Runtime Analysis of an Ant Colony Optimization Algorithm for TSP Instances

Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime.     

Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2-D time-dependent synthetic and vector fields from computational fluid dynamics.     

一种改进的求解TSP问题的近似算法

旅行商问题(TSP)是典型的具有NPC复杂性的组合优化问题。在现有求解TSP问题的2-近似算法closest-point算法基础上,通过对插入点的插入位置进行改进,提出了一种有效的近似算法最近点前后插入法(CPBOA),并采用TSPLIB中的一些典型实例对该算法进行了测试,同时与典型的常数近似比算法MST-PRIM算法和closest-point算法进行了比较。实验结果表明,该算法在求解质量上与closest-point和MST-PRIM算法相比都有很大的改进,而且速度也很快。     

Efficient global penetration depth computation for articulated models

We present an algorithm for computing the global penetration depth between an articulated model and an obstacle or between the distinctive links of an articulated model. In so doing, we use a formulation of penetration depth derived in configuration space. We first compute an approximation of the boundary of the obstacle regions using a support vector machine in a learning stage. Then, we employ a nearest neighbor search to perform a runtime query for penetration depth. The computational complexity of the runtime query depends on the number of support vectors, and its computational time varies from 0.03 to 3 milliseconds in our benchmarks. We can guarantee that the configuration realizing the penetration depth is penetration free, and the algorithm can handle general articulated models. We tested our algorithm in robot motion planning and grasping simulations using many high degree of freedom (DOF) articulated models. Our algorithm is the first to efficiently compute global penetration depth for high-DOF articulated models.     

RMAP: a rectangular cuboid approximation framework for 3D environment mapping

This paper presents a rectangular cuboid approximation framework (RMAP) for 3D mapping. The goal of RMAP is to provide computational and memory efficient environment representations for 3D robotic mapping using axis aligned rectangular cuboids (RC). This paper focuses on two aspects of the RMAP framework: (i) An occupancy grid approach and (ii) A RC approximation of 3D environments based on point cloud density. The RMAP occupancy grid is based on the Rtree data structure which is composed of a hierarchy of RC. The proposed approach is capable of generating probabilistic 3D representations with multiresolution capabilities. It reduces the memory complexity in large scale 3D occupancy grids by avoiding explicit modelling of free space. In contrast to point cloud and fixed resolution cell representations based on beam end point observations, an approximation approach using point cloud density is presented. The proposed approach generates variable sized RC approximations that are memory efficient for axis aligned surfaces. Evaluation of the RMAP occupancy grid and approximation approach based on computational and memory complexity on different datasets shows the effectiveness of this framework for 3D mapping.     

Extraction of Distinguished Hyperbolic Trajectories for 2D Time-Dependent Vector Field Topology

This paper does two main contributions to 2D time-dependent vector field topology. First, we present a technique for robust, accurate, and efficient extraction of distinguished hyperbolic trajectories (DHT), the generative structures of 2D time-dependent vector field topology. It is based on refinement of initial candidate curves. In contrast to previous approaches, it is robust because the refinement converges for reasonably close initial candidates, it is accurate due to its adaptive scheme, and it is efficient due to its high convergence speed. Second, we provide a detailed evaluation and discussion of previous approaches for the extraction of DHTs and time-dependent vector field topology in general. We demonstrate the utility of our approach using analytical flows, as well as data from computational fluid dynamics.     

Applications of Forman's discrete Morse theory to topology visualization and mesh compression

Morse theory is a powerful tool for investigating the topology of smooth manifolds. It has been widely used by the computational topology, computer graphics, and geometric modeling communities to devise topology-based algorithms and data structures. Forman introduced a discrete version of this theory which is purely combinatorial. We aim to build, visualize, and apply the basic elements of Forman's discrete Morse theory. We intend to use some of those concepts to visually study the topology of an object. As a basis, an algorithmic construction of optimal Forman's discrete gradient vector fields is provided. This construction is then used to topologically analyze mesh compression schemes, such as Edgebreaker and Grow&Fold. In particular, we prove that the complexity class of the strategy optimization of Grow&Fold is MAX-SNP hard.     

