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Low-rank generalized alternating direction implicit iteration method for solving matrix equations

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arXiv 2024年

作者： Zhang, Juan Xun, Wenlu Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient low-rank formulation, which is a variant of the Cholesky decomposition in the Lyapunov GADI method, saving storage space and making it computationally effective. When solving the continuous-time algebraic Riccati matrix equation, the Riccati equation is first simplified to a Lyapunov equation using the Newton method, and then the R-GADI method is employed for computation. Additionally, we analyze the convergence of the R-GADI method and prove its consistency with the convergence of the GADI method. Finally, the effectiveness of the new algorithm is demonstrated through corresponding numerical experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

A general alternating direction implicit iteration method for solving complex symmetric linear systems

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arXiv 2024年

We have introduced the generalized alternating direction implicit iteration (GADI) method for solving large sparse complex symmetric linear systems and proved its convergence properties. Additionally, some numerical results have demonstrated the effectiveness of this algorithm. Furthermore, as an application of the GADI method in solving complex symmetric linear systems, we utilized the flattening operator and Kronecker product properties to solve Lyapunov and Riccati equations with complex coefficients using the GADI method. In solving the Riccati equation, we combined inner and outer iterations, first simplifying the Riccati equation into a Lyapunov equation using the Newton method, and then applying the GADI method for solution. Finally, we provided convergence analysis of the method and corresponding numerical results. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

Critical Node Detection for Sequential Attacks in Complex Networks via Multi-objective Optimization 2

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Critical Node Detection for Sequential Attacks in Complex Ne...

2nd International Conference on Industrial Artificial Intelligence, IAI 2020

作者： Zhang, Lei Liu, Qing Xia, Jiajun Yang, Haipeng Zhang, Xingyi Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Computer Science and Technology Anhui University China

ISBN: (纸本)9781728182162

The critical node detection for sequential attacks based on cascading failure model is an important way for analyzing network vulnerability, which has attracted the attention of many researchers in the field of complex network recently. However, most of the existing cascading critical node detection algorithms focus on designing effective attack strategies leading to the maximal damage to the network (i.e. attack effect), while ignoring the cost of attacks. To this end, we transform the cascading critical node detection for sequential attacks as a bi-objective optimization problem (named BCVNDSeq), where the attack cost and the attack effect are simultaneously optimized. In order to solve the transformed problem, we propose a multiobjective cascading critical node detection algorithm (named MO-BCVNDSeq), which can provide decision makers with a holistic view for analyzing the network vulnerability. In MO-BCVNDSeq, a local search strategy based on sequential matrix is proposed to accelerate the population convergence and an individual repairing strategy is also suggested to further improve the search efficiency. Finally, the experimental results on 6 real-world complex networks demonstrate the effectiveness of the proposed algorithm compared with several representative baselines. © 2020 IEEE.

关键词： Multiobjective optimization

Optimization methods for solving matrix equations

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arXiv 2024年

作者： Zhang, Juan Luo, Xiao Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a constrained convex optimization method (CCOM) to solve the Sylvester matrix equation with 2,1-norm, where we provide a convergence analysis and numerical examples of CCOM;however, the results show that the algorithm is not efficient. To address this issue, we employ classical quasi-Newton methods such as DFP and BFGS algorithms to solve the Sylvester matrix equation and present the convergence and numerical results of the algorithm. Additionally, we compare these algorithms with the CG algorithm and AR algorithm, and our results demonstrate that the presented algorithms are effective. Furthermore, we propose a unified framework of the alternating direction multiplier method (ADMM) for directly solving the continuous algebraic Riccati equation (CARE), and we provide the convergence and numerical results of ADMM. Our experimental results indicate that ADMM is an effective optimization algorithm for solving CARE. Finally, to improve the effectiveness of the optimization method for solving Riccati equation, we propose the Newton-ADMM algorithm framework, where the outer iteration of this method is the classical Newton method, and the inner iteration involves using ADMM to solve Lyapunov matrix equations inexactly. We also provide the convergence and numerical results of this algorithm, which our results demonstrate are more efficient than ADMM for solving CARE. Copyright © 2024, The Authors. All rights reserved.

关键词： Newton-Raphson method

Data Fusion Based on Temporal-Spatial Composite Sequential Three-Way Decision

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SSRN

SSRN 2022年

作者： Xu, Yi Qiu, Ziheng Sun, Xiaojun Department of Computer Science and Technology Anhui University Hefei230601 China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei230601 China

Three-way decision is the representative of trisecting-acting-outcome(TAO) model. Considering the temporality, in dynamic information systems, the objects may be inserted or deleted,attributes may be added or removed, and attributes values may be updated or modified. These variations can be reflected by the TAO model, which cares about consideration at different levels, acquisition of strategies, and handling of issues based on Strategies. Considering the spatiality, different levels, and different perspectives of granular structure are created by the sequential approach of three-way decision. In this paper, in order to fuse hybrid data, a sequential three-way decision is proposed by the combination of temporality and spatiality. Firstly, We present the frameworks of spatiality-based and temporality-based and focus on temporal-spatial three-way decision. Then we provide three operations to construct the composite POS structure by combining a family of approximations. Based on the composite POS structure, three different strategies for the fusion of dynamic hybrid data are adopted. Finally, we design the algorithm and implement a series of comparison experiments to verify our model is effective. © 2022, The Authors. All rights reserved.

关键词： Data fusion

A Fine-Grained Anomaly Detection Method Fusing Isolation Forest and Knowledge Graph Reasoning 19th

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A Fine-Grained Anomaly Detection Method Fusing Isolation For...

