基于Visual C++的旅行售货员问题的分支限界算法

旅行售货员问题是经典的NP问题。本文对旅行售货员问题的分支限界算法进行了分析,给出了算法过程,并用Visual C++实现该算法。     

石油传输网络最少增压器问题的回溯与分支限界解法

回溯法和分支限界法是用于解决诸多问题的重要而有效的方法。本文首先提出石油传输网络中的最少增压器问题,然后介绍了基于回溯法和分支限界法的两种有效算法,最后对这两种算法进行了比较和讨论。实验结果验证了算法的有效性。     

搜索问题的代数描述及其算法

文中给出了搜索问题的一种代数描述方法，在这种描述方法的基础上，给出了一个算法模式。以货郎担问题的动态规划－分支限界法为例，讨论了如何用所给出的算法模式来设计饱含多咱算法设计技术的算法，称这种算法为混合（ｈｙｂｒｉｄ）算法。还讨论了如何用面向对象的方法进行程序设计。这种求解问题的方法不仅为算法的自支生成提供了一种有力的工具，如果用面向对象的方法进行程序设计，还能提高代码的利用率。     

测试用例自动生成中等式约束处理算法

为了解决测试用例自动生成中等式约束的求解问题,提出一种加入等式处理策略的分支限界搜索算法.首先将线性代数中判定线性方程组是否有解的方法引入分支限界测试用例生成框架之中;然后在已有算法模型的基础上提出集成等式处理分支限界搜索算法,以支持多种变量类型的等式处理;最后将等式约束分为等式无解、等式多解和等式唯一解三大类进行处理,包含了等式约束求解问题的所有情况.实验结果表明,文中算法可以实现对一部分不可达路径的检测,在很大程度上减少测试用例生成的时间并提高覆盖率;对大工程的测试以及同开源约束求解工具Choco的对比实验,也证明了该算法可以提升测试效率.     

时间依赖无向中国邮路问题的分支限界算法

时间依赖网络相比传统网络模型有更广泛的应用领域,比如会交网络和通信网络都可以抽象成为时间依赖的网络模型。当模型中弧的访问代价为时间依赖的变量时,中国邮路问题的求解将变得非常困难。首先分析了传统的中国邮路问题求解算法,如奇偶图上作业法和Edmonds& Johnson算法,以及不能有效求解时间依赖中国邮路问题的根本原因;其次给出了一般时变无向中国邮路问题的特性,并在此基础上设计了该问题的分支限界最优化算法;然后针对FIFO(First In First Out)这一类特殊时变网络,设计了新的剪枝条件,从而得到了更有效求解FIFO网络的时变无向中国邮路问题的分支限界最优化算法;最后对算法进行了实验,算法实验结果正确。     

基于启发式搜索的移动机器人主动定位

提出了一种基于启发式搜索的主动定位算法.首先利用自适应粒子聚类算法对粒子进行聚类;然后分别构造路径规划树和解空间树,并根据优先级评估函数计算解空间树中所有节点的优先级,利用优先队列式分支限界法解决路径搜索问题;最后针对单个粒子簇分散问题提出了一种定位精度主动提升方法.仿真实验验证了所提出方法的有效性.     

多跳无线网络中基于分支限界法的广播算法

现有的广播算法一般采用分层的方法构建近似的最多叶子最短生成树作为广播树。分析此类算法存在的不足,提出利用分支限界的思想建立最多叶子最短生成树引导广播操作的方法。分析和仿真结果表明,与基于分层的广播算法相比,基于分支限界法的广播算法具有更低的转发比且不增加广播树的深度,能更有效地节省带宽和能量资源。     

空间数据库引擎的R树索引

介绍了空间数据库引擎(SDBE)的R树索引结构，给出系统使用R树索引的方式，并描述了利用R树索引实现最近邻居查询的分支—限界算法，包括代价函数及其上、下界函数的定义，以及算法的伪码形式。     

求图符号控制数的完全算法研究

确定图的符号控制数是NP-难度的问题。针对求解该问题的完全算法即能求得精确最优解的算法进行了研究,提出了几个启发式的限界策略,给出了两个完全算法:回溯算法和A算法。计算实验表明,针对随机产生的问题实例,用这两个算法求解时所生成的结点数目还不到其状态空间树中结点总数目的千分之五。对这两个算法也进行了比较。     

给定限界要求的联盟结构生成

联盟形成是多Agent系统中的一个关键问题,目的是通过寻找使联盟值的总和最大的联盟结构来使系统得到最大的效益。但通常可能的联盟结构的数目太大,不允许穷尽搜索来找出最优解。当实际问题提出最坏情况的具体限界要求时,如何以最小的搜索达到这个要求是需要解决的。文中给出的算法对给定的限界要求K*≥2以最少的搜索层数解决了这个问题。Sandholm等人已经证明,要建立最坏情况下的限界K（n),搜索联盟结构图的最底两层是必要且是充分的,此时限界是n(系统的Agent 数）。以此为基础,文中给出了算法,在搜索最底两层之后,只要搜索一层就能保证K(n)≤3;而在搜索最底两层之后,最多搜索两层就能保证K(n)≤2。与Samdholm等人给出的算法相比,文中给出的算法达到指定限界的搜索量显著减少。     

Scheduling two-machine no-wait open shops to minimize makespan

This paper examines the problem of scheduling two-machine no-wait open shops to minimize makespan. The problem is known to be strongly NP-hard. An exact algorithm, based on a branch-and-bound scheme, is developed to optimally solve medium-size problems. A number of dominance rules are proposed to improve the search efficiency of the branch-and-bound algorithm. An efficient two-phase heuristic algorithm is presented for solving large-size problems. Computational results show that the branch-and-bound algorithm can solve problems with up to 100 jobs within a reasonable amount of time. For large-size problems, the solution obtained by the heuristic algorithm has an average percentage deviation of 0.24% from a lower bound value.     

