Optimal control problems with multiple characteristic time points in the objective and constraints

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved.     

基于p2-不变量的透视变换下的点模式匹配方法

点模式匹配是计算机视觉和模式识别领域中的一个重要问题。通过研究,在假定待匹配的两个点模式中已知有三对点整体对应的前提下,基于射影坐标以及对投景变换和排序变换同时保持不变的ｐ＾２－－不变量等理论,通过定义一种广义距离,给出了一种求解透视变换下,点数不等的两个平面点模式匹配问题的新算法。理论分析和仿真实验表明,该算法是快速、有效的。     

An approximate dynamic programming based approach to dual adaptive control

In this paper, an approximate dynamic programming (ADP) based strategy is applied to the dual adaptive control problem. The ADP strategy provides a computationally amenable way to build a significantly improved policy by solving dynamic programming on only those points of the hyper-state space sampled during closed-loop Monte Carlo simulations performed under known suboptimal control policies. The potentials of the ADP approach for generating a significantly improved policy are illustrated on an ARX process with unknown/varying parameters.     

Solving a rich vehicle routing and inventory problem using column generation

The livestock collection problem (LCP) is a rich vehicle routing problem (VRP) extended with inventory constraints. The LCP is a complex planning problem taken from the meat industry, and the goal is to construct a set of vehicle routes to collect animals from farms for slaughter at a slaughterhouse. Several constraints dealing with animal welfare are added, some of these lead to a loading problem where the vehicle capacity depends on the loading sequence. In addition, global constraints to handle production and inventory at the slaughterhouse are needed. This paper presents an exact solution method for the LCP, based on column generation, that solves much larger instances to optimality than what has been done before. The algorithm presented here also solves a richer model that is closer to the underlying real-world problem than previously published work on exact methods for this problem is based on.     

The Hardness of Approximating Spanner Problems

This paper examines a number of variants of the sparse k-spanner problem and presents hardness results concerning their approximability. Previously, it was known that most k-spanner problems are weakly inapproximable (namely, they are NP-hard to approximate with ratio O(log n), for every k ≥ 2) and that the unit-length k-spanner problem for constant stretch requirement k ≥ 5 is strongly inapproximable (namely, it is NP-hard to approximate with ratio ). The results of this paper significantly expand the ranges of hardness for k-spanner problems. In general, strong hardness is shown for a number of k-spanner problems, for certain ranges of the stretch requirement k depending on the particular variant at hand. The problems studied differ by the types of edge weights and lengths used, and they include directed, augmentation and client-server variants. The paper also considers k-spanner problems in which the stretch requirement k is relaxed (e.g., . For these cases, no inapproximability results were known (even for a constant approximation ratio) for any spanner problem. Moreover, some versions of the k-spanner problem are known to enjoy the ratio-degradation property; namely, their complexity decreases exponentially with the inverse of the stretch requirement. So far, no hardness result existed precluding any k-spanner problem from enjoying this property. This paper establishes strong inapproximability results for the case of relaxed stretch requirement (up to , for any ), for a large variety of k-spanner problems. It is also shown that these problems do not enjoy the ratio-degradation property.     

基于p2-不变量的透视变换下的点模式匹配方法

点模式匹配是计算机视觉和模式识别领域中的一个重要问题 .通过研究 ,在假定待匹配的两个点模式中已知有三对点整体对应的前提下 ,基于射影坐标以及对投影变换和排序变换同时保持不变的 p2 -不变量等理论 ,通过定义一种广义距离 ,给出了一种求解透视变换下 ,点数不等的两个平面点模式匹配问题的新算法 .理论分析和仿真实验表明 ,该算法是快速、有效的     

Sufficient Conditions to Impose Derivative Constraints on MISO Takagi–Sugeno Fuzzy Logic Systems

A fuzzy logic system (FLS) can be completely described through its behavioral function. If the analytical expression of this function is known, then the system synthesis consists in the realization of a structure implementing it in the most convenient way. So, the problem of the FLS design can be considered as a function approximation problem. Many methods have been proposed in literature to minimize a certain error parameter. Nevertheless, sometimes the specifications of the problem need some further analytical properties of the approximating function. This paper analyzes multiple-input–single-output (MISO) FLSs with polynomial membership functions inspecting the case of two input variables. In particular, it will be shown what characteristics such systems should have in order to respect the constraints imposed on the derivatives of the implemented function, such as their continuity up to a desired order and even their value in the grid points of the input space. Furthermore, we prove that these systems can uniformly approximate, under certain conditions, any multivariate function with a desired approximation accuracy both on the target function and its partial derivatives. Proper illustrative examples will show the behavior of these FLSs comparing their performance with other methods proposed in literature.     

On robotic optimal path planning in polygonal regions with pseudo-Euclidean metrics.

