基于邻接矩阵利用Excel求距离矩阵

利用Excel中的函数研究了邻接矩阵的幂矩阵,以及通过幂矩阵求解有向图的距离矩阵的Excel解法,尤其是图中结点较多时使该问题变得非常容易求解。     

探索求解TSP的另一方案

在引入距离循环矩阵的基础上,采用了基于遗传算的局部贪婪搜索方法,对TSP的求解进行探索。由于采用了具有自身关联特性的距离循环矩阵,所以使得求解TSP的运算次数大大减少,速度提高,且易得较优解。     

基于鱼群算法的舰队补给最短路径即仿真

舰队补给是现在海军作战中的一个重点问题,本文通过模拟鱼类的觅食,聚群,追尾,随机等行为,在搜索域中进行寻优,建立了求解TSP问题的鱼群算法。由于在求解过程中,舰队是行驶的,所以与普通TSP问题不同,本文所构建的距离矩阵是动态矩阵。在最后本文进行了Matlab仿真,得出优化结果。     

本体算法中相似度矩阵的学习

本体图中顶点之间的相似度计算是各类本体算法的本质所在.本体图中各个顶点对的相似度组成本体相似度矩阵,因此得到一个最优相似度矩阵是本体应用的实质.本文提出一种通过计算距离矩阵来得到本体相似度矩阵的方法,该方法着眼于降维过程的稀疏化和解的光滑性.从样本集得到相似顶点对集合S和不相似度顶点对集合D,由此得到三元组Γ.将Γ的信息融入到计算模型中,进而使得距离矩阵保持了原本体图中顶点间的距离结构特征.借鉴凸最小最大优化模型的光滑逼近法,得到距离矩阵计算模型的求解策略.最后,通过两个具体实验表明,本文所给的相似度矩阵计算方法对于特定应用领域中的本体相似度计算和不同本体间建立本体映射具有较高的效率.     

不确定性问题中逻辑关系方程的置换矩阵解法

本文给出了在不确定性问题中逻辑关系方程有解 ,有唯一解的充分必要条件 ,并把求解逻辑关系方程的问题转化为求解一些系数矩阵是置换矩阵的逻辑方程组问题 ,从而给出一种求解逻辑关系方程的新算法     

一种求解图着色问题的优化组合遗传算法①

图着色算法是一种典型的NP-完全问题。在逆序算子、对偶算子和矩阵遗传算子的性能研究基础上,采用自然数与二进制相互转换的编码方案,应用图着色问题的约束条件建立适应度评价函数,将具有良好局部搜索性能的矩阵遗传算子与具有良好局部搜索性能的逆序与对偶组合算子优化组合应用,构造了一种用于求解图着色问题的优化组合遗传算法,保证了算法的全局收敛性。与基本遗传算法相比较,实验结果表明,该算法对图着色问题有较好的求解性能。     

遗传算法求解图的染色问题

探讨了用遗传算法求解图的染色问题,对问题进行转换后给 出了基于“近邻归类法”的两种遗传编码,并给出了用遗传算法求解的具体实施过程。     

基于符号零压缩二叉决策图的装配可行性判定方法

为了扩大装配序列规划的求解规模并提高求解效率,提升装配自动化水平,给出了装配体联接矩阵和干涉矩阵的零压缩二叉决策图描述,建立了基于符号零压缩二叉决策图的装配操作可行性判定方法。基于该方法,可以高效地求解出一个装配体的可行装配操作。结合实例验证了基于符号零压缩二叉决策图的装配体模型和可行装配操作判定方法的正确性和可行性。     

属性关系图匹配的神经网络实现及其应用

属性关系图中存在着有向弧和多重弧,它是一种不对称的图,Hopfield网络是对称联接 的,通过定义节点属性距离和节点对关系弧属性距离,解决了不对称问题,从而把属性关系图 的匹配转化成可用Hopfield网络求解的形式.同时,又把误差校正思想引入了神经网络,使 网络可以实现随机语义网的匹配.     

基于距离度量的多样性图排序方法

有效结合查询相关性和多样性的扩展相关性是多样性图排序问题的一种优化目标.基于扩展相关性的多样性图排序可建模为一个子模函数优化问题,贪心子模优化算法可近似求解该问题.然而,扩展相关性不能直接度量节点间的不相似性.子模优化算法是串行算法不能充分利用诸如Spark等集群计算平台有效提高算法效率.针对这些问题,本文提出一种描述节点间不相似性的距离度量.基于此距离度量,将多样性图排序问题建模为一个在查询相关节点集上构造的带权完全图的最大和k-dispersion优化问题.提出了求解该问题的多项式时间2-近似算法.鉴于不同节点对的距离度量计算是相互独立的,进一步地提出了基于MapReduce编程模型的并行化多样性图排序算法.最后,在真实图数据集上验证了本文提出算法的高效性和有效性.     

