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A Quasipolynomial Time Approximation Scheme for Euclidean Capacitated Vehicle Routing

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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Interactive building and updating of a 3D database for teleoperation

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ROBOTICA 1997年第0期15卷 511-521页

作者： NZi, EC Mallem, M Chavand, F CEMIF Systemes Complexes 40 rue du Pelvoux CE 1455 Courcouronnes 91020 Evry Cedex France E-mail: mallem@cemif.univ-evry.fr

The paper deals with the modelling of unknown objects and location determination of known ones. The operator models objects using data issued from the video image and a time of flight infra red range finder. We present methods to build an embodying volume for unknown objects. These methods are available for polyhedral and conical objects, which represent the basis of most industrial environments. The location determination of known objects is determined using 2D clues obtained through video image. A two-step algorithm is implemented and assessed. The first step is available in case of object large motion, it is a geometric algorithm, which doesn't use redundant data;it provides a first estimate of the pose. The second step is available in case of object small motion. A linear approach is carried out to determine the pose. It allows the use of redundant data, so it improves the accuracy achieved after the first step.

关键词： telerobotics 3D databases images matching geometric algorithm

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LINEAR TIME algorithmS FOR 2-VARIABLE AND 3-VARIABLE LINEAR-PROGRAMS

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SIAM JOURNAL ON COMPUTING 1984年第1期13卷 31-45页

作者： DYER, ME Teesside Polytechnic Dep of Mathematics & Statistics Middlesbrough Engl Teesside Polytechnic Dep of Mathematics & Statistics Middlesbrough Engl

$O(n)$ time algorithms for linear programming problems with two or three variables and n constraints are described. The approach uses convexity, dominance of linear functions and linear-time median finding algorithms.... 详细信息

关键词： linear programming computational complexity 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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Fast and efficient particle packing algorithms based on triangular mesh

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POWDER TECHNOLOGY 2020年 366卷 448-459页

作者： Zhang, Kaiyu Liu, Feng Zhao, Gaofeng Xia, Kaiwen Tianjin Univ Sch Civil Engn State Key Lab Hydraul Engn Simulat & Safety Tianjin 300072 Peoples R China Monash Univ Dept Civil Engn Clayton Vic 3800 Australia

The point of departure for the particle-based discrete element simulations is the generation of disk or sphere packing of interest domain. In this paper, based on a triangular mesh, two geometric packing algorithms are proposed for 2D problems. New disk(s) are obtained element-wise by solving system of equations, which can be easily derived according to the local topological relationships. In this way, the adjacent disks are guaranteed to be in contact with each other exactly. Related issues are discussed in detail, such as boundary treatment for good definition of the boundaries, elimination of incorrect overlaps, random perturbation for avoiding over-homogeneous packing. The main advantages of these two algorithms are the high efficiency and applicability for arbitrary domains. Furthermore, with a refined mesh, a refined packing can be easily obtained, which is a potential alternative for multiscale simulations. The proposed methods are verified by several examples. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Specimen generation Random packing Disk packing geometric algorithm Distinct element method

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A geometric method for model selection in support vector machine

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EXPERT SYSTEMS WITH APPLICATIONS 2009年第3期36卷 5745-5749页

作者： Peng, Xinjun Wang, Yifei Shanghai Normal Univ Dept Computat Math Shanghai 200234 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

Support vector machine (SVM) has become one of the most popular methods in machine learning during the last years. The parameters' selection in SVM is an important step in achieving a high performance learning machine. Some methods are proposed by minimizing an estimate of generalization error based on bound of leave-one-out (LOO) bound, empirical error, etc. These methods have to optimize many quadratic programming problems and compute an inversion of the Gram-Schmidt matrix, which cause to be time-consuming in large-scale problems. This paper introduces a fast incremental method to optimize the kernel parameters in SVM by combining a geometric algorithm on SVM and an approximation of the gradient of the empirical error. This method shows an online way to update the kernel parameters and work set in incremental learning, which reduces the resources required both CPU time and storage space. The numerical tests on some benchmarks confirm our method. Crown Copyright (C) 2008 Published by Elsevier Ltd. All rights reserved.

关键词： Support vector machine Model selection Parameter geometric algorithm Optimize

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A novel geometry-based feature-selection technique for hyperspectral imagery

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2007年第1期4卷 171-175页

作者： Wang, Liguo Jia, Xiuping Zhang, Ye Harbin Inst Technol Dept Informat Engn Harbin 150001 Heilongjiang Peoples R China Univ New S Wales Univ Coll Sch Informat Technol & Elect Engn Australian Def Force Acad Canberra ACT 2600 Australia

In this letter, a geometry-based feature-selection method is proposed for efficient analysis of hyperspectral imagery. It searches the vertices that form the largest simplex iteratively in pixel space. These vertices are representative subsets of spectral bands. A distance measure is introduced in the simplex volume comparison for fast implementation of the proposed method. Fast principal component analysis and spectral band indexing are suggested for data preprocessing. This method can be implemented in supervised or unsupervised manner. It is automatic, fast, and distribution-free. Experimental results show the superiority of the proposed method in terms of quality and speed.

关键词： feature selection (FS) geometric algorithm hyperspectral imagery (HSI)

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geometric projection twin support vector machine for pattern classification

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MULTIMEDIA TOOLS AND APPLICATIONS 2021年第15期80卷 23073-23089页

作者： Chen, Xiaobo Xiao, Yan Jiangsu Univ Automot Engn Res Inst Zhenjiang 212013 Jiangsu Peoples R China Jiangsu Univ Sch Automot & Traff Engn Zhenjiang 212013 Jiangsu Peoples R China

In this paper, a novel binary classifier termed as GPTSVM (projection twin support vector machine via geometric Interpretation) is presented. In the spirit of original PTSVM, GPTSVM tries to seek two projection axes, one for each class, such that the projected samples of one class are well separated from that of the other class along its own projection axis. A pair of parameters (nu) are introduced in GPTSVM to control the bounds of the fractions of the support vectors and the error margins. Moreover, GPTSVM can be interpreted as a pair of minimum Mahalanobis norm problems on two reduced convex hulls (RCHs). Then, an efficient geometric algorithm for GPTSVM is presented based on the well-known Gilbert's algorithm. By doing so, the dual problem of GPTSVM can be solved very fast without resorting to any specialized optimization toolbox. The experimental results on several UCI benchmark data sets, traffic accident prediction data, and large scale NDCC database show the feasibility and effectiveness of the proposed algorithm.

关键词： Support vector machine Quadratic programming Reduced convex hull geometric algorithm Multiple plane classifier

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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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Mixed-radix Naccache-Stern encryption

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JOURNAL OF CRYPTOGRAPHIC ENGINEERING 2019年第3期9卷 277-282页

作者： Geraud, Remi Naccache, David PSL Res Univ ENS CNRS Dept InformatInformat Secur Grp Paris France

In this work, we explore a combinatorial optimization problem stemming from the Naccache-Stern cryptosystem. We show that solving this problem results in bandwidth improvements, and suggest a polynomial-time approximation algorithm to find an optimal solution. Our work suggests that using optimal radix encoding results in an asymptotic 50% increase in bandwidth.

关键词： Non-linear optimization Public-key encryption geometric algorithm Naccache-Stern cryptosystem Numeration systems

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