行满秩Toeplitz型矩阵Moore-Penrose逆的快速算法

通过构造对称分块矩阵给出了秩为m的m×n阶Toeplitz型矩阵Moore-Penrose逆的快速算法。该算法计算复杂度为O（mn）+O（m²）,而由T^T（TT^T）^-1直接求解所需运算量为O（m²n）+O（m3）。数值算例表明了该快速算法的有效性。     

未建模误差补偿Elman网络直接广义预测控制

针对一类非线性系统,提出了Elman网络直接广义预测控制算法。先将非线性系统等价转换成线性系统,然后对未建模动态误差进行估计,最后利用Elman网络进行预测控制器设计,并根据跟踪误差对控制器参数中的未知向量进行自适应调整,理论证明了误差收敛到原点一个小邻域内。该方法不需要求解Diophantine方程和矩阵求逆,只需要辨识一个参数θ（k）,因此减少了在线计算量,提高了实时性。仿真结果验证了该方法的有效性。     

一种基于共轭梯度的LMBP改进学习算法

对神经网络中的LMBP（Levenberg-Marquardt BP）算法的收敛速度慢进行分析,针对矩阵J^TJ+µI求逆过程运算量过大而造成收敛速度慢的缺陷,根据无约束优化理论,提出一种基于共轭梯度方法的改进LMBP网络学习算法,利用求解大规模线性方程组的共轭梯度方法,避免了烦琐的求逆过程,降低了计算复杂度,加快了网络的收敛速度,通过Matlab仿真,比较了算法的收敛速度,证明了方法的有效性。     

基于二进制可分辨矩阵的快速求核算法

目前,求核算法存在以下不足：求得的核与正区域的核不一致,求核算法的时间复杂度和空间复杂度不理想。针对上述问题,给出一种二进制可分辨矩阵的定义及其求核性质,并证明了由该性质获得的核与正区域的核是等价的,然后设计求核算法,该算法的时间复杂度为max{O（|C||U/C|²）,O（|C||U|）},空间复杂度为O（|C||U/C|²）。最后实例说明该方法的可行性和有效性。     

基于有序差别集的高效属性约简算法

基于可分辨矩阵的属性约简算法需要占用大量的存储空间,可分辨矩阵中许多元素项对约简是多余的;并且随着问题规模的增大,该类算法的效率并不理想。针对上述不足,提出一种基于有序差别集的属性约简算法,该算法不需要创建可分辨矩阵和生成多余的元素项,大大降低了存储量和计算量,从而提高了属性约简效率,使算法的时间复杂度和空间复杂度分别降为max{O（|C|² |U/C|²）,O（|C|²|MsCount|）}和O（|MsCount|）。实验表明该算法是有效的、高效的。     

基于PDEs的图像平滑数值方法

对基于PDEs的图像平滑技术进行了探讨,在对四阶模型u/t=-▽² [c（|▽²u|）▽²u] 解的分析基础上,给出一种求解该模型的数值方法,数值实验结果给出了良好的去噪效果。     

基于变精度粗糙集的不完备信息系统知识约简

基于变精度的思想,提出了一种新的不完备信息系统变精度粗糙集模型。基于该模型给出了不完备信息系统的β上（下）分布约简和β上（下）近似约简。给出了求解不完备信息系统β上（下）分布约简的辨识矩阵方法。     

三态编码方法及实现电路的研究

定义了（N,M）三态编码电路模型。基于三态数据编码（BCT）算法,讨论了三态编码的硬件设计方法。设计了“除3求余”电路模块,并采用“模块组合”设计方法,实现了任意（N,M）模型的三态编码电路。该方法的主要优点是能够适应定义模型下的不同规模的动态需求。最后,作为示例,给出了（4,2）三态编码模型的硬件结构电路。     

《线性代数》典型题解①

第一章 矩阵和行列式 一、矩阵的运算计算ＡＢ,ＡＢ—ＢＡ解：ＡＢ＝ＢＡ＝ＡＢ－ＢＡ＝２．计算解： ３．设ｆ（λ）＝,Ａ是ｎ阶方阵,定义ｆ（Ａ）＝已知ｆ（λ）＝,求ｆ（Ａ）。解：ｆ（Ａ）＝４．设Ａ＝Ｂ＝解：ＡＢ＝二、逆矩阵１．求矩阵Ａ＝的逆矩阵解一：,故Ａ为非奇异矩阵。解二：用行初等变换求Ａ－１。所以Ａ－１＝２．设Ａ＝解一：将Ａ写成对角阵,Ａ＝＝Ａ’一ＳＡ＋３,Ａ＝１１．求ｆ（Ａ）ｎ ＼一３ ３／二、逆矩阵１．求矩阵Ａ＝的逆矩阵。解一：＝６一０,故Ａ为非奇异矩阵。解Ｈ：用行初等变换求Ａ‘。所以Ａ－１二…     