This paper presents several results on some cost-minimizing path problems in polygonal regions. For these types of problems, an approach often used to compute approximate optimal paths is to apply a discrete search algorithm to a graph G(epsilon) constructed from a discretization of the problem; this graph is guaranteed to contain an epsilon-good approximate optimal path, i.e., a path with a cost within (1 + epsilon) factor of that of an optimal path, between given source and destination points. Here, epsilon > 0 is the user-defined error tolerance ratio. We introduce a class of piecewise pseudo-Euclidean optimal path problems that includes several non-Euclidean optimal path problems previously studied and show that the BUSHWHACK algorithm, which was formerly designed for the weighted region optimal path problem, can be generalized to solve any optimal path problem of this class. We also introduce an empirical method called the adaptive discretization method that improves the performance of the approximation algorithms by placing discretization points densely only in areas that may contain optimal paths. It proceeds in multiple iterations, and in each iteration, it varies the approximation parameters and fine tunes the discretization.     

基于相似压缩的近似线性SVM

为了解决模式识别中的近似线性可分问题,提出了一种新的近似线性支持向量机(SVM).首先对近似线性分类中的训练集所形成的两类凸壳进行了相似压缩,使压缩后的凸壳线性可分;基于压缩后线性可分的凸壳,再用平分最近点和最大间隔法求出最优的分划超平面.然后再通过求解最大间隔法的对偶问题,得到基于相似压缩的近似线性SVM.最后,从理论和实证分析两个方面,将该方法与线性可分SVM及推广的平分最近点法进行了对比分析,说明了该方法的优越性与合理性.     

Computing the fault tolerance of multi-agent deployment

A deployment of a multi-agent system on a network refers to the placement of one or more copies of each agent on network hosts, in such a manner that the memory constraints of each node are satisfied. Finding the deployment that is most likely to tolerate faults (i.e. have at least one copy of each agent functioning and in communication with other agents) is a challenge. In this paper, we address the problem of finding the probability of survival of a deployment (i.e. the probability that a deployment will tolerate faults), under the assumption that node failures are independent. We show that the problem of computing the survival probability of a deployment is at least NP-hard. Moreover, it is hard to approximate. We produce two algorithms to accurately compute the probability of survival of a deployment—these algorithms are expectedly exponential. We also produce five heuristic algorithms to estimate survival probabilities—these algorithms work in acceptable time frames. We report on a detailed set of experiments to determine the conditions under which some of these algorithms perform better than the others.     

Optimization-based approach for curve and surface reconstruction

This paper introduces an optimization-based approach for the curve reconstruction problem, where piecewise linear approximations are computed from sets of points sampled from target curves. In this approach, the problem is formulated as an optimization problem. To be more concrete, at first the Delaunay triangulation for the sample points is computed, and a weight is assigned with each Delaunay edge. Then the problem becomes minimization or maximization of the total weights of the edges that constitute the reconstruction. This paper proposes one exact method and two approximate methods, and shows that the obtained results are improved both theoretically and empirically. In addition, the optimization-based approach is further extended to three dimensions, where surfaces are to be reconstructed, and the quality of the reconstructions is examined.     

Relay pursuit of a maneuvering target using dynamic Voronoi diagrams

This paper addresses the problem of the pursuit of a maneuvering target by a group of pursuers distributed in the plane. This pursuit problem is solved by associating it with a Voronoi-like partitioning problem that characterizes the set of initial positions from which the target can be intercepted by a given pursuer faster than any other pursuer from the same group. In the formulation of this partitioning problem, the target does not necessarily travel along prescribed trajectories, as it is typically assumed in the literature, but, instead, it can apply an “evading” strategy in an effort to delay or, if possible, escape capture. We characterize an approximate solution to this problem by associating it with a standard Voronoi partitioning problem. Subsequently, we propose a relay pursuit strategy, that is, a special group pursuit scheme such that, at each instant of time, only one pursuer is assigned the task of capturing the maneuvering target. During the course of the relay pursuit, the pursuer–target assignment changes dynamically with time based on the (time varying) proximity relations between the pursuers and the target. This proximity information is encoded in the solution of the Voronoi-like partitioning problem. Simulation results are presented to highlight the theoretical developments.     

An evolutionary image matching approach

Bee colony optimization (BCO) is a meta-heuristic technique inspired by natural behavior of the bee colony. In this paper, the BCO technique is exploited to tackle the shape matching problem with the aim to find the matching between two shapes represented via sets of contour points. A number of bees are used to collaboratively search the optimal matching using a proposed proximity-regularized cost function. Furthermore, the proposed cost function considers the proximity information of the matched contour points; this is in the contrast to that these contour points are treated independently in the conventional approaches. Experimental results are presented to demonstrate that the proposed approach is able to provide more accurate shape matching than the conventional approaches.     

Registration of point clouds using sample-sphere and adaptive distance restriction

Registration of point clouds is a fundamental problem in shape acquisition and shape modeling. In this paper, a?novel technique, the sample-sphere method, is proposed to register a pair of point clouds in arbitrary initial positions. This method roughly aligns point clouds by matching pairs of triplets of points, which are approximately congruent under rigid transformation. For a given triplet of points, this method can find all its approximately congruent triplets in O(knlog?n) time, where n is the number of points in the point cloud, and k is a constant depending only on a given tolerance to the rotation error. By employing the techniques of wide bases and largest common point set (LCP), our method is resilient to noise and outliers. Another contribution of this paper is proposing an adaptive distance restriction to improve ICP (iterative closest point) algorithm, which is a classical method to refine rough alignments. With this restriction, the improved ICP is able to reject unreasonable corresponding point pairs during each iteration, so it can precisely align the point clouds which have large non-overlapping regions.     

