Convergence condition and efficient implementation of the fuzzy curve-tracing (FCT) algorithm

The fuzzy curve-tracing (FCT) algorithm can be used to extract a smooth curve from unordered noisy data. In this paper, we analyze the convergence property of the algorithm based on the diagonal dominance requirement of the matrix used in the clustering procedure and prove that the algorithm is guaranteed to converge if the weighting coefficient for the smoothness constraint is chosen properly. Based on the convergence condition, we develop several methods for fast and reliable implementation of the algorithm. We show that the algorithm can be initialized with a user-defined curve in many cases, that a multiresolution clustering based approach and an image down-sampling scheme can be used to improve the algorithm stability and speed and that two types of traps can be removed to correct the mistakes in curve tracing. We demonstrate several advantages of our algorithm over the commonly used snake models for boundary detection and several methods for principle curve extraction.     

自适应人工蜂群算法的盲源分离

盲源分离(BSS)是传感器信号处理领域研究热点,针对传统盲源分离算法大多存在收敛速度慢、分离精度低、适用场合窄的缺点,提出了一种基于自适应人工蜂群算法的盲源分离.利用Givens旋转变换降低计算量,搜索策略引入自适应全局指导项动态调节最优解导向作用,选择策略采用自适应Boltz-mann轮盘赌作改进平衡迭代各阶段选择压力集中程度.实验表明:基于自适应人工蜂群算法的盲源分离,能够加快收敛速度并显著提高分离精度至约3个数量级.     

Blind channel identification via stochastic approximation: constant step-size algorithms

This work is devoted to the study of a class of recursive algorithms for blind channel identification. Using weak convergence methods, the convergence of the algorithm is obtained and the rate of convergence is ascertained. The technique discussed can also be used in the analysis of rates of convergence for decreasing step-size algorithms.     

Isoparametric C 0 interior penalty methods for plate bending problems on smooth domains

In this paper we develop isoparametric C ⁰ interior penalty methods for plate bending problems on smooth domains. The orders of convergence of these methods are shown to be optimal in the energy norm. We also consider the convergence of these methods in lower order Sobolev norms and discuss subparametric C ⁰ interior penalty methods. Numerical results that illustrate the performance of these methods are presented.     

Optimal Quadratic and Cubic Spline Collocation on Nonuniform Partitions

We develop optimal quadratic and cubic spline collocation methods for solving linear second-order two-point boundary value problems on non-uniform partitions. To develop optimal nonuniform partition methods, we use a mapping function from uniform to nonuniform partitions and develop expansions of the error at the nonuniform collocation points of some appropriately defined spline interpolants. The existence and uniqueness of the spline collocation approximations are shown, under some conditions. Optimal global and local orders of convergence of the spline collocation approximations and derivatives are derived, similar to those of the respective methods for uniform partitions. Numerical results on a variety of problems, including a boundary-layer problem, and a nonlinear problem, verify the optimal convergence of the methods, even under more relaxed conditions than those assumed by theory.     

Lookup-Table-Based Secure Client-Side Embedding for Spread-Spectrum Watermarks

Today, mass-scale electronic content distribution systems embed forensic tracking watermarks primarily at the distribution server. For limiting the bandwidth usage and server complexity and enhancing scalability, it is preferable to embed the watermark at the client. Embedding in these untrusted clients requires secure embedding methods that do not leak unmarked content or the watermarking secrets. In this work, we propose a secure watermark embedding scheme based on lookup tables for spread-spectrum watermarks, which are robust to noise and can be detected without comparison to the original content. We also develop fast detection mechanisms that make the watermark detection feasible for tracking systems with a large number of clients. Our fast detection algorithm improves detection speed of existing methods by six orders of magnitude in a typical system with millions of clients.      

改进遗传算法在磁性材料组炉优化问题中的应用

牌号、交货日期、优先级、需求量等是磁性材料生产工单的属性,计划员需要依据上述属性寻求最优的生产工单组合以最小化生产成本并提高生产效率.针对磁性材料企业人工组炉存在的组炉时间长,组炉结果不优化问题.本文建立了磁性材料生产工单组炉优化模型.提出将该组炉问题转化为伪旅行商问题,并采用一种改进遗传算法求解.染色体编码采用从1到N的自然数编码方式,并设计一种基于最早完工日期规则的初始种群产生方法.引入精英选择策略和改进的贪心三交叉算子,优化遗传算法收敛速度和精度;引入逆转算子,提高遗传算法全局搜索能力.基于实际生产数据的仿真实验表明,建立的磁性材料组炉优化模型是合适的,所提改进算法是有效的.     

On asymptotic properties of a constant-step-size sign-error algorithm for adaptive filtering

This work is devoted to asymptotic properties of a sign-error adaptive filtering algorithm with constant step size. Under much weaker conditions than those that appear in the literature, we obtain convergence and rate of convergence by using weak convergence methods. An example is provided to demonstrate the performance of the algorithm.     

