正则化方法在非线性分析中的应用

本文用正则化方法给出了麦夸脱方法的一个误差估计式.     

可招回秘书问题

可招回秘书问题已由Yang,Petrucceol,Choe及Bal研究过。本文将这个问题纳入Snell框架,用相对最好者的位置函数Wn代替通常的相对名次,我们得到了各种招回概率下的最优停止规则,这些结果推广了文[7]—[9]。     

压入法中的接触问题

针对表面工程中测量膜基材料性能或结合强度的压入法,分析了其实验过程中所涉及的重要而又困难的接触问题。在引入适当的假设后,文中首次对二维、三维问题等一般情况,分别给出了控制接触的边界条件方程,并进一步使用半解析的数值方法——线法,针对二维情况使用,球形压头和楔形压头分别进行了数值模拟,并将计算结果和不考虑接触情况下的结果进行了比较结果表明:剪应力差别巨大,这说明接触问题的考虑对于正确地处理实际问题是非常必要的。     

基于多假设跟踪弹道导弹主动段跟踪算法

针对弹道导弹主动段防御中多枚弹道导弹同时跟踪问题,提出了基于多假设思想的主动段跟踪算法.重点阐述了该算法中假设生成、假设概率计算、假设约简以及假设剪枝等环节.从工程实用的角度出发,采用求解一个线性分配问题(LAP)方法得到M个最优假设,大大减少了假设数量,并运用N-scan回溯剪枝方法对假设进行剪枝,确定要输出的航迹,提高了算法的效率和实用性.仿真实验表明,该算法能够对主动段多枚弹道导弹目标准确关联跟踪.     

面向多最优解组合优化问题的决策求解算法

针对具有固定物品总和、多最优解特征的组合优化问题,以固定总和实数子集问题和购买鸡翅问题为例,给出了这类多最优解组合优化问题的形式化表示。在分析枚举等经典算法基础上,提出了基于整数状态表示和实数状态表示的0-1决策递归搜索多最优解动态规划算法。针对该算法在最优解数量较大时,时间复杂度趋向O(mⁿ)的问题,提出了基于相同决策路径合并和基于0-x决策的两种改进算法。实验中两种改进算法的计算时间基本符合与O(nb+nm)的正比关系,表明对于这类多最优解组合优化问题具有良好的求解性能。     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

Transformations of node‐balanced routing problems

This article describes a polynomial transformation for a class of unit‐demand vehicle routing problems, named node‐balanced routing problems (BRP), where the number of nodes on each route is restricted to be in an interval such that the workload across the routes is balanced. The transformation is general in that it can be applied to single or multiple depot, homogeneous or heterogeneous fleet BRPs, and any combination thereof. At the heart of the procedure lies transforming the BRP into a generalized traveling salesman problem (TSP), which can then be transformed into a TSP. The transformed graph exhibits special properties which can be exploited to significantly reduce the number of arcs, and used to construct a formulation for the resulting TSP that amounts to no more than that of a constrained assignment problem. Computational results on a number of instances are presented. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 370–387, 2015     

《兵团教育学院学报》2009-2013年载文计量分析

《兵团教育学院学报》作为主要反映本校教学、科研及兵团中小学教育教学成果为内容的综合性学术理论刊物,在推动学校的学科建设、学术研究、培养人才及促进兵团各级各类教育发展等方面发挥着重大作用。本文对学报2009-2013刊登的学术论文进行了计量分析,厘清学报的发展脉络,同时也发现了学报中存在的一些问题如:特色栏目不突出,高质量稿源匮乏,学报宣传力度不大等并提出相应解决措施。     

二阶非线性常微分方程组边值问题的正解

研究一类二阶常微分方程组两点边值问题,利用Krasnoselskii’s不动点定理,得到当f和g满足超线性或次线性时边值问题一个正解存在的充分条件.