各向异性体半平面问题的边界元法

应用中向异性休平面问题的复应力函数基本解，给出了应用边界元法求解半平面多连通域问题时的一些常用公式，具体算例验证了本文解的正确性。     

使用I—DEAS软件进行产品结构标准的计算

介绍了产品结构(product architecture)的定义和研究背景。目前有若干种方法来衡量产品结构，其中一种是结合实体建模程序自动完成量化工作，文中重点介绍了此方法。采用I—DEAS软件，基于Steiner方法，所编程序植入I—DEAS，从而实现产品结构的计算。     

自适应粒子群算法的制造单元集成布局方法

在考虑制造单元出入点具体位置与最短物流路径的情况下,对单元间布局两个环节的问题——确定单元在车间平面上的位置,确定出入点间最短物流路径——作了集成研究,避免分步研究导致的解空间缺失;基于割树策略建立了单元布局模型,设计了结构化编码的自适应粒子群算法,使车间平面形成整齐连续的布局;通过将车间平面布局转化成连通图,在算法中嵌入改进Dijkstra算法,量化了各单元出入点之间的最短物流距离;从而使布局结果更加符合生产实际。     

用广义协调方法推导的平面四节点等参单元

对平面四节点Q4单元采用优选的广义协调条件进行推导,将广义协调理论的应用拓展到最基本的平面问题单元。基于Q6以及QM6中基于内部参数的二次附加位移场,在Q4单元基础上增加满足广义协调条件的内参位移场,从而构造了一个满足广义协调条件的平面四节点等参元GQM6。数值算例表明,虽然采用了相同次数的位移场,但GQM6单元中采用的广义协调条件较QM6中采用的数值积分方法,可以进一步放松单元边界的约束,从而使单元的性能进一步提高,尤其在抗网格畸变能力方面。研究表明,将广义协调理论与一些传统单元进行深入融合仍然有着重要价值。     

基于最短路径的蛋白质相互作用网络拓扑分析

为了进行对蛋白质相互作用网络的拓扑分析,应用最短路径技术对蛋白质相互作用数据库(DIP)中包括酵母在内的7个物种的8个蛋白质相互作用网络进行了研究,包括对网络直径、特征路径长度、连通效率、顶点介数与顶点度的相关性以及高介数边和长间隔边在网络连通中的作用的研究.分析发现,这些网络对随机移除一定数量的蛋白质顶点(或边)具有很好的健壮性,但对高介数顶点(或边)的确定性移除却相当脆弱,而且按顺序移除2%高介数顶点所引起的网络连通效率下降明显大于随机移除10%顶点所引起的网络连通效率变化;所研究的7个物种的网络都存在不同比例的边缺失替代路径,绝大多数网络在移除一定比例的长间隔边后网络连通效率下降.     

基于连通可靠度约束的分簇算法研究

在研究了一些分簇算法基础上,提出基于连通可靠度约束的、适合大规模随机部署的快速成簇算法。仿真表明基于连通可靠度约束的快速成簇算法得到的分簇覆盖面广、簇头分布合理、稳定性强,与最小ID分簇及优化的最大连接数分簇算法相比,得到簇头数量少,分簇更合理,各成员节点与簇头的连通可靠度好,能保证网络的稳定性与健壮性,大大减少重构开销带来的通信代价,有利于均衡网络能量消耗,延长网络生命周期。     

自由边界平面连通域的Voronoi图生成方法研究

平面连通域的Vorono,图被广泛应用于许多领域,常用的分治法等算法实现较为复杂,影响了其应用范围在凸多边形中轴算法的基础上,提出一种建立自由边界平面连通域的Voronoi图的新方法.通过求解相邻边界元素的平分线,计算出相邻平分线的交点,由距离最小的平分线交点实现Voronoi图边的增长,最终建立完整的平面单连通域的Voronoi图.同时,还介绍了平面多连通域的内外边界的Voronoi图的合并算法.     