一种二值图像的阈值可视密码方案

目前提出的许多关于二值可视密码方案的论文都致力于研究在可视秘密共享方案里如何使像素扩展比较小或恢复图像的对比度比较高的问题。基于Shamir的秘密共享方案的思想,提出一种新的二值图像（k,n）-VCS可视密码方案。该方案利用二元域上线性方程组解的特征及多层（k,k）-VCS构造基础矩阵S⁰,S¹,给出一个强的访问结构,从而获得（k,n）-VCS可视密码方案更小的像素扩展。     

Simulation–optimization mechanism for expansion strategy using real option theory

A right expansion strategy can bring a company more market shares and profits, and hence increase shareholders’ equities. However, limited financial resources and various uncertainties require business practitioners to achieve their goals while controlling the risks incurred at an acceptable level. Therefore, justification of expansion investments is an important and complex topic in industry. The traditional investment analysis tools such as net present value (NPV) often tend to undervalue investment decisions. We formulate the expansion investments using real options, and develop a financial model to assess the option value. Monte Carlo simulation is considered a good way to estimate the value of the option. This valuation gives decision makers a way to choose the appropriate expansion strategy based on an integrated view of the market dynamics, but optimization is still a difficult problem to resolve. This paper presents a model of optimization under uncertainty combining system simulation with GA-based optimization to resolve the expansion problem. An industry case is used to demonstrate the application of real options to value expansion investment by using simulation–optimization. This approach also provides some new insights for the real options theory.     

A novel reduction approach for Petri net systems based on matching theory

In this paper, an efficient method is presented to solve the state explosion problem in Petri nets by using matching theory. It is difficult to analyze a Petri net when there are too many existing states. In order to solve such a problem, it is addressed to label a weight value on a transition according to the relationship between a place and a transition. Then, the transition with the largest weight value is selected. The selected transition is the most important and connective in the entire Petri net. After selecting each transition for several times, the last one denotes the least connective in the whole Petri net and the redundant place is obtained. Furthermore, the Petri net model can be reduced by fusing the transition with the largest weight value and the redundant place. In this novel approach, an incidence matrix, a weight vector, a matching matrix, a compressed incidence matrix, and a reduced and compressed incidence matrix are sequentially built based on the original Petri net model so as to obtain a reduced and compressed Petri net model. Finally, the experimental results regarding the CAVE automatic virtual reality environment demonstrate the high viability of the proposed approach.     

Maximum Singular Value of Matrix and its Economic Interpretation

We prove that the maximum singular value of the matrix and the corresponding singular vectors are the optimal solution for a special quadratic optimization problem. We consider the economic interpretation of the optimal solution for the linear model of production and for the productive Leontief model. We relate the optimal solution to the Frobenius number and vectors and compare the Frobenius numbers and maximum singular values for Leontief inverse matrix in the 15-sectoral balance of Ukraine for 2003–2009.     

相关数据集的最小二乘处理方法

数据的最小二乘处理可以归结为求解线性方程组Ａｘ＝ｂ，不论在何种情形下（常定，超定或欠定），它都有最小二乘意义下的最优解．这要求数据矩阵Ａ的相关矩阵的逆矩阵存在，即欠定增况下的ＡＡＴ或超定情况下的ＡＴＡ是满秩的．对于降秩的ＡＡＴ或ＡＴＡ的情况，文中提出用奇异值分解的方法求其矩阵伪逆，使数据的最小二乘处理适应于相关数据集的处理．同直接对数据矩阵Ａ进行奇异值分解求ＡＸ＝ｂ的最小二乘解相比，本文提出的方法只需对阶数较低的对称方阵进行分解，可在微机上实现高维数据的处理．     

Random assignment method based on genetic algorithms and its application in resource allocation

Assignment problem is considered a well-known optimization problem in manufacturing and management processes in which a decision maker’s point of view is merged into a decision process and a valid solution is established. In this study, taking the complementary relations between expected value and variance in decision making and the synthesizing effect of random variables into consideration, a new model for random assignment problems is proposed; in which the characteristic of assignment problems are considered to present a concrete scheme based on genetic algorithms (denoted by SE ⊕ GA-SAF, for short). We study the model’s convergence using the Markov chain theory, and analyze its performance through simulation. All of these indicate that this solution model can effectively aid decision making in the assignment process, and that it possesses the desirable features such as interpretability and computational efficiency, as such it can be widely used in many aspects including manufacturing, operations, logistics, etc.     

An AHP-based decision-making tool for the solution of multiproduct batch plant design problem under imprecise demand

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessarily involves the way that equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem. This work relies on a previous study, which proposed an alternative treatment of the imprecision (demands) by introducing fuzzy concepts, embedded in a multi-objective Genetic Algorithm (GA) that takes into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The results showed that an additional interpretation step might be necessary to help the managers choosing among the non-dominated solutions provided by the GA. The analytic hierarchy process (AHP) is a strategy commonly used in Operations Research for the solution of this kind of multicriteria decision problems, allowing the apprehension of manager subjective judgments. The major aim of this study is thus to propose a software integrating the AHP theory for the analysis of the GA Pareto-optimal solutions, as an alternative decision-support tool for the batch plant design problem solution.     

Scheduling Multi-Mode Projects under Uncertainty to Optimize Cash Flows: A Monte Carlo Ant Colony System Approach

Project scheduling under uncertainty is a challenging field of research that has attracted increasing attention. While most existing studies only consider the single-mode project scheduling problem under uncertainty, this paper aims to deal with a more realistic model called the stochastic multi-mode resource constrained project scheduling problem with discounted cash flows (S-MRCPSPDCF). In the model, activity durations and costs are given by random variables. The objective is to find an optimal baseline schedule so that the expected net present value (NPV) of cash flows is maximized. To solve the problem, an ant colony system (ACS) based approach is designed. The algorithm dispatches a group of ants to build baseline schedules iteratively using pheromones and an expected discounted cost (EDC) heuristic. Since it is impossible to evaluate the expected NPV directly due to the presence of random variables, the algorithm adopts the Monte Carlo (MC) simulation technique. As the ACS algorithm only uses the best-so-far solution to update pheromone values, it is found that a rough simulation with a small number of random scenarios is enough for evaluation. Thus the computational cost is reduced. Experimental results on 33 instances demonstrate the effectiveness of the proposed model and the ACS approach.     

A coordinated approach to hedge the risks in stochastic inventory-routing problem

The inventory routing problem (IRP) studied in this research involves repeated delivery of products from a depot to a set of retailers that face stochastic demands over a long period. The main objective in the IRP is to design the set of routes and delivery quantities that minimize transportation cost while controlling inventory costs. Traditional IRP focuses on risk-neutral decision makers, i.e., characterizing replenishment policies that maximize expected total net present value, or equivalently, minimize expected total cost over a planning horizon. In this research, for incorporating risk aversion, a hedge-based stochastic inventory-routing system (HSIRS) integrated with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and Forward Option Pricing (FOP)model based on Black-Scholes model, from hedge point of view, is proposed to solve the multi-product multi-period inventory routing problem with stochastic demand. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to maximize the net present value at an acceptable service level. As a result, an optimal portfolio (R, s, S) system of product group can be generated to maximize the net present value under an acceptable service level in a given planning horizon. Meanwhile, the target group needed to be served and the relative transportation policy also can be determined accordingly based on the time required to be served as a priori partition to minimize the average transportation costs; hence, the routing assignment problem can be successfully optimized through a Predicting Particle Swarm Optimization algorithm.     

Uncertain location–allocation decisions for a bi-objective two-stage supply chain network design problem with environmental impacts

In the cases that the historical data of an uncertain event is not available, belief degree-based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi-objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree-based uncertainty theory. This article is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance-constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi-objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.     

Error analysis and minimum bound method for atmospheric remote sensing

In this study, we present an error analysis for Tikhonov regularization in a semi-stochastic setting. The analysis is carried out in such a way that it can be applied to any kind of inverse problem in atmospheric remote sensing. A method for selecting the optimal regularization parameter relying on the minimization of an estimator of the bound of the error between the first iterate and the exact solution is also discussed. Numerical simulations are performed for NO₂ retrieval from SCIAMACHY limb scatter measurements.