Co-clustering over multiple dynamic data streams based on non-negative matrix factorization

Clustering multiple data streams has become an active area of research with many practical applications. Most of the early work in this area focused on one-sided clustering, i.e., clustering data streams based on feature correlation. However, recent research has shown that data streams can be grouped based on the distribution of their features, while features can be grouped based on their distribution across data streams. In this paper, an evolutionary clustering algorithm is proposed for multiple data streams using graph regularization non-negative matrix factorization (EC-NMF) in which the geometric structure of both the data and feature manifold is considered. Instead of directly clustering multiple data streams periodically, EC-NMF works in the low-rank approximation subspace and incorporates prior knowledge from historic results with temporal smoothness. Furthermore, we develop an iterative algorithm and provide convergence and correctness proofs from a theoretical standpoint. The effectiveness and efficiency of the algorithm are both demonstrated in experiments on real and synthetic data sets. The results show that the proposed EC-NMF algorithm outperforms existing methods for clustering multiple data streams evolving over time.     

Scheduling algorithms for a semiconductor probing facility

This paper focuses on a scheduling problem in a semiconductor wafer probing facility. In the probing facility, wafer lots with distinct ready times are processed on a series of workstations, each with identical parallel machines. We develop a heuristic algorithm for the problem with the objective of minimizing total tardiness of orders. The algorithm employs a bottleneck-focused scheduling method, in which a schedule at the bottleneck workstation is constructed first and then schedules for other workstations are constructed based on the schedule at the bottleneck. For scheduling wafer lots at the bottleneck workstation, we consider prospective tardiness of the lots as well as sequence-dependent setup times required between different types of wafer lots. We also present a rolling horizon method for implementation of the scheduling method on a dynamic situation. The suggested methods are evaluated through a series of computational experiments and results show that the methods work better than existing heuristic methods.     

Higher-order numeric Wazwaz–El-Sayed modified Adomian decomposition algorithms

In this paper, we develop new numeric modified Adomian decomposition algorithms by using the Wazwaz–El-Sayed modified decomposition recursion scheme, and investigate their practicality and efficiency for several nonlinear examples. We show how we can conveniently generate higher-order numeric algorithms at will by this new approach, including, by using examples, 12th-order and 20th-order numeric algorithms. Furthermore, we show how we can achieve a much larger effective region of convergence using these new discrete solutions. We also demonstrate the superior robustness of these numeric modified decomposition algorithms including a 4th-order numeric modified decomposition algorithm over the classic 4th-order Runge–Kutta algorithm by example. The efficiency of our subroutines is guaranteed by the inclusion of the fast algorithms and subroutines as published by Duan for generation of the Adomian polynomials to high orders.     

A fast successive over-relaxation algorithm for force-directed network graph drawing

Force-directed approach is one of the most widely used methods in graph drawing research. There are two main problems with the traditional force-directed algorithms. First, there is no mature theory to ensure the convergence of iteration sequence used in the algorithm and further, it is hard to estimate the rate of convergence even if the convergence is satisfied. Second, the running time cost is increased intolerablely in drawing largescale graphs, and therefore the advantages of the force-directed approach are limited in practice. This paper is focused on these problems and presents a sufficient condition for ensuring the convergence of iterations. We then develop a practical heuristic algorithm for speeding up the iteration in force-directed approach using a successive over-relaxation (SOR) strategy. The results of computational tests on the several benchmark graph datasets used widely in graph drawing research show that our algorithm can dramatically improve the performance of force-directed approach by decreasing both the number of iterations and running time, and is 1.5 times faster than the latter on average.     

Multiplier method and optimal control problems with terminal state constraints

The multiplier method for constrained optimization problems is considered geometrically with the concept of supporting hypersurfaces. This geometric interpretation simplifies the comparison of the multiplier method with other existing methods and provides a basis from which to develop new algorithms. Moreover, though it is proved that the algorithm of the multiplier method can be derived from different viewpoints, the convergence of the multiplier method as a successive approximation algorithm is verified in this paper. Finally, the multiplier method is applied to optimal control problems with terminal state constraints, and some numerical experiments are presented.     

A mixed strategy of combining evolutionary algorithms with multigrid methods

Multigrid methods have been proven to be an efficient approach in accelerating the convergence rate of numerical algorithms for solving partial differential equations. This paper investigates whether multigrid methods are helpful to accelerate the convergence rate of evolutionary algorithms for solving global optimization problems. A novel multigrid evolutionary algorithm is proposed and its convergence is proven. The algorithm is tested on a set of 13 well-known benchmark functions. Experiment results demonstrate that multigrid methods can accelerate the convergence rate of evolutionary algorithms and improve their performance.     