二维复杂域结构性三角形网格自动生成程序

本文介绍了如何利用板缝式边界拟合坐标变任意平面区域（包括多连通域）自动生成有结构的三角形单元的方法及其程序设计。利用本文程序仅需入工输入为数不多的边界点坐标及其它基本控制参数，自动生成三角形网络，并对其自动进行单元，结点编码，文中给出了网络自动剖分的例子，并通过对具有圆形孔口无限大板应力集中问题的计算，验证了本文编制程序。     

交换交叉立方网络的可靠性研究

针对传统的基于连通度分析交换交叉立方网络可靠性的方法的不足,提出一种基于超连通度的可靠性分析方法,因为用超连通度衡量互连网络的稳定性和容错能力较之用连通度更为准确。在研究了交换交叉立方网络的拓朴结构的基础上证明了交换交叉立方网络的点连通度和边连通度均是s+1(s≤t),证明了交换交叉立方网的超点连通度和超边连通度均是2s(s≤t),也就是说,当移除交换交叉立方网络的2s个点或者2s条边,会得到不包括孤立点的非连通图。当交换交叉立方网络被用来构建大型并行计算/通信系统时,运用上述成果能够更加准确地为系统的稳定性和容错能力提供支持。     

传感器网络中最小 k-连通 m-控制集问题的近似算法?

在当前无线传感器网络的相关研究中,虚拟骨干网的构造引起广泛的关注.通过引进虚拟骨干网来设计路由协议,使得路由更加可靠和高效,从而减少广播风暴.无线传感器网络中具有容错功能的虚拟骨干网的构造可转化为圆盘图中的最小 k-连通 m-控制集问题.本文研究了具有不同传输半径的双向圆盘图中的最小 k-连通 m-控制集问题,给出了一个构造最小 k-连通 m-控制集的多项式时间近似算法,理论分析表明该算法具有较好的近似比.最后,在不同的网络拓扑上进行了仿真实验,仿真结果进一步验证了算法的有效性.     

Optimization of underground mine development system using fuzzy shortest path length algorithm

Graphic mine design elements denote physical entities such as shafts, declines, and drives. Ore deposits are often composed of independent orebodies that must be interconnected into one integrated system. In this paper, we examine a case where access points to orebodies lie in the Euclidean plane. The key question is how to interconnect these points at minimal cost. This design problem is modeled as a network and the solution technique is outlined. We supposed that the locations of access points had been previously determined. To define the ore reserves in each orebody, we used linguistic variables and their transformation to fuzzy triangular numbers. At first, we used Kruskal’s algorithm to identify the minimum spanning tree. After that, by inserting Steiner points we defined a Steiner minimal tree as the global minimum. In a network created in such a way, it is necessary to locate a point called the major mass concentration point to which excavated ore will be delivered; from there, the excavated ore will be hauled or hoisted to a surface breakout point via an optimal development system. In this paper, we use the fuzzy shortest path length procedure to select an optimal development system.     

HILL-CLIMBING,SIMULATED ANNEALING AND THE STEINER PROBLEM IN GRAPHS

This paper considers the use of local optimization or improvement heuristics on the Steiner problem in graphs. By considering any Steiner tree as a disjoint union of paths we show it is possible to define a neighbourhood structure on the set of feasible solutions which can be used in a k-opt exchange heuristic. These ideas are then extended to a simulated annealing method. Computational experience, comparing these new methods with one of the best existing heuristics is presented.     

Evolutionary algorithms applied to reliable communication network design

Several evolutionary algorithms (EAs) applied to a wide class of communication network design problems modelled under the generalized Steiner problem (GSP) are evaluated. In order to provide a fault-tolerant design, a solution to this problem consists of a preset number of independent paths linking each pair of potentially communicating terminal nodes. This usually requires considering intermediate non-terminal nodes (Steiner nodes), which are used to ensure path redundancy, while trying to minimize the overall cost. The GSP is an NP-hard problem for which few algorithms have been proposed. This article presents a comparative study of pure and hybrid EAs applied to the GSP, codified over MALLBA, a general purpose library for combinatorial optimization. The algorithms were tested on several GSPs, and asset efficient numerical results are reported for both serial and distributed models of the evaluated algorithms.     

