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12th Annual International Conference on Combinatorial Optimization and Applications (COCOA)

作者： Mozafari, Amirhossein Shermer, Thomas C. Simon Fraser Univ Sch Comp Sci Burnaby BC Canada

ISBN: (纸本)9783030046514;9783030046507

In this paper, we introduce the problem of transmitting particles to a target point by the effect of a repulsion actuator (RA). In this problem, we are given a polygonal domain P and a target point t inside it. Also, there is a particle at each point of P. The question is which particles can get to the target point t by activating a RA in P. We present the first polynomial time algorithm to solve this problem.

关键词： geometric algorithm Polygonal domain Repulsion actuator Polynomial time algorithm

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Higher-order Extension of the Breiter-Nesborny-Vokrouhlicky geometric algorithm for Nonautonomous Poisson Systems and Its Application to the Exactly Solvable Model of a Classical Spin in a Rotating Magnetic Field

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JOURNAL OF THE KOREAN PHYSICAL SOCIETY 2012年第4期60卷 613-620页

作者： Oh, Suhk Kun Chungbuk Natl Univ Dept Phys Chonju 361763 South Korea Chungbuk Natl Univ Phys Program BK21 Chonju 361763 South Korea

The Breiter-Nesborny-Vokrouhlicky geometric algorithm for nonautonomous Poisson systems is extended to higher orders. The effectiveness of this extension is exemplified by numerically solving the exactly solvable model of a classical single spin in a rotating magnetic field. Because this model exhibits very complicated periodic motion, after long time elapsed, the usual fourth-order Runge-Kutta algorithm yields a decaying trajectory that has departed significantly from the exact trajectory. We found that the fourth-order Breiter-Nesborny-Vokrouhlicky geometric algorithm of type B remained close to the exact trajectory even when we chose large time-steps for which the Runge-Kutta fourth-order algorithm miserably fails even at relatively short times.

关键词： Classical spin dynamics Poisson system Numerical simulations geometric algorithm

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algorithmic approach to geometric solution of generalized Paden-Kahan subproblem and its extension

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2018年第1期15卷

作者： Dimovski, Igor Trompeska, Mirjana Samak, Samoil Dukovski, Vladimir Cvetkoska, Dijana Inst Adv Composites & Robot Prilep Macedonia SS Cyril & Methodius Univ Skopje Fac Mech Engn Skopje Macedonia

Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systemsopposite to conventional Denavit-Hartenberg approach, where at least n + 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit-Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden-Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden-Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden-Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions.

关键词： Screw motion Paden-Kahan subproblem geometric algorithm inverse kinematics mathematical foundations

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An efficient dense and stable particular elements generation method based on geometry

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2017年第11期110卷 1003-1020页

作者： OuYang, Y. P. Yang, Q. Yu, L. Shanghai Jiao Tong Univ Collaborat Innovat Ctr Adv Ship & Deep Sea Explor State Key Lab Ocean Engn Shanghai 200240 Peoples R China

In this paper, a new discrete elements generation method based on geometry is proposed to fill geometric domains with particles (disks or spheres). By generating particles each one with a random radius or with a radius calculated from the iteration to ensure no overlaps exist between particles and identifying unstable particles and changing them to stable ones, a dense and stable packing can be created. A partitioning particle radius interval method and a particle stability inspection and improvement method are introduced to guarantee the algorithm's success and the stability of the particles. Some packings were created to evaluate the performances of the new method. The results showed that the algorithm was very efficient and was able to create isotropic packings of low porosities and large coordinate numbers. The partitioning particle radius interval method improved the generation efficiency significantly and increased the packing densities. Through the comparisons with several existing methods proposed recently, the method proposed in this work is found to be more efficient and can fill geometric domains with the lowest porosities. In addition, the stability of the particles is guaranteed and no complex triangular or tetrahedral mesh is required in particle generation, thereby making the new method simpler. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： particle generation discrete elements geometric algorithm coordinate number porosity

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An efficient algorithm to generate random sphere packs in arbitrary domains

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第8期71卷 1586-1601页

作者： Lozano, Elias Roehl, Deane Celes, Waldemar Gattass, Marcelo Pontificia Univ Catolica Rio de Janeiro Inst Tecgraf Rio de Janeiro Brazil Pontificia Univ Catolica Rio de Janeiro Dept Engn Civil Rio de Janeiro Brazil

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Sphere packing Advancing-front approach geometric algorithm Distance field applications

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A generalized Mitchell-Dem'yanov-Malozemov algorithm for one-class support vector machine

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KNOWLEDGE-BASED SYSTEMS 2016年第0期109卷 17-24页

作者： Zeng, Ming Yang, Yu Cheng, Junsheng Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Hunan Univ Coll Mech & Vehicle Engn Changsha 410082 Hunan Peoples R China

The dual problem of one-class support vector machine (OCSVM) can be interpreted as a minimum norm problem associated with the reduced convex hull. Based on this geometric interpretation, a generalized Mitchell-Dem'yanov-Malozemov (GMDM) algorithm is proposed for OCSVM. The GMDM algorithm finds the minimum norm point in the reduced convex hull of training samples and employs such a point to construct the separating hyper-plane. Numerical experiments are conducted to compare the proposed geometric algorithm with some existing algorithms such as two modified sequential minimal optimization algorithms and the generalized Gilbert algorithm. The experimental results show that the GMDM algorithm exhibits better performance in terms of computational efficiency while achieving comparable classification accuracies to other algorithms. (C) 2016 Elsevier B.V. All rights reserved.