MC-CDMA系统中的自适应半盲多用户检测算法

研究多载波CDMA(MC-CDMA)上行半盲多用户检测技术，对基于Chebyshev逼近算法实现的最小输出能量(MOE)盲多用户检测进行改进，提出MC-CDMA系统下一种基于子空间跟踪和Chebyshev逼近的自适应半盲多用户检测算法。该算法基于MOE线性检测器原理，充分利用小区内所有用户的扩频码，设计了一种基于MOE准则的半盲检测器，很好地消除了多址干扰。为了减少计算复杂度，将修正的PASTd算法应用于Chebyshev逼近算法估计MOE半盲检测器的最优权向量。该算法计算复杂度低，具有较好的抗多址干扰性能和检测性能。仿真结果验证了该算法的可行性和优越性。     

Parallel probabilistic relaxation labelling based on Markov random fields for spectral-spatial hyperspectral image classification

The large volume of data and computational complexity of algorithms limit the application of hyperspectral image classification to real-time operations. This work addresses the use of different parallel processing techniques to speed up the Markov random field (MRF)-based method to perform spectral-spatial classification of hyperspectral imagery. The Metropolis relaxation labelling approach is modified to take advantage of multi-core central processing units (CPUs) and to adapt it to massively parallel processing systems like graphics processing units (GPUs). The experiments on different hyperspectral data sets revealed that the implementation approach has a huge impact on the execution time of the algorithm. The results demonstrated that the modified MRF algorithm produced classification accuracy similar to conventional methods with greatly improved computational performance. With modern multi-core CPUs, good computational speed-up can be achieved even without additional hardware support. The CPU-GPU hybrid framework rendered the otherwise computationally expensive approach suitable for time-constrained applications.     

Topology optimization for hybrid additive-subtractive manufacturing

Hybrid additive-subtractive manufacturing is gaining popularity by making full use of geometry complexity produced by additive manufacturing and dimensional accuracy derived from subtractive machining. Part design for this hybrid manufacturing approach has been done by trial-and-error, and no dedicated design methodology exists for this manufacturing approach. To address this issue, this work presents a topology optimization method for hybrid additive and subtractive manufacturing. To be specific, the boundary segments of the input design domain are categorized into two types: (i) Freeform boundary segments freely evolve through the casting SIMP method, and (ii) shape preserved boundary segments suppress the freeform evolvement and are composed of machining features through a feature fitting algorithm. Given the manufacturing strategy, the topology design is produced through additive manufacturing and the shape preserved boundary segments will be processed by post-machining. This novel topology optimization algorithm is developed under a unified SIMP and level set framework. The effectiveness of the algorithm is proved through a few numerical case studies.     

Towards mass customized interoperability

This paper describes an approach to interoperability in design projects that is based on computational agents customizing the representation of product data to individual design tools. The agents can augment their translator capabilities autonomously at runtime. This has the potential to lessen the need to manually pre-define an appropriate set of tool translators. The process of generating tailored product models uses an approach to organizing agent knowledge that limits computational complexity when large numbers of tools are involved. We report the implementation and evaluation of an agent-based system that demonstrates the fundamental features of mass customized interoperability. Results include an average reduction of manual work by 88% using this approach.     

Exact admission-control for integrated aperiodic and periodic tasks

Admission-controllers are used to prevent overload in systems with dynamically arriving tasks. Typically, these admission-controllers are based on sufficient (but not necessary) capacity bounds in order to maintain a low computational complexity. In this paper we present how exact admission-control for aperiodic tasks can be efficiently obtained. Our first result is an admission-controller for purely aperiodic task sets where the test has the same runtime complexity as utilization-based tests. Our second result is an extension of the previous controller for a baseload of periodic tasks. The runtime complexity of this test is lower than for any known exact admission-controller. In addition to presenting our main algorithm and evaluating its performance, we also discuss some general issues concerning admission-controllers and their implementation.     

Fast evaluation of vector splines in three dimensions

Vector spline techniques have been developed as general-purpose methods for vector field reconstruction. However, such vector splines involve high computational complexity, which precludes applications of this technique to many problems using large data sets. In this paper, we develop a fast multipole method for the rapid evaluation of the vector spline in three dimensions. The algorithm depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation and a downward local Taylor series approximation. In comparison with the CPU time of direct calculation, which increases at a quadratic rate with the number of points, the presented fast algorithm achieves a higher speed in evaluation at a linear rate. The theoretical error bounds are derived to ensure that the fast method works well with a specific accuracy. Numerical simulations are performed in order to demonstrate the speed and the accuracy of the proposed fast method.     