三对角矩阵的行列式的并行计算方法

文章针对三对角矩阵,利用矩阵的Schur余子式求矩阵行列式的方法,提出了一种并行求解三对角矩阵及其逆的行列式的算法,应用该算法可以得到较好的加速度。     

Matrix Trees

We propose a new data representation for octrees and kd‐trees that improves upon memory size and algorithm speed of existing techniques. While pointerless approaches exploit the regular structure of the tree to facilitate efficient data access, their memory footprint becomes prohibitively large as the height of the tree increases. Pointerbased trees require memory consumption proportional to the number of tree nodes, thus exploiting the typical sparsity of large trees. Yet, their traversal is slowed by the need to follow explicit pointers across the different levels. Our solution is a pointerless approach that represents each tree level with its own matrix, as opposed to traditional pointerless trees that use only a single vector. This novel data organization allows us to fully exploit the tree's regular structure and improve the performance of tree operations. By using a sparse matrix data structure we obtain a representation that is suited for sparse and dense trees alike. In particular, it uses less total memory than pointer‐based trees even when the data set is extremely sparse. We show how our approach is easily implemented on the GPU and illustrate its performance in typical visualization scenarios.     

Matrix Code

Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition form. The computations of a code matrix are characterized by powers of the matrix when it is interpreted as a transformation in a space of vectors of logical conditions. Correctness of a code matrix is expressed in terms of a fixpoint of the transformation. The abstract machine for Matrix Code is the dual-state machine, which we present as a variant of the classical finite-state machine.     

二进制区分矩阵的简化方法

粗集是一种处理不确定性知识的重要工具,针对粗集理论中的二进制区分矩阵的空间和时间上的不必要开销,基于动态的思想和概率论,提出了一种可降低二进制区分矩阵空间及时间开销的方法.     

关于区间矩阵的稳定性

文献[1]试图给出由端点矩阵的稳定性来保证区间矩阵的稳定性,文[2,3]指出文[1]的主要结果是错的.本文给出了端点矩阵的稳定性在一定条件下可以保证区间矩阵的稳定性,其结果比文[4]更精确,适用范围更大,且对具有分解的区间矩阵给出了其稳定及不稳定的充分条件.     

Rank Conditions on the Multiple-View Matrix

Geometric relationships governing multiple images of points and lines and associated algorithms have been studied to a large extent separately in multiple-view geometry. The previous studies led to a characterization based on multilinear constraints, which have been extensively used for structure and motion recovery, feature matching and image transfer. In this paper we present a universal rank condition on the so-called multiple-view matrix M for arbitrarily combined point and line features across multiple views. The condition gives rise to a complete set of constraints among multiple images. All previously known multilinear constraints become simple instantiations of the new condition. In particular, the relationship between bilinear, trilinear and quadrilinear constraints can be clearly revealed from this new approach. The theory enables us to carry out global geometric analysis for multiple images, as well as systematically characterize all degenerate configurations, without breaking image sequence into pairwise or triple-wise sets of views. This global treatment allows us to utilize all incidence conditions governing all features in all images simultaneously for a consistent recovery of motion and structure from multiple views. In particular, a rank-based multiple-view factorization algorithm for motion and structure recovery is derived from the rank condition. Simulation results are presented to validate the multiple-view matrix based approach.     

Matrix decomposition on the star graph

We present and evaluate, for the first time, a parallel algorithm for solving the LU decomposition problem on the star graph. The proposed parallel algorithm is of O(N³/n!) computation complexity and uses O(Nn) communication time to decompose a matrix of order N on a star graph of dimension n, where N⩾(n-1)!. The incurred communication time is better than the best known results for the hypercube, O(Nlogn!), and the mesh, O(N√n!), each with approximately n! nodes. The proposed parallel algorithm takes advantage of the attractive topological qualities of the star graph in order to reduce the communication time involved in tasks such as pivoting, row/column interchanges, and pivot row and multipliers column broadcasts     

基于公理化设计矩阵与设计结构矩阵同步演化的产品设计

基于公理化设计与设计结构矩阵具有互补性这一特点,提出了公理化设计矩阵与设计结构矩阵同步演化的设计思想.讨论了如何通过公理化设计矩阵与设计结构矩阵的同步演化来实现产品创新设计中的发散与收敛思维, 即通过公理化设计矩阵进行功能需求的发散性求解,基于设计结构矩阵进行收敛行评价.最后通过轧纸机构设计实例,具体阐述了公理化设计矩阵与设计结构矩阵同步演化过程.