AN ADAPTIVE VARIANT OF CGNR ALGORITHM

1　IntroductionConsider large linear systemAx =b, ( 1 .1 )where A and b are given,A isa nonsingularn×n real matrix,and b is an n-vector.When A issymmetric positive definite ( s.p.d.) ,the classical conjugate gradient method ( CG) [7] used inconjunction with incomplete factorization preconditioning technique[1 0 ] is a succesful method inview of the high robustness and efficiency.But for general non-s.p.d.systems,the situationis less satisfactory.The generalized minimal residual algorithm( …     

Cooley-Tukey FFT在高维的算法

A new fast algorithm is presented for multidimensional DFT in this paper. This algorithm is derived based on an interesting coding technique for multidimensional integral point, named the technique vector coding. And called the algorithm VCFFT (vector coding fast Fourier transform). Since the VC-FFT is the extension of Cooley-Tukey algorithm from one-dimensional to multidimensional, its structure of program is simple as Cooley-Tukey FFT, and significantly reduces multiplications and recursive stages.     

多层线性规划问题的整体优化算法

本文研究了求解多层线性规划问题的整体优化算法,利用流动等值面技术,证明了算法的有限终止性,并给出实际例子验证了算法的有效性.     

Exponentially convergent parallel algorithm for nonlinear eigenvalue problems

A. V. Klimenko, V. L. Makarov ^{A new algorithm for nonlinear eigenvalue problems is proposed.The numerical technique is based on a perturbation of the coefficientsof differential equation combined with the Adomian decompositionmethod for the nonlinear part. The approach provides an exponentialconvergence rate with a base which is inversely proportionalto the index of the eigenvalue under consideration. The eigenpairscan be computed in parallel. Numerical examples are presentedto support the theory. They are in good agreement with the spectralasymptotics obtained by other authors.}     

Minimum entropy control of chaos via online particle swarm optimization method

One of the recently developed approaches for control of chaos is the minimum entropy (ME) control technique. In this method an entropy function based on the Shannon definition, is defined for a chaotic system. The control action is designed such that the entropy as a cost function is minimized which results in more regular pattern of motion for the system trajectories. In this paper an online optimization technique using particle swarm optimization (PSO) method is developed to calculate the control action based on ME strategy. The method is examined on some standard chaotic maps with error feedback and delayed feedback forms. Considering the fact that the optimization is online, simulation results show very good effectiveness of the presented technique in controlling chaos.     

一类约束优化问题的非单调信赖域算法

本文就一类等式约束优化问题,结合当前比较流行的非单调技术,提出了一类新的求解等式约束优化的非单调信赖域算法.其非单调程度由算法自适应控制,计算预测下降量和实际下降量的比值时,采用前m(k)个点的信息,这不同于以前在计算预测下降量和实际下降量的比值时,仅仅采用当前-个点的信息.在没有正则性条件的假设下我们证明了算法是有定义的.并且通过对不同情况的讨论证明了算法的全局收敛性.基本的数值试验表明算法是有效的,且说明提出的非单调信赖域算法比单调信赖域算法有效.     

An efficient interval computing technique for bound-constrained uncertain optimization problems

In this article, a competent interval-oriented approach is proposed to solve bound-constrained uncertain optimization problems. This new class of problems is considered here as an extension of the classical bound-constrained optimization problems in an inexact environment. The proposed technique is nothing but an imitation of the well-known interval analysis-based branch-and-bound optimization approach. Efficiency of this technique is strongly dependent on division, bounding, selection/rejection and termination criteria. The technique involves a multisection division criterion of the accepted/proposed search region. Then, we have employed the interval-ranking definitions with respect to the pessimistic decision makers’ point of view given by Mahato and Bhunia [Interval-arithmetic-oriented interval computing technique for global optimization, Appl. Math. Res. Express 2006 (2006), pp. 1–19] to compare the interval-valued objectives calculated in each subregion and also to select the subregion containing the best interval objective value. The process is continued until the interval width for each variable in the accepted subregion is negligible and ultimately the global or close-to-global interval-valued optimal solution is obtained. The proposed technique has been evaluated numerically using a wide set of newly introduced univariate/multivariate test problems. Finally, to compare the computational results obtained by the proposed method, the graphical representation for some test problems is given.     