三维矢量场的流动拓扑结构抽取

提出一种基于关键点分类的三维矢量场流动拓扑结构抽取算法,可应用于三维曲线网格、结构化网格和分块网格中.在许多计算流体力学计算中,存在非滑移边界,这种边界上流体的速度为0.通过分析流场边界的表面摩擦场的拓扑,展示绕壁面流体的流动结构;使用图标定位关键点,可交互式地标记和显示涡核区域,并通过选择暗示螺旋流动的图标,沿着该关键点的实特征值对应的特征矢量方向积分流线来完成.测试结果清晰地展示了关键特征区域的流体流动特征.     

Dynamic response topology optimization in the time domain using model reduction method

The dynamic response topology optimization problems are usually computationally expensive, so it is necessary to employ the model reduction methods to reduce computational cost. This work will investigate the effectiveness of the mode displacement method(MDM) and mode acceleration method(MAM) for time-domain response problems within the framework of density-based topology optimization. Three objective functions, the mean dynamic compliance, mean strain energy and mean squared displacement are considered. It is found that, in general cases, MDM is not suitable for time-domain response topology optimization problems due to its low accuracy of approximation, while MAM works well for problems of a wide range, and when there are many time steps, the MAM based topology optimization approach is more efficient than the direct integration based approach. So for practical applications, when the problem needs many time steps, the MAM based approach is preferred and otherwise, the direct integration based approach is suggested.     

Constrained Self Organizing Maps for Data Clusters Visualization

High dimensional data visualization is one of the main tasks in the field of data mining and pattern recognition. The self organizing maps (SOM) is one of the topology visualizing tool that contains a set of neurons that gradually adapt to input data space by competitive learning and form clusters. The topology preservation of the SOM strongly depends on the learning process. Due to this limitation one cannot guarantee the convergence of the SOM in data sets with clusters of arbitrary shape. In this paper, we introduce Constrained SOM (CSOM), the new version of the SOM by modifying the learning algorithm. The idea is to introduce an adaptive constraint parameter to the learning process to improve the topology preservation and mapping quality of the basic SOM. The computational complexity of the CSOM is less than those with the SOM. The proposed algorithm is compared with similar topology preservation algorithms and the numerical results on eight small to large real-world data sets demonstrate the efficiency of the proposed algorithm.     

基于分布式压缩感知的联合检测与跟踪算法

多基雷达系统对隐身目标的检测与跟踪具有良好的效果,但是在集中式融合框架下应用于 多基雷达的检测与跟踪算法具有计算复杂、计算量大的缺点.对此,提出一种应用于 多基雷达系统的基于分布式压缩感知的联合检测与跟踪算法.首先,应用分布式紧凑感知 矩阵追踪算法直接重构出表征目标状态空间信息的稀疏网格反射向量;然后,应用检测 前跟踪算法得到精确的目标运动状态和轨迹.仿真实验表明了所提出算法的有效性.     

Approximate polynomial preconditionings applied to biharmonic equations

Applying a finite difference approximation to a biharmonic equation results in a very ill conditioned system of equations. This paper examines the conjugate gradient method used with polynomial preconditioning techniques for solving such linear systems. A new approach using an approximate polynomial preconditioner is described. The preconditioner is constructed from a series approximation based on the Laplacian finite difference matrix. A particularly attractive feature of this approach is that the Laplacian matrix consists of far fewer non-zero entries than the biharmonic finite difference matrix. Moreover, analytical estimates and computational results show that this preconditioner is more effective (in terms of the rate of convergence and the computational work required per iteration) than the polynomial preconditioner based on the original biharmonic matrix operator. The conjugate gradient algorithm and the preconditioning step can be efficiently implemented on a vector super-computer such as the CDC CYBER 205.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada Grant U0375; and in part by NASA (funded under the Space Act Agreement C99066G) while the author was visiting ICOMP, NASA Lewis Research Center.The work of this author was supported by an Izaak Walton Killam Memorial Scholarship.