19th International Conference on Web Information Systems and Applications, WISA 2022

作者： Xu, Jie Zhou, Jiantao College of Computer Science Engineering Research Center of Ecological Big Data Ministry of Education National and Local Joint Engineering Research Center of Mongolian Intelligent Information Processing Technology Inner Mongolia Cloud Computing and Service Software Engineering Laboratory Inner Mongolia Social Computing and Data Processing Key Laboratory Inner Mongolia Discipline Inspection and Supervision Big Data Key Laboratory Inner Mongolia Big Data Analysis Technology Engineering Laboratory Inner Mongolia University Hohhot China

ISBN: (纸本)9783031203084

Anomaly detection aims to find outliers data that do not conform to expected behaviors in a specific scenario, which is indispensable and critical in current safety environments related studies. However, when performing outlier detection on a large-scale multidimensional dataset, most of the traditional methods make no distinctions between classes of outliers and lack the reasoning ability and the explainability of the analysis results, which leads to the low accuracy of global outlier detection and the inability to effectively identify local outliers. In this paper, we propose a fine-grained anomaly detection method which well utilizes isolation forest and knowledge graph reasoning tactics. First, a better extracting data feature method and a more reasonable weighted strategy are used to find global outliers based on the traditional isolation forest algorithm, and then we construct a custom rule base according to the in-depth research and analysis of global abnormal data, and at last the ontology knowledge is reasoned based on such rule base to achieve the detection of local outliers. Through analysis of extensive experiment results, our method could effectively discover more abnormal data without big loss of time costs, has strong generalization, and correspondingly improves the performance for abnormal detection. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Anomaly detection

Dual-layer Broadband High-gain Circularly Polarized Patch Antenna with L-shaped Stub

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Dual-layer Broadband High-gain Circularly Polarized Patch An...

IEEE International Workshop on Electromagnetics, Applications and Student Innovation (iWEM)

作者： Wen Li Wei Xue Yingsong Li Tian Hong Loh Kwok L. Chung College of Information and Communication Engineering Harbin Engineering University Harbin China The Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University Hefei China Electromagnetic and Eletrochemical Technologies Department National Physical Laboratory Middlesex UK School of Computing Science and Engineering Huizhou University Huizhou China

This paper introduced a dual-layer broadband high-gain circularly polarized (CP) antenna. The proposed broadband CP antenna consists of the radiating patch and couping structure, which is made up of opening slot patch and L-shaped stub. An axial-ratio bandwidth of 26 % (4.36-5.66 GHz) is shown by this proposed dual-layer CP patch antenna with a simulated -10-dB reflection coefficient bandwidth of 37 % (4.23-6.15 GHz). The broadband characteristics offered by this CP antenna are promising for a wide range of future applications.

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A novel dual-stage algorithm for capacitated arc routing problems with time-dependent service costs

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arXiv 2024年

作者： Li, Qingya Liu, Shengcai Zou, Juan Tang, Ke Guangdong Key Laboratory of Brain-Inspired Intelligent Computation Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China The Key Laboratory of Hunan Province for Internet of Things and Information Security Xiangtan University Xiangtan411105 China The Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Xiangtan University Xiangtan411105 China

This paper focuses on solving the capacitated arc routing problem with time-dependent service costs (CARPTDSC), which is motivated by winter gritting applications. In the current literature, exact algorithms designed for CARPTDSC can only handle small-scale instances, while heuristic algorithms fail to obtain high-quality solutions. To overcome these limitations, we propose a novel dual-stage algorithm, called MAENS-GN, that consists of a routing stage and a vehicle departure time optimization stage. The former obtains the routing plan, while the the latter determines the vehicle departure time. Importantly, existing literature often ignores the characteristic information contained in the relationship between the route cost and the vehicle departure time. The most significant innovation in this paper lies in the exploitation of this characteristic information during the vehicle departure time optimization stage. Specifically, we conduct a detailed analysis of this relationship under various scenarios and employ tailored methods to obtain the (approximately) optimal vehicle departure time. Furthermore, we propose an improved initialization strategy that considers time-dependent characteristics to achieve better solution quality. In addition to the modified benchmark test sets, we also experiment on a real-world test set. Experimental results demonstrate that MAENS-GN can obtain high-quality solutions on both small-scale and larger-scale instances of CARPTDSC. Copyright © 2024, The Authors. All rights reserved.

关键词： Combinatorial optimization

A Novel Dual-Stage Algorithm for Capacitated Arc Routing Problems with Time-Dependent Service Costs

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SSRN

SSRN 2024年

This paper focuses on solving the capacitated arc routing problem with time-dependent service costs (CARPTDSC), which is motivated by winter gritting applications. In the current literature, exact algorithms designed for CARPTDSC can only handle small-scale instances, while heuristic algorithms fail to obtain high-quality solutions. To overcome these limitations, we propose a novel dual-stage algorithm, called MAENS-GN, that consists of a routing stage and a vehicle departure time optimization stage. The former obtains the routing plan, while the the latter determines the vehicle departure time. Importantly, existing literature often ignores the characteristic information contained in the relationship between the route cost and the vehicle departure time. The most signiﬁcant innovation in this paper lies in the exploitation of this characteristic information during the vehicle departure time optimization stage. Speciﬁcally, we conduct a detailed analysis of this relationship under various scenarios and employ tailored methods to obtain the (approximately) optimal vehicle departure time. Furthermore, we propose an improved initialization strategy that considers time-dependent characteristics to achieve better solution quality. In addition to the modiﬁed benchmark test sets, we also experