数控机床边界强度过程的非等周期不完全预防维修

基于边界强度过程理论，提出了数控机床在可靠度限制下任意维修质量的非等周期不完全预防维修方法，建立了综合考虑维修对役龄的影响和故障强度随时间增加的混合模型，并且假设修复质量和故障强度增加值均为服从均匀分布的随机变量，以平均维修费用为目标函数，用迭代方法给出了非等周期预防维修周期和最佳的维修次数，并结合工程实例讨论了费用参数对平均维修费用的影响.     

Strategic Robust Mixed Model Assembly Line Balancing Based on Scenario Planning

Assembly line balancing involves assigning a series of task elements to uniform sequential stations with certain restrictions. Decision makers often discover that a task assignment which is optimal with respect to a deterministic or stochastic/fuzzy model yields quite poor performance in reality. In real environments, assembly line balancing robustness is a more appropriate decision selection guide. A robust model based on the α worst case scenario is developed to compensate for the drawbacks of traditional robust criteria. A robust genetic algorithm is used to solve the problem. Comprehensive computational experiments to study the effect of the solution procedure show that the model generates more flexible robust solutions. Careful tuning the value of α allows the decision maker to balance robustness and conservativeness of as- sembly line task element assignments.     

New Voronoi Diagram Algorithm of Multiply-Connected Planar Areas in the Selective Laser Melting

This paper studies the practical generation of Voronoi diagrams for multiply-connected planar areas bounded by line segments. The core of the algorithm was calculating Voronoi polygon of every Voronoi object in planar areas independently. The main approach had two steps. The first step was calculating all relevant bisectors of every Voronoi object. The second was combining obtained bisectors into completed Voronoi polygons individually. All code was implemented in Visual C++ platform. The resulting code was extensively tested in real-world data and its practical running time grew only linearly. Three statistical CPU-consumption charts had been drawn with the Voronoi diagrams computation data, and compared with other published codes for computing Voronoi diagrams. The algorithm was applied to compute offsetting of slice area consisting of large-scale line segments for the selective laser melting (SLM) trajectory scanning technology which is a kind of rapid prototyping (RP). The experimental results of offsetting for slice area based on Voronoi diagrams show that the approach is effective and simple for polygon offsetting problems. The method is helpful to those offsetting work and can provide more effective offsetting solution.     

基于最小扰动相关去噪法股票投资组合风险优化

金融相关矩阵的计算是构建金融投资组合的基础.为解决金融相关矩阵的“维数灾祸”问题,进而促进金融投资组合风险的优化,受基于随机矩阵理论(RMT)和特征向量的Krzanowski稳定性的KR去噪法的启发,对收益相关矩阵特征值增大时的特征向量最小扰动进行了数学推导,并将以该扰动衡量的特征向量的Krzanowski稳定性引入到RMT去噪法中,进而建立对金融收益相关矩阵去噪的KRMIN方法. KRMIN法对KR法的算法进行了两方面的优化.一方面, KRMIN法对KR法的特征值设定方法进行了扩展; 另一方面, KRMIN法采用模拟退火算法计算特征值.理论研究表明,由于在收益相关矩阵特征向量的稳定性和特征值算法准确性上的优势, KRMIN方法将获得比KR法更好的组合风险优化效果.通过bootstrap方法,开展了将LCPB法、PG+法、KR法和KRMIN法用于不同数量股票的投资组合优化的实证研究.结果表明: LCPB法、PG+法、KR法和KRMIN法都能通过股票收益相关矩阵去噪而带来投资组合风险的优化;基于收益相关矩阵特征向量的Krzanowski稳定性的KR法和KRMIN法的组合风险比其他两种方法更低;由KRMIN法得到的收益相关矩阵的特征向量稳定性和组合风险优化效果好于KR法.     

基于契约的计划生育策略的建模分析

提出了一种基于契约的计划生育策略. 依据该策略, 公民可在结婚时通过契约形式自由选择成功生育一个男孩, 一个女孩, 或者两个孩子作为终止生育的条件. 用概率分析和随机过程分析的手段从数学上论证了这项策略的可行性. 结果表明, 该策略在满足公民对生育子女性别或数量的基本选择权基础上, 使得一对夫妇的平均生育数量接近2, 可以总体上保证人口数量的平稳, 也不会造成男女性别比例的失衡.     

基于层次性的交通网络资源优化配置方法

利用交通网络层次性这一基本特征,研究随机交通配流算法与交通网络资源优化配置方法。在分析算法的设计基础上,定义层次因子,并提出利用复杂网络拓扑特征或交通关联度来确定交通网络的层次数目和层次因子,在Dial算法的基础上利用层次性设计层次随机交通分配算法(HSTAA);通过算例验证与分析HSTAA算法,提出基于层次性的交通网络资源的优化配置方法。研究结果表明:由HSTAA算法得到的交通网络总阻抗在层次因子的某一合理取值范围内小于Dial算法所得的总阻抗,且交通网络的总阻抗随较高层次路段层次的提高而减小,但交通网络的尾气排放总量却随较高层次路段层次的提高而增大,但它始终小于由Dial算法所得到的结果;将网络层次状况控制在合理范围内就能有效地调节和优化交通网络资源配置。     

Construction of protograph LDPC codes with circular generator matrices

The application of protograph low density parity check(LDPC) codes involves the encoding complexity problem.Since the generator matrices are dense,and if the positions of "1" s are irregularity,the encoder needs to store every "1" of the generator matrices by using huge chip area.In order to solve this problem,we need to design the protograph LDPC codes with circular generator matrices.A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed.The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix.This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices,and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem.Simulation results in additive white Gaussian noise(AWGN) channels show that the bit error rate(BER) performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.     

渐近拟非扩张型的映像不动点的Ishikawa迭代逼近

在新的条件之下,研究了渐近拟非扩张型的映像具误差项的Ishikawa迭代逼近不动点的问题,同时给出了强收敛定理。在主要结果中,满足有界Ishikawa迭代序列{xn}的某些条件下,不需要集合K和T的值域的有界性。     

大学考试时间表问题的混合遗传算法求解

考试时间表问题是一类典型的组合优化问题,也是NP难问题。分析了大学考试时间表编排的特点,给出了一种解决考试时间冲突的自动生成考试时间表的可行时段-查找算法。为进一步解决时间间隔问题,将可行时段-查找算法嵌入到遗传算法中形成混合遗传算法。实验结果表明,本文提出的混合遗传算法能快速、有效的解决大学考试时间表问题。