Nearest Neighbor Queries in Shared-Nothing Environments

In this paper, we propose an efficient solution to the problem of nearest neighbor query processing in declustered spatial databases. Recently a branch-and-bound nearest neighbor finding (BB-NNF) algorithm has been designed to process nearest neighbor queries in R-trees. However, this algorithm is strictly serial (branch-and-bound oriented) and its performance degrades, during processing of a nearest neighbor query, if applied to a parallel environment, since it does not exploit any kind of parallelization. We develop an efficient query processing strategy for parallel nearest neighbor finding (P-NNF), assuming a shared nothing multi-processor architecture, where the processors communicate via a network. In our method, the relevant sites are activated simultaneously. In order to achieve this goal, statistical information is used. The efficiency measure is the response time of a given query. Experimental results, based on real-life and synthetic datasets, show that the proposed method outperforms the branch-and-bound method by factors.     

A computational analysis of LCP methods for bilinear and concave quadratic programming

The use of a sequential linear complementarity problem (SLCP) algorithm for finding a global minimum of bilinear programming problem (BLP) or a concave quadratic program (CQP) is examined. The algorithm consists of solving a sequence of linear complementarity problems (LCP). A branch-and-bound method is also considered in this study. This algorithm is based on the reformulation of a BLP into an LCP with a linear function to minimize. Computational experience with small and medium scale BLPs and CQPs indicates that the SLCP algorithm is quite efficient in finding a global minimum (or at least a solution that is quite near the optimum), but it is, in general, unable to establish that such a solution has been found. An algorithm to find a lower-bound for the BLP can overcome this drawback in some cases. Furthermore the SLCP algorithm is shown to be robust and compares favorably with the branch-and-bound method and another alternative technique.     

A hybrid polynomial-time algorithm for the dynamic quantity discount lot size model with resale

We propose an efficient optimal algorithm for determining the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system with single price break point and resale of the excess units is acceptable at the ordering time. The problem is divided into the sub-plans with specific properties by the dynamic programming (DP) method already presented. By modifying the main structure of the DP method, we present a branch-and-bound algorithm to obtain the optimal ordering policy for each sub-plans. Furthermore, we prove some useful fathoming rules to make the branch-and-bound algorithm very efficient. It has also been shown that the worst-case time complexity function of the presented algorithm is O(N⁴) where N is the number of periods in the planning horizon. Finally, we show the efficiency of the presented algorithm and its fathoming rules by solving some test problems which are randomly generated in various environments.     

使用R树进行k-NN搜索

在地理信息系统中经常要做k-NN搜索，进行这些查询用到的算法与位置和范围查询的算法不同，需要专门进行研究，介绍了一种分支界限遍历R树算法，并将该算法概括为k-NN算法。文中讨论了两种方法。对R树进行结点内MBR的排序以及剪枝过程，以减少搜索空间中需访问结点的数量，有效地进行k-NN搜索。     

分枝定界算法设计模式研究与应用

分枝定界算法是传统算法设计方法中重要算法之一,很多重要问题可以用它来解决。本文在对分枝定界算法进行深入研究的基础上,将其抽象成分枝定界算法设计模式,并使用C＋＋的模板机制加以实现。最后通过具体实例说明本文开发的分枝定界算法模板具有较高的可重用性、可编程性和可靠性。     

Efficient parallel branch-and-bound algorithm for constructing minimum ultrametric trees

The construction of evolutionary trees is important for computational biology, especially for the development of biological taxonomies. The ultrametric tree (UT) is a commonly used model for evolutionary trees assuming that the rate of evolution is constant (molecular clock hypothesis). However, the construction of minimum ultrametric trees (MUTs, principle of minimum evolution) has been shown to be NP-hard even from a metric distance matrix. The branch-and-bound algorithm is generally used to solve a wide variety of NP-hard problems. In previous work, a sequential branch-and-bound algorithm for constructing MUTs (BBU) was presented and the experimental results showed that it is useful for MUT construction. Hence, in this study, an efficient parallel branch-and-bound algorithm (PBBU) for constructing MUTs or near-MUTs from a metric distance matrix was designed. A random data set as well as some practical data sets of Human + Chimpanzee Mitochondrial and Bacteriophage T7 DNAs were used to test the PBBU. The experimental results show that the PBBU found an optimal solution for 36 species on 16 PCs within a reasonable time. To the best of our knowledge, no algorithm has been found to solve this problem even for 25 species. Moreover, the PBBU achieved satisfying speed-up ratios for most of the test cases.     

Minimizing the weighted sum of squared tardiness on a single machine

This paper considers a problem in which there is a set of jobs to be sequenced on a single machine. Each job has a weight and the objective is to sequence the jobs to minimize total weighted squared tardiness. A branch-and-bound algorithm is developed for optimally solving the problem. Several dominance conditions are presented for possible inclusion in the branch-and-bound algorithm. The dominance conditions are included in the branch-and-bound algorithm, which is tested on randomly generated problems of various numbers of jobs, due date tightness and due date ranges. The results show that the dominance conditions dramatically improve the efficiency of the branch-and-bound algorithm.