rule does not need all the conditional attribute values. This results in a reduced, or not fully connected, neural network. The structure of the neural network is relatively small and thus the weights to be trained decrease. The genetic algorithm is used to search the optimal discretization of the continuous attributes. The NFRSGA approach has been applied in the practical application of building a soft sensor model for estimating the freezing point of the light diesel fuel in a Fluid Catalytic Cracking Unit (FCCU), and satisfying results are obtained.

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.

Existence and Algorithm of Solutions for Generalized Set-valued Strongly Nonlinear Mixed Variational-like Type Inequalities

The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.

Local Search-Inspired Rough Sets for Improving Multiobjective Evolutionary Algorithm

In this paper we present a new optimization algorithm, and the proposed algorithm operates in two phases. In the first one, multiobjective version of genetic algorithm is used as search engine in order to generate approximate true Pareto front. This algorithm is based on concept of co-evolution and repair algorithm for handling nonlinear constraints. Also it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept e-dominance. Then, in the second stage, rough set theory is adopted as local search engine in order to improve the spread of the solutions found so far. The results, provided by the proposed algorithm for benchmark problems, are promising when compared with exiting well-known algorithms. Also, our results suggest that our algorithm is better applicable for solving real-world application problems.

A Modified Genetic Algorithm for Maximum Independent Set Problems

genetic algorithm is proposed for maximum independent set problems. A specially designed mutation operato is adopted to search the solution space more efficienily, where adjacen relation of a graph is inte-grated. The DIMACS benchmark graphs are used to test our algorithm, and the results show that the algorithm outper-forms our previous version. Moreover two new low bounds are found for graphs in DIMACS.

Rough Set Assisted Meta-Learning Method to Select Learning Algorithms

In this paper,we propose a Rough Set assisted Meta-Learning method on how to select the most-suited machine-learning algorithms with minimal effort for a new given dataset. A k-Nearest Neighbor (k-NN) algorithm is used to recognize the most similar datasets that have been performed by all of the candidate algorithms.By matching the most similar datasets we found,the corresponding performance of the candidate algorithms is used to generate recommendation to the user.The performance derives from a multi-criteria evaluation measure-ARR,which contains both accuracy and time.Furthermore,after applying Rough Set theory,we can find the redundant properties of the dataset.Thus,we can speed up the ranking process and increase the accuracy by using the reduct of the meta attributes.

Efficient Information Set Decoding Based on Genetic Algorithms

In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the generating matrix G. Then we present a new soft-decision decoding based on HDGA and the Chase algorithm (SDGA). The performance of some binary and non-binary Linear Block Codes are given for HDGA and SDGA over Gaussian and Rayleigh channels. The performances show that the HDGA decoder has the same performances as the Berlekamp-Massey Algorithm (BMA) in various transmission channels. On the other hand, the performances of SDGA are equivalent to soft-decision decoding using Chase algorithm and BMA (Chase-BMA). The complexity of decoders proposed is also discussed and compared to those of other decoders.

Neural network fault diagnosis method optimization with rough set and genetic algorithms

Aiming at the disadvantages of BP model in artificial neural networks applied to intelligent fault diagnosis, neural network fault diagnosis optimization method with rough sets and genetic algorithms are presented. The neural network nodes of the input layer can be calculated and simplified through rough sets theory; The neural network nodes of the middle layer are designed through genetic algorithms training; the neural network bottom-up weights and bias are obtained finally through the combination of genetic algorithms and BP algorithms. The analysis in this paper illustrates that the optimization method can improve the performance of the neural network fault diagnosis method greatly.

Active set truncated-Newton algorithm for simultaneous optimization of distillation column

An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.

Approximation Algorithms for the Connected Dominating Set Problem in Unit Disk Graphs

The connected dominating set （CDS） problem, which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs （UDGs）. This paper focuses on the CDS problem in wireless networks. Investigation of some properties of independent set （IS） in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms. Several constant factor approximation algorithms are presented for the CDS problem in UDGs. Simulation results show that the proposed algorithms perform better than some known ones.

An Algorithm for the Feedback Vertex Set Problem on a Normal Helly Circular-Arc Graph

The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.

Bi-extrapolated subgradient projection algorithm for solving multiple-sets split feasibility problem

This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.

Granularity of Knowledge Computed by Genetic Algorithms Based on Rough Sets Theory

Rough set philosophy hinges on the granularity of data, which is used to build all its basic concepts, like approximations, dependencies, reduction etc. Genetic Algorithms provides a general frame to optimize problem solution of complex system without depending on the domain of problem.It is robust to many kinds of problems.The paper combines Genetic Algorithms and rough sets theory to compute granular of knowledge through an example of information table. The combination enable us to compute granular of knowledge effectively.It is also useful for computer auto-computing and information processing.

基于Pareto蚁群算法的双目标路径规划研究

针对复杂建筑环境人员应急疏散单一路径不能满足火灾环境变化需求的问题,基于改进蚁群算法,结合Pareto双目标解集思想,提出一种组合优化解集的双目标蚁群算法,通过排序优化的思想,实现人员多路径动态疏散规划。在构造Pareto解集的阶段协同考虑疏散路径长度以及火灾风险程度2个优化目标,计算各个解之间的支配关系。利用排序优化蚁群算法的正反馈机制将各组解的信息素按一定比例作为最优路径信息素的积累,加快解集的寻找。最后将其与传统双目标蚁群算法相比较,结果表明:优化后的双目标算法更加适合复杂建筑人员疏散路径规划问题,在寻找多组满足要求解的同时展示目标之间的利弊关系,供决策者选择合适的路径,提高疏散效率。