On an extension of Weber problem with Euclidean distance

The paper is an extension of the authors previous work [5] in which an approximate discrete technique is proposed to solve the Weber problem with the Euclidean distance. Now, it is assumed that the cost of connection (the cost associated with two points in the plane) depends upon the distance stronger than linearly. A model is formulated and an approximate discrete technique analogous to that in [5] is proposed. Its validity is proved. Both the numerical complexity and the practical efficiency of the algorithm are considered. An example is given     

Dynamic Global Constraints in Backtracking Based Environments

Global constraints provide strong filtering algorithms to reduce the search space when solving large combinatorial problems. In this paper we propose to make the global constraints dynamic, i.e., to allow extending the set of constrained variables during search. We describe a generic dynamisation technique for an arbitrary monotonic global constraint and we compare it with the semantic-based dynamisation for the alldifferent constraint. At the end we sketch a dynamisation technique for non-monotonic global constraints. A comparison with existing methods to model dynamic problems is given as well.     

A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS

In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.     

A Nonmonotone Trust Region Algorithm for Nonlinear Optimization Subject to General Constraints

In this paperwe present a nonmonotone trust region algorthm for general nonlinear constrained optimization problems.The main idea of this paper is to combine Yuan‘‘‘‘s technique[1]with a nonmonotone method similar to Ke and Han[2].This new algorithm may not only keep the robust properties of the algorithm given by Yuan,but also have some advantages led by the nonmonotone technique.Under very mild conditions,global convergence for the algorithm is given.Numerical experiments demostrate the efficency of the algorithm.     

An overview on the simplex algorithm

In this paper, the simplex algorithm and its variants are investigated. First, we define a new concept called formal tableau, which leads to derive easily the dual solution from the latest primal table; without any distinction between the original variables and the slack ones. Second, we propose a new method for initializing the simplex algorithm. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. The computational results reveal that this new method is very favorable especially when the number of artificial variables is significant. Finally, this method will be combined with the notion of formal tableau leading naturally to a second new approach.     

Conjugacy classes in finite permutation groups via homomorphic images

The lifting of results from factor groups to the full group is a standard technique for solvable groups. This paper shows how to utilize this approach in the case of non-solvable normal subgroups to compute the conjugacy classes of a finite group.

     

A regularization of the Frank—Wolfe method and unification of certain nonlinear programming methods

The Frank—Wolfe linearization technique is a popular feasible direction algorithm for the solution of certain linearly constrained nonlinear problems. The popularity of this technique is due in part to its ability to exploit special constraint structures, such as network structures, and in part to the fact that it decomposes nonseparable problems over Cartesian product sets. However, the linearization which induces these advantages is also the source of the main disadvantages of the method: a sublinear rate of convergence and zigzagging behaviour. In order to avoid these disadvantages, a regularization penalty term is added to the objective of the direction generating subproblem. This results in a generic feasible direction method which also includes certain known nonlinear programming methods.     

Hybrid harmony search algorithm and fuzzy mechanism for solving congestion management problem in an electricity market

A hybrid technique for solving the congestion management problem in an electricity market based on harmony search algorithm (HAS) and Fuzzy mechanism is presented in this article. This algorithm does not require initial value setting for the variables and does not require differential gradients, thus it can consider discontinuous functions as well as continuous functions. The HAS is a recently developed powerful evolutionary algorithm, inspired by the improvisation process of musicians, for solving single/multiobjective optimization problems. In the proposed technique, each musician plays a note for finding a best harmony all together. Transmission pricing and congestion management are the key elements of a competitive electricity market based on direct access. They also focus of much of the debate concerning alternative approaches to the market design and the implementation of a common carrier electricity system. This article focuses on the tradeoffs between simplicity and economic efficiency in meeting the objectives of a transmission pricing and congestion management scheme. The effectiveness of the proposed technique is applied on 30 and 118 bus IEEE standard power system in comparison with CPSO, PSO‐TVAC, and PSO‐TVIW. The numerical results demonstrate that the proposed technique is better and superior than other compared methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 90–98, 2016     

