Graphical models and point pattern matching

This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.     

A minisum location problem with regional demand considering farthest Euclidean distances

We consider a continuous multi-facility location-allocation problem that aims to minimize the sum of weighted farthest Euclidean distances between (closed convex) polygonal and/or circular demand regions, and facilities they are assigned to. We show that the single facility version of the problem has a straightforward second-order cone programming formulation and can therefore be efficiently solved to optimality. To solve large size instances, we adapt a multi-dimensional direct search descent algorithm to our problem which is not guaranteed to find the optimal solution. In a special case with circular and rectangular demand regions, this algorithm, if converges, finds the optimal solution. We also apply a simple subgradient method to the problem. Furthermore, we review the algorithms proposed for the problem in the literature and compare all these algorithms in terms of both solution quality and time. Finally, we consider the multi-facility version of the problem and model it as a mixed integer second-order cone programming problem. As this formulation is weak, we use the alternate location-allocation heuristic to solve large size instances.     

Dynamic programming for detecting, tracking, and matchingdeformable contours

The problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision. Terzopoulos et al. (1987) proposed an approach to detect the contour regions of complex shapes, assuming a user selected initial contour not very far from the desired solution. We propose to further explore the information provided by the user's selected points and apply an optimal method to detect contours which allows a segmentation of the image. The method is based on dynamic programming (DP), and applies to a wide variety of shapes. It is exact and not iterative. We also consider a multiscale approach capable of speeding up the algorithm by a factor of 20, although at the expense of losing the guaranteed optimality characteristic. The problem of tracking and matching these contours is addressed. For tracking, the final contour obtained at one frame is sampled and used as initial points for the next frame. Then, the same DP process is applied. For matching, a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not. The algorithm is again based on DP and the optimal solution is guaranteed. We have demonstrated the algorithms on natural objects in a large spectrum of applications, including interactive segmentation and automatic tracking of the regions of interest in medical images     

物流运输网络优化研究

物流运输网络中的固定费用运输问题(fcTP)是物流运输中的高级问题,较难得到最优解。本文提出一种基于免疫克隆遗传算法来解决多目标固定费用运输问题。该算法将运输问题的目标函数和约束条件作为抗原,将问题的可行解作为抗体,而抗体与抗原之间的亲和度就用可行解的目标函数值来表示,通过判断抗体与抗原的亲和度和抗体的浓度来克隆选择个体进入下一代。仿真结果表明,免疫克隆遗传算法在固定费用运输问题应用中得到较好的Pareto最优集和Pareto边界。     

A Sparse Multiscale Algorithm for Dense Optimal Transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport, we provide a framework to verify global optimality of a discrete transport plan locally. This allows the construction of an algorithm to solve large dense problems by considering a sequence of sparse problems instead. The algorithm lends itself to being combined with a hierarchical multiscale scheme. Any existing discrete solver can be used as internal black-box. We explicitly describe how to select the sparse sub-problems for several cost functions, including the noisy squared Euclidean distance. Significant reductions in run-time and memory requirements have been observed.     

基于改进模拟退火算法的搬运机器人路径规划

针对传统搬运机器人路径规划方法易陷入局部最优解,以及缺乏对环境普遍适应性的问题。应用栅格法创建搬运机器人工作环境模型,以一种建立搜索禁忌表的改进贪心算法为基础,通过加入遗传算法中“优胜劣汰”的思想,重新定义了模拟退火系数和栅格系数,提出了一种可以解决贪心算法局部收敛问题的改进模拟退火算法。最后通过仿真和具体实物实验,验证了该算法具有的可行性以及对于不同环境的适应性,能够有效地提高搬运机器人路径规划的质量。     

对等网端到端多路径选择建模及算法研究*

在对等网上利用多路径分发视频是一种重要的机制,虽然在一对节点之间找出符合条件的多条路径并不困难,但发送端如何从可用路径集中选出最优路径子集,并为其最优地分配发送速率仍是一个难题。为此,提出一种新的对等网端到端最优多路径选择与速率分配(OMPSRA)算法。首先,应用排队论建立OMPSRA模型,并推导出一种新的OMPSRA公式,公式既给出最优分配的计算方法,也给出路径的最优速率分配与各路径最大可用带宽之间的关系,利用此关系可选出最优路径子集。最后基于公式实现OMPSRA算法。理论分析和仿真实验结果表明提出的算法能对通信量进行全局最优分配,最小化视频传输的端到端时延,有效提高视频传输质量,比同类算法有更好的性能。     

基于高维点云分布的最优传输问题的研究

最优传输问题是寻求相对于给定的代价函数,把一种分布转化为另一种分布的最有效的方式,其具有较为深远的价值,其中基于点云的最优传输问题更是得到广泛的关注。针对高维的点云分布的最优传输问题,利用了分片最优传输的理论及其对应的优化模型,提出一个改进梯度迭代的算法,以二维、三维点云分布为例进行数值实验,并将其与经典的方法进行比较...     