基于狄克斯特拉算法的车间动态生产能力评估与实现

本文基于Dijkstra算法思想上提出一套快速评估车间动态生产能力的方法,该方法在确保订单不延迟的情况下,能够有效合理地安排生产过程。本文通过对车间工序建立数学模型,应用改进的算法对所有订单进行评估,确定所有订单每道工序的最早完成时间和最迟发生时间,从而实现对生产能力动态评估。本算法适用于严格按订单组织生产的企业,企业可以利用该算法对订单进行评估,确定是否可以接受订单。     

Nash equilibrium seeking with prescribed performance

In thiswork,we study aNash equilibrium (NE) seeking problem for stronglymonotone non-cooperative games with prescribed performance. Unlike general NE seeking algorithms, the proposed prescribed-performance NE seeking laws ensure that the convergence error evolves within a predefined region. Thus, the settling time, convergence rate, and maximum overshoot of the algorithm can be guaranteed. First, we develop a second-order Newton-like algorithm that can guarantee prescribed performance and asymptotically converge to the NE of the game. Then, we develop a first-order gradient-based algorithm. To remove some restrictions on this first-order algorithm, we propose two discontinuous dynamical system-based algorithms using tools from non-smooth analysis and adaptive control. We study the special case in optimization problems. Then, we investigate the robustness of the algorithms. It can be proven that the proposed algorithms can guarantee asymptotic convergence to the Nash equilibrium with prescribed performance in the presence of bounded disturbances. Furthermore, we consider a second-order dynamical system solution. The simulation results verify the effectiveness and efficiency of the algorithms, in terms of their convergence rate and disturbance rejection ability.     

Efficient methods for estimating constrained parameters with applications to lasso logistic regression

Fitting logistic regression models is challenging when their parameters are restricted. In this article, we first develop a quadratic lower-bound (QLB) algorithm for optimization with box or linear inequality constraints and derive the fastest QLB algorithm corresponding to the smallest global majorization matrix. The proposed QLB algorithm is particularly suited to problems to which the EM-type algorithms are not applicable (e.g., logistic, multinomial logistic, and Cox’s proportional hazards models) while it retains the same EM ascent property and thus assures the monotonic convergence. Secondly, we generalize the QLB algorithm to penalized problems in which the penalty functions may not be totally differentiable. The proposed method thus provides an alternative algorithm for estimation in lasso logistic regression, where the convergence of the existing lasso algorithm is not generally ensured. Finally, by relaxing the ascent requirement, convergence speed can be further accelerated. We introduce a pseudo-Newton method that retains the simplicity of the QLB algorithm and the fast convergence of the Newton method. Theoretical justification and numerical examples show that the pseudo-Newton method is up to 71 (in terms of CPU time) or 107 (in terms of number of iterations) times faster than the fastest QLB algorithm and thus makes bootstrap variance estimation feasible. Simulations and comparisons are performed and three real examples (Down syndrome data, kyphosis data, and colon microarray data) are analyzed to illustrate the proposed methods.     

Convergence speed of a fractional order consensus algorithm over undirected scale‐free networks

Scale‐free networks have been rediscovered universally in natural and man‐made systems, and the consensus protocols have been tremendously studied over the last decade. Motivated by the fractional‐order dynamics of bacteria colonies, a fractional‐order protocol is employed to achieve the consensus over scale‐free networks. The most remarkable property of scale‐free networks lies in the inverse power‐law degree distributions. The present work concerns the convergence speed with different fractional orders corresponding to different power‐law parameters. The analytic solutions of consensus protocols are given and its property is discussed, explaining the quick convergence speed in the early stage of the consensus process, and the slower performance later. Inspired by such behavior, a switching order consensus protocol is proposed, which efficiently increases the convergence speed and ensures the exponential convergence as time tends to infinity. The disagreement of the system during the consensus procedure is investigated. Theoretic analysis and simulations demonstrate that, for certain scale‐free networks, an optimal order exists so that the fractional‐order consensus algorithm can minimize the disagreement or its integral. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Modified particle swarm optimization for BMDS interceptor resource planning

One important mission of the strategic defense is to develop an integrated, layered Ballistic Missile Defense System (BMDS). We consider the problem of assigning interceptors to multiple waves of incoming ballistic missiles. This work addresses the issue of shot time constraints and directly allocates multiple targets to interceptors in the single engagement problem. A mathematical model and method for BMDS Interceptor resource planning (IRP) is presented. In addition to mathematical model, a modified particle swarm optimization RPPSO algorithm has been developed for solving complex IRP problem. This algorithm adapted a basic PSO algorithm to make it compatible with reasonable engineering problems. RPPSO was developed by embedding a reverse predictor within the basic algorithm to avoid premature convergence without significantly reducing convergence speed, and adding a repulsive force to keep the diversity of both local and global optima. Algorithm performance and experimental examples verified the benefits and specific applications of paper work.     

基于多种群进化的遗传算法

针对单个种群的遗传算法容易陷入局部收敛而出现早熟的情况,提出了一种新的多种群遗传算法,用多线程并行处理的方法实现种群之间同步进化。实验证明,基于多种群的遗传算法能够有效地避免局部收敛问题,通过与简单遗传算法进行比较,所提出的新算法不仅收敛速度快,而且收敛效率高,是一种可行、有效的算法。