关键词： One-class support vector machine Generalized Mitchell-Dem'yanov-Malozemov algorithm Minimum norm problem geometric algorithm

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Bio-inspired kinematical control of redundant robotic manipulators

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ASSEMBLY AUTOMATION 2016年第2期36卷 200-215页

作者： Shoushtari, Ali Leylavi Mazzoleni, Stefano Dario, Paolo Scuola Super Sant Anna Inst BioRobot Pontedara Italy Auxilium Vitae Rehabil Ctr Lab Rehabil Bioengn Volterra Italy

Purpose - This paper aims to propose an innovative kinematic control algorithm for redundant robotic manipulators. The algorithm takes advantage of a bio-inspired approach. Design/methodology/approach - A simplified two-degree-of-freedom model is presented to handle kinematic redundancy in the x-y plane;an extension to three-dimensional tracking tasks is presented as well. A set of sample trajectories was used to evaluate the performances of the proposed algorithm. Findings - The results from the simulations confirm the continuity and accuracy of generated joint profiles for given end-effector trajectories as well as algorithm robustness, singularity and self-collision avoidance. Originality/value - This paper shows how to control a redundant robotic arm by applying human upper arm-inspired concept of inter-joint dependency.

关键词： Robotics Redundancy Motion control geometric algorithm Joint angles synergy Motion planning

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Local geometric algorithm for hole boundary detection in sensor networks

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SECURITY AND COMMUNICATION NETWORKS 2011年第9期4卷 1003-1012页

作者： Shirsat, Amit Bhargava, Bharat US Off Santa Clara CA 95054 USA US Off W Lafayette IN 47907 USA

We present a hole boundary detection algorithm for sensor network which identifies the geographical boundary of voids in the network assuming the relative geographic information of only 2-hop neighbors. We formalize the fuzzy notion of a hole by relating it to the graph theoretic concept of a chordless cycle enclosing a face in an arrangement of lines. Furthermore, the algorithm for detecting such topological holes is distributed, O(k) per node computation (for k 2-hop neighbors) and requires synchronization between nodes that are no more than 2-hops away. The algorithm takes a local best-effort approach and does not verify if the nodes indeed form a closed polygonal loop. We believe that this local effort is sufficient based on theoretical observations and experiments. In the simulation tests we conducted, this was hardly a restriction in correctly identifying the simple, closed polygonal loops. We discuss the security implications of the hole detection framework in the context of sensor networks. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： geometric algorithm hole detection security sensor networks

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Self-supporting rhombic infill structures for additive manufacturing

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COMPUTER-AIDED DESIGN 2016年第0期80卷 32-42页

作者： Wu, Jun Wang, Charlie C. L. Zhang, Xiaoting Westermann, Ruediger Tech Univ Denmark Dept Mech Engn Lyngby Denmark Delft Univ Technol Dept Design Engn NL-2600 AA Delft Netherlands Chinese Univ Hong Kong Dept Mech & Automat Engn Hong Kong Hong Kong Peoples R China Tech Univ Munich Dept Informat D-80290 Munich Germany

Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties, such as resistance to external loads. A widely used practice to fabricate such models is by layer-based additive manufacturing (AM), which however suffers from the problem of adding and removing interior supporting structures. In this paper, we present a novel method for generating application-specific infill structures on rhombic cells so that the resultant structures can automatically satisfy manufacturing requirements on overhang-angle and wall-thickness. Additional supporting structures can be avoided entirely in our framework. To achieve this, we introduce the usage of an adaptive rhombic grid, which is built from an input surface model. Starting from the initial sparse set of rhombic cells, via numerical optimization techniques an objective function can be improved by adaptively subdividing the rhombic grid and thus adding more walls in cells. We demonstrate the effectiveness of our method for generating interior designs in the applications of improving mechanical stiffness and static stability. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Infill Self-supporting geometric algorithm Optimization Additive manufacturing

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A Quasipolynomial Time Approximation Scheme for Euclidean Capacitated Vehicle Routing

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algorithmICA 2015年第1期73卷 115-142页

作者： Das, Aparna Mathieu, Claire Brown Univ Providence RI 02912 USA

In the capacitated vehicle routing problem we are given the locations of customers and depots, along with a vehicle of capacity . The objective is to find a minimum length collection of tours covering all customers such that each tour starts and end at a depot and visits at most customers. The problem is a generalization of the traveling salesman problem. We present a quasipolynomial time approximation scheme for the Euclidean setting of the problem when all points lie in for constant dimension .

关键词： geometric algorithm Approximation algorithms Vehicle routing Combinatorial optimization

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