3D boundary recovery by constrained Delaunay tetrahedralization

Three‐dimensional boundary recovery is a fundamental problem in mesh generation. In this paper, we propose a practical algorithm for solving this problem. Our algorithm is based on the construction of a constrained Delaunay tetrahedralization (CDT) for a set of constraints (segments and facets). The algorithm adds additional points (so‐called Steiner points) on segments only. The Steiner points are chosen in such a way that the resulting subsegments are Delaunay and their lengths are not unnecessarily short. It is theoretically guaranteed that the facets can be recovered without using Steiner points. The complexity of this algorithm is analyzed. The proposed algorithm has been implemented. Its performance is reported through various application examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Dominant graphs for rectilinear network design with barriers

Given a set of points on a Cartesian plane and the coordinate axes, the rectilinear network design problem is to find a network, with arcs parallel to either one of the axes, that minimizes the fixed and the variable costs of interactions between a specified set of pairs of points. We show that, even in the presence of arbitrary barriers, an optimal solution to the problem (when feasible) is contained in a grid graph defined by the set of given points and the barriers. This converts the spatial problem to a combinatorial problem. Finally we show connections between the rectilinear network design problem and a number of well-known problems. Thus this paper unifies the known dominating set results for these problems and extends the results to the case with barriers.     

带弧费用约束的最短路径问题

对一类带弧费用约束的最短路径问题进行了研究,即对于网络中两个给定的顶点s,t,找出s和t之间的一条路,使得在满足总费用不超过一个给定正整数的s和t之间所有的路中,该条路的长度最短.通过将背包问题多项式时间变换为该问题的判定问题,证明了该问题是NP-完全的.并给出了求解此问题的一个动态规划算法.最后,我们得到了最优值的一个下界估计.     

A Maximin Location Problem with Maximum Distance Constraints

This paper deal with the problem where a facility must be placed among n points so that the shortest weighted distance to a point is as large as possible. At the same time the facility must be within a pre-specified distance from each point; the facility is to be located on a plane and Euclidean distances are used. Applications include the location of facilities that are obnoxious in the sense that they should be placed as far away from certain points as possible but still be within a pre-specified “reach” of these points.     

AN 0 (N log N) HEURISTIC ALGORITHM FOR THE RECTILINEAR STEINER MINIMAL TREE PROBLEM

This paper presents an 0 (n log n) heuristic algorithm for the Rectilinear Steiner Minimal Tree (RSMT) problem. The algorithm is based on a decomposition approach which first partitions the vertex set into triangles via the L₁ Delaunay triangulation, then constructs the Steiner minimal tree according to the properties of the Voronoi diagram and the Minimum Spanning Tree (MST) of the point set. The algorithm was implemented in FORTRAN-IV and tested on a number of randomly generated point sets in the plane drawn from a uniform distribution. Comparison of the 0 (n log n) algorithms with 0 (n₄) algorithms indicates that the 0 (n log n) algorithm achieves equally good reductions over the MST although the 0 (n₄) algorithms actually examine more potential Steiner points and RSMT configurations.     

A minimum trajectory for machine tool dynamics

This paper presents an algorithmic approach to solving the problem of excessive travel in machine tools, by efficiently computing the shortest path between given sets of points (origin and destination) in R² (x, y) plane. When a workpiece is located (as an obstacle) between sets of points, it is proved that the optimum path between these points would be formed by sequences of connected straight line segments whose intermediate end points are vertices of an appropriate polygonal (closed control barrier). The case of one origin, one destination, and a set of barriers is considered.     

Finding a cluster of points and the grey pattern quadratic assignment problem

In this paper we propose a model which aims at selecting a tight cluster from a set of points. The same formulation applies also to the grey pattern problem where the objective is to find a set of black dots in a rectangular grid with a given density so that the dots are spread as evenly as possible. A branch and bound algorithm and five heuristic approaches are proposed. Computational results demonstrate the efficiency of these approaches. Seven grey pattern problems are solved to optimality and for eight additional grey pattern problems the best known solution is improved. The cluster problem on a network is solved for 40 problems with the number of points ranging between 100 and 900 and the size of the cluster ranging between 5 and 200. Twenty one problems were solved optimally and the remaining 19 problems were heuristically solved in a very short computer time with excellent results.