Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulat...Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn Tucker conditions.展开更多
Constrained clustering,such as k-means with instance-level Must-Link(ML)and Cannot-Link(CL)auxiliary information as the constraints,has been extensively studied recently,due to its broad applications in data science a...Constrained clustering,such as k-means with instance-level Must-Link(ML)and Cannot-Link(CL)auxiliary information as the constraints,has been extensively studied recently,due to its broad applications in data science and AI.Despite some heuristic approaches,there has not been any algorithm providing a non-trivial approximation ratio to the constrained k-means problem.To address this issue,we propose an algorithm with a provable approximation ratio of O(logk)when only ML constraints are considered.We also empirically evaluate the performance of our algorithm on real-world datasets having artificial ML and disjoint CL constraints.The experimental results show that our algorithm outperforms the existing greedy-based heuristic methods in clustering accuracy.展开更多
The k-means clustering algorithm is one of the most commonly used algorithms for clustering analysis. The traditional k-means algorithm is, however, inefficient while working on large numbers of data sets and improvin...The k-means clustering algorithm is one of the most commonly used algorithms for clustering analysis. The traditional k-means algorithm is, however, inefficient while working on large numbers of data sets and improving the algorithm efficiency remains a problem. This paper focuses on the efficiency issues of cluster algorithms. A refined initial cluster centers method is designed to reduce the number of iterative procedures in the algorithm. A parallel k-means algorithm is also studied for the problem of the operation limitation of a single processor machine when given huge data sets. The analytical results demonstrate that these improvements can greatly enhance the efficiency of the k-means algorithm, i.e., allow the grouping of a large number of data sets more accurately and more quickly. The analysis has theoretical and practical importance for work on the improvement and parallelism of cluster algorithms.展开更多
This paper presents a redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator with two rotational and one translational coupling degrees of freedom.The kinematics analysis is firstly carried out and...This paper presents a redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator with two rotational and one translational coupling degrees of freedom.The kinematics analysis is firstly carried out and the mapping relationship of the velocity,acceleration and the independent parameters between the actuator joint and the moving platform are deduced by using the vector dot product and cross product operation.By employing d′Alembert′s principle and the principle of virtual work,the dynamics equilibrium equation is derived,and the simplified dynamics mathematical model of the parallel manipulator is further derived.Simultaneously,the generalized inertia matrix which can characterize the acceleration performance between joint space and operation space is further separated,and the performance indices including the dynamics dexterity,inertia coupling characteristics,energy transmission efficiency and driving force/torque balance are introduced.The analysis results show that the proposed redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator in comparison with the existing non-redundant one has better dynamic comprehensive performance,which can be demonstrated practically by the successful application of the parallel kinematic machine head module of the hybrid machine tool.展开更多
This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignore...This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.展开更多
In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construc...In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.展开更多
文摘Remarks on a benchmark nonlinear constrained optimization problem are made. Due to a citation error, two absolutely different results for the benchmark problem are obtained by independent researchers. Parallel simulated annealing using simplex method is employed in our study to solve the benchmark nonlinear constrained problem with mistaken formula and the best-known solution is obtained, whose optimality is testified by the Kuhn Tucker conditions.
基金This work was supported by the National Natural Science Foundation of China(Nos.12271098 and 61772005)the Outstanding Youth Innovation Team Project for Universities of Shandong Province(No.2020KJN008)。
文摘Constrained clustering,such as k-means with instance-level Must-Link(ML)and Cannot-Link(CL)auxiliary information as the constraints,has been extensively studied recently,due to its broad applications in data science and AI.Despite some heuristic approaches,there has not been any algorithm providing a non-trivial approximation ratio to the constrained k-means problem.To address this issue,we propose an algorithm with a provable approximation ratio of O(logk)when only ML constraints are considered.We also empirically evaluate the performance of our algorithm on real-world datasets having artificial ML and disjoint CL constraints.The experimental results show that our algorithm outperforms the existing greedy-based heuristic methods in clustering accuracy.
基金Supported by the National Defence Science and Technology Research Foundation of China (No. 99J15.3.2.JW0116)
文摘The k-means clustering algorithm is one of the most commonly used algorithms for clustering analysis. The traditional k-means algorithm is, however, inefficient while working on large numbers of data sets and improving the algorithm efficiency remains a problem. This paper focuses on the efficiency issues of cluster algorithms. A refined initial cluster centers method is designed to reduce the number of iterative procedures in the algorithm. A parallel k-means algorithm is also studied for the problem of the operation limitation of a single processor machine when given huge data sets. The analytical results demonstrate that these improvements can greatly enhance the efficiency of the k-means algorithm, i.e., allow the grouping of a large number of data sets more accurately and more quickly. The analysis has theoretical and practical importance for work on the improvement and parallelism of cluster algorithms.
基金supported by the Fundamental Research Funds for the Central Universities (Nos. 2018JBZ007, 2018YJS136 and 2017YJS158)China Scholarship Council (CSC) (No. 201807090079)National Natural Science Foundation of China (No. 51675037)
文摘This paper presents a redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator with two rotational and one translational coupling degrees of freedom.The kinematics analysis is firstly carried out and the mapping relationship of the velocity,acceleration and the independent parameters between the actuator joint and the moving platform are deduced by using the vector dot product and cross product operation.By employing d′Alembert′s principle and the principle of virtual work,the dynamics equilibrium equation is derived,and the simplified dynamics mathematical model of the parallel manipulator is further derived.Simultaneously,the generalized inertia matrix which can characterize the acceleration performance between joint space and operation space is further separated,and the performance indices including the dynamics dexterity,inertia coupling characteristics,energy transmission efficiency and driving force/torque balance are introduced.The analysis results show that the proposed redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator in comparison with the existing non-redundant one has better dynamic comprehensive performance,which can be demonstrated practically by the successful application of the parallel kinematic machine head module of the hybrid machine tool.
基金supported by the National Natural Science Foundation of China [No. 51475321]Tianjin Research Program of Application Foundation and Advanced Technology [No. 15JCZDJC38900 and 16JCYBJC19300]the International Postdoctoral Exchange Fellowship Program [No. 32 Document of OCPC, 2017]
文摘This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.
基金Supported by the National Natural Science Foundation of China(No.11101420,11331012,71271204)
文摘In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.