Testing approximate symmetry in the plane is NP-hard

Let A be a set of n points in the Euclidean plane. We would like to know its symmetry group. If the input points are given by rational coordinates (which is the normal case for a computer), then this problem degenerates to a trivial case. This is why we introduce the notion of approximate symmetry. In this notion, we consider a fixed tolerance factor and ask for the maximal symmetry group that is possible for a set A' consisting of n points in the -neighborhoods of the points in A, each point of A' belonging to a different point of A. We prove that the corresponding decision problem is NP-hard even when and the symmetry group we ask for is fixed. This is a rather surprising result, because a similar concept has been developed for approximate congruence recently and several polynomial algorithms are known for that related problem.     

针对经典排序问题的一种新算法的近似比分析

给定m台平行机(同型机),n个工件,寻找一种分配方案,使得把这n个工件分配到m台机器后,整体完工时间尽可能短,这个NP-难问题被称为经典排序问题.如果每个工件的加工时间满足一定的条件,则有望能在多项式时间内有效地得到最优的分配方案.Yue等对加工时间满足整除性质的经典排序问题考虑了一种新的算法,该算法总是能得到这种特殊...     

A Systematic Study of Failure Proximity

Software end-users are the best testers, who keep revealing bugs in software that has undergone rigorous in-house testing. In order to leverage their testing efforts, failure reporting components have been widely deployed in released software. Many utilities of the collected failure data depend on an effective failure indexing technique, which, at the optimal case, would index all failures due to the same bug together. Unfortunately, the problem of failure proximity, which underpins the effectiveness of an indexing technique, has not been systematically studied. This article presents the first systematic study of failure proximity. A failure proximity consists of two components: a fingerprinting function that extracts signatures from failures, and a distance function that calculates the likelihood of two failures being due to the same bug. By considering different instantiations of the two functions, we study an array of six failure proximities (two of them are new) in this article. These proximities range from the simplest approach that checks failure points to the most sophisticated approach that utilizes fault localization algorithms to extract failure signatures. Besides presenting technical details of each proximity, we also study the properties of each proximity and tradeoffs between proximities. These altogether deliver a systematic view of failure proximity.     

Finding aggregate proximity relationships and commonalities inspatial data mining

Studies two spatial knowledge discovery problems involving proximity relationships between clusters and features. The first problem is: given a cluster of points, how can we efficiently find features (represented as polygons) that are closest to the majority of points in the cluster? We measure proximity in an aggregate sense due to the nonuniform distribution of points in a cluster (e.g. houses on a map), and the different shapes and sizes of features (e.g. natural or man-made geographic features). The second problem is: given n clusters of points, how can we extract the aggregate proximity commonalities (i.e. features) that apply to most, if not all, of the n clusters? Regarding the first problem, the main contribution of the paper is the development of Algorithm CRH (Circle, Rectangle and Hull), which uses geometric approximations (i.e. encompassing circles, isothetic rectangles and convex hulls) to filter and select features. The highly scalable and incremental Algorithm CRH can examine over 50,000 features and their spatial relationships with a given cluster in approximately one second of CPU time. Regarding the second problem, the key contribution is the development of Algorithm GenCom (Generalization for Commonality extraction) that makes use of concept generalization to effectively derive many meaningful commonalities that cannot be found otherwise     

带权区域上任意两点间的近似最优路径算法调研

自1991年由Mitchell和Papadimitriou提出带权值区域问题以来,人们开始认识到带权值模型的通用性较强,陆续有很多学者开始研究这个问题。在二维带权区域近似最优路径问题中,一个二维空间被划分成n个三角形区域,每个三角形区域与一个正的权值相关联,不同的三角形区域权值可以不同。如何快速求解出任意两点间的一条路径并使其代价最少就是文中研究的内容。对此问题的国内外现状进行了详细阐述与比较,并提出一个能获得更为逼近最优路径的结果且牺牲运行时间较少的可行方案,最后指出此问题的发展趋势。     

An Improved Algorithm for Online Unit Clustering

We revisit the online unit clustering problem in one dimension which we recently introduced at WAOA’06: given a sequence of n points on the line, the objective is to partition the points into a minimum number of subsets, each enclosable by a unit interval. We present a new randomized online algorithm that achieves expected competitive ratio 11/6 against oblivious adversaries, improving the previous ratio of 15/8. This immediately leads to improved upper bounds for the problem in two and higher dimensions as well. A preliminary version of this paper appeared in the Proceedings of the 13th Annual International Computing and Combinatorics Conference (COCOON 2007), LNCS 4598, pp. 383–393.