基于改进粒子群优化的无标记数据鲁棒聚类算法

已有的聚类算法大多仅考虑单一的目标,导致对某些形状的数据集性能较弱,对此提出一种基于改进粒子群优化的无标记数据鲁棒聚类算法。优化阶段:首先,采用多目标粒子群优化的经典形式生成聚类解集合;然后,使用K-means算法生成随机分布的初始化种群,并为其分配随机初始化的速度;最终,采用MaxiMin策略确定帕累托最优解。决策阶段：测量帕累托解集与理想解的距离,将距离最短的帕累托解作为最终聚类解。对比实验结果表明,本算法对不同形状的数据集均可获得较优的类簇数量,对目标问题的复杂度具有较好的鲁棒性。     

Solving a maximin location problem on the plane with given accuracy

We consider the optimal placement problem in a bounded region on a plane with fixed objects. We specify minimal admissible distances between placed and fixed objects. The optimization criterion is to maximize the minimal weighted distances from placed objects to fixed ones. We propose a quasipolynomial combinatorial algorithm to solve this problem with a given accuracy. We show the results of a computational experiment with the integer programming model and the IBM ILOG CPLEX suite.     

An efficient procedure for finding best compromise solutions to the multi-objective assignment problem

In this paper, we consider the problem of determining a best compromise solution for the multi-objective assignment problem. Such a solution minimizes a scalarizing function, such as the weighted Tchebychev norm or reference point achievement functions. To solve this problem, we resort to a ranking (or k-best) algorithm which enumerates feasible solutions according to an appropriate weighted sum until a condition, ensuring that an optimal solution has been found, is met. The ranking algorithm is based on a branch and bound scheme. We study how to implement efficiently this procedure by considering different algorithmic variants within the procedure: choice of the weighted sum, branching and bounding schemes. We present an experimental analysis that enables us to point out the best variants, and we provide experimental results showing the remarkable efficiency of the procedure, even for large size instances.     

Existence and computation of infinite horizon model predictive control with active steady-state input constraints

This note addresses the existence and implementation of the infinite-horizon controller for the case of active steady-state input constraints. This case is important because, in many practical applications, controllers are required to operate at the boundary of the feasible region (for instance, in order to maximize global economic objectives). For this case, the usual finite horizon parameterizations with terminal cost cannot be applied, and optimal solutions are not generally available. We propose here an iterative algorithm that generates two finite-horizon approximations to the true infinite-horizon problem, where the solution to one of the approximations yields an upper bound on the true optimum, while the other approximation yields a lower bound. We show convergence of both bounding approximations to the optimal solution, as the horizon length in the approximations is increased. We outline a procedure, based on this result, to provide a solution to the infinite-horizon problem that is exact to within any user-specified tolerance. Finally, we present an example that includes a comparison between optimal and suboptimal controllers.     

An improved ant colony optimization-based approach with mobile sink for wireless sensor networks

Traditional wireless sensor networks (WSNs) with one static sink node suffer from the well-known hot spot problem, that of sensor nodes near the static sink bear more traffic load than outlying nodes. Thus, the overall network lifetime is reduced due to the fact some nodes deplete their energy reserves much faster compared to the rest. Recently, adopting sink mobility has been considered as a good strategy to overcome the hot spot problem. Mobile sink(s) physically move within the network and communicate with selected nodes, such as cluster heads (CHs), to perform direct data collection through short-range communications that requires no routing. Finding an optimal mobility trajectory for the mobile sink is critical in order to achieve energy efficiency. Taking hints from nature, the ant colony optimization (ACO) algorithm has been seen as a good solution to finding an optimal traversal path. Whereas the traditional ACO algorithm will guide ants to take a small step to the next node using current information, over time they will deviate from the target. Likewise, a mobile sink may communicate with selected node for a relatively long time making the traditional ACO algorithm delays not suitable for high real-time WSNs applications. In this paper, we propose an improved ACO algorithm approach for WSNs that use mobile sinks by considering CH distances. In this research, the network is divided into several clusters and each cluster has one CH. While the distance between CHs is considered under the traditional ACO algorithm, the mobile sink node finds an optimal mobility trajectory to communicate with CHs under our improved ACO algorithm. Simulation results show that the proposed algorithm can significantly improve wireless sensor network performance compared to other routing algorithms.     