A Hybrid Genetic Algorithm for the Single Machine Scheduling Problem

A hybrid genetic algorithm (HGA) is proposed for the single machine, single stage, scheduling problem in a sequence dependent setup time environment within a fixed planning horizon (SSSDP). It incorporates the elitist ranking method, genetic operators, and a hill-climbing technique in each searching area. To improve the performance and efficiency, hill climbing is performed by uniting the Wagner-Whitin Algorithm with the problem-specific knowledge. The objective of the HGA is to minimize the sum of setup cost, inventory cost, and backlog cost. The HGA is able to obtain a superior solution, if it is not optimal, in a reasonable time. The computational results of this algorithm on real life SSSDP problems are promising. In our test cases, the HGA performed up to 50% better than the Just-In-Time heuristics and 30% better than the complete batching heuristics.     

基于免疫克隆算法的蒙古文形近元素聚类

文本聚类是聚类技术的重要研究领域.该技术根据文本的相似特征或相似表达式对文本进行聚类,使得属于同类的文本具有最大的相似性,而属不同类文本具有最大的差异性.与其它文字相比,蒙古文的结构和书写方式具有许多特征.本文结合K-means与克隆免疫算法提出了一种称为ICKM的新型聚类技术.四种元素集上的仿真实验说明了我们提出的方法在蒙古文聚类的有效性.     

A global best artificial bee colony algorithm for global optimization

The artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, there is still an insufficiency in the ABC algorithm regarding its solution search equation, which is good at exploration but poor at exploitation. Inspired by differential evolution (DE), we propose a modified ABC algorithm (denoted as ABC/best), which is based on that each bee searches only around the best solution of the previous iteration in order to improve the exploitation. In addition, to enhance the global convergence, when producing the initial population and scout bees, both chaotic systems and opposition-based learning method are employed. Experiments are conducted on a set of 26 benchmark functions. The results demonstrate good performance of ABC/best in solving complex numerical optimization problems when compared with two ABC based algorithms.     

Increasing the Efficiency of Selected Grid Search Procedures Through the Introduction of a Best Step Mechanism

In this paper, several new developments are suggested in order to increase the efficiency of grid search procedures used within vertex enumeration solution algorithms based on both the classical cobweb technique (a two constraint approach) and a single constraint approach. The gains in efficiency (and robustness) are demonstrated by incorporating the developments into a grid search procedure (which is a part of a heuristic solution algorithm used to obtain solutions to a non-linear bi-level multi-period model of an aluminium smelter) and applying it to a test suite of problems. The classical cobweb technique is shown to have some serious problems when used in this application but with step size improvements suggested in the paper, is shown to be very competitive. The developments are also incorporated into a single constraint based approach which does not suffer from the cobweb specific difficulties. The improvements considered include the use of a step mechanism initially with a step size calculated {a priori} and then finally with a tailored (best) one. The latter development when applied to the cobweb approach, requires the approximation of the two constraints (and hence the intersection of their graphs) using second degree polynomials.     

Using local search to find MSSes and MUSes

In this paper, a new complete technique to compute Maximal Satisfiable Subsets (MSSes) and Minimally Unsatisfiable Subformulas (MUSes) of sets of Boolean clauses is introduced. The approach improves the currently most efficient complete technique in several ways. It makes use of the powerful concept of critical clause and of a computationally inexpensive local search oracle to boost an exhaustive algorithm proposed by Liffiton and Sakallah. These features can allow exponential efficiency gains to be obtained. Accordingly, experimental studies show that this new approach outperforms the best current existing exhaustive ones.