中心B样条二进小波多尺度边缘提取

分析了截尾的Canny算子在多尺度边缘提取时对运算速度造成的影响,提出了中 心B样条二进小波多尺度边缘提取,详尽地研究了Canny算子与中心B样条函数的若干性 质,中心B样条函数具有紧支集,以极快的速度逼近高斯函数,四阶中心B样条函数的导数 比Canny算子更接近最佳边缘检测滤波器.四阶中心B样条函数是二阶平滑问题的唯一最 优解,并且它的时频测不准关系值非常接近时频测不准关系下界.从对计算结果的讨论中也 得出中心B样条二进小波优于Canny算子的结论.     

基于混沌优化的最优运输路径问题研究

在分析Logistic混沌序列遍历性的基础上,将Logistic混沌序列映射到多极点目标函数的搜索区间来搜索全局最优解。研究混沌优化算法的一般步骤和算例分析,并将混沌优化算法应用于运输路径的最优化选择问题中。研究结果表明了混沌优化算法具有较好的全局搜索最优解能力,同时也验证了其在最优运输路径选择上的可行性和有效性。     

Structured sparse matrix-vector multiplication on massively parallel SIMD architectures

We propose an algorithm for the cost-effective evaluation of structured sparse matrix-vector multiplications on massively parallel SIMD computers with distributed memory. Under the assumption that a large percentage of the nonzero entries of the matrix is concentrated on almost full diagonals, a specific data transport problem arises, for which we derive an equivalent graph theoretical formulation. We find an optimal solution of this communication problem in terms of a minimum-cost spanning tree.

We demonstrate the efficiency of our matrix-vector multiplication on a MP-1 with 16,384 processors.     

Branch-and-bound algorithm for a competitive facility location problem

We study a mathematical model generalizing the well-known facility location problem. In this model we consider two competing sides successively placing their facilities and aiming to “capture” consumers, in order to make maximal profit. We state the problem as a bilevel integer programming problem, regarding optimal noncooperative solutions as optimal solutions. We propose a branch-and-bound algorithm for finding the optimal noncooperative solution. While constructing the algorithm, we represent our problem as the problem of maximizing a pseudo-Boolean function. An important ingredient of the algorithm is a method for calculating an upper bound for the values of the pseudo-Boolean function on subsets of solutions. We present the results of a simulation demonstrating the computational capabilities of the proposed algorithm.     

Assignment and scheduling communicating periodic tasks indistributed real-time systems

Presents an optimal solution to the problem of allocating communicating periodic tasks to heterogeneous processing nodes (PNs) in a distributed real-time system. The solution is optimal in the sense of minimizing the maximum normalized task response time, called the system hazard, subject to the precedence constraints resulting from intercommunication among the tasks to be allocated. Minimization of the system hazard ensures that the solution algorithm allocates tasks so as to meet all task deadlines under an optimal schedule, whenever such an allocation exists. The task system is modeled with a task graph (TG), in which computation and communication modules, communication delays and intertask precedence constraints are clearly described. Tasks described by this TG are assigned to PNs by using a branch-and-bound (B&B) search algorithm. The algorithm traverses a search tree whose leaves correspond to potential solutions to the task allocation problem. We use a bounding method that prunes, in polynomial time, nonleaf vertices that cannot lead to an optimal solution, while ensuring that the search path leading to an optimal solution will never be pruned. For each generated leaf vertex, we compute the exact cost using the algorithm developed by Peng and Shin (1993). The lowest-cost leaf vertex (one with the least system hazard) represents an optimal task allocation. Computational experiences and examples are provided to demonstrate the concept, utility and power of the proposed approach     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

一维下料的改进遗传算法优化

针对一维下料优化问题,在对一维下料方案数学模型分析的基础上,提出了基于改进遗传算法的优化求解方案。主要思想是把零件的一个顺序作为一种下料方案,定义了遗传算法中的关键问题:编码、解码方法、遗传算子和适应度函数的定义。该算法设计了一种新颖的遗传算子,包括顺序交叉算子、线性变异算子、扩展选择算子。根据这一算法开发出了一维下料方案的优化系统。实际应用表明,该算法逼近理论最优值,而且收敛速度快,较好地解决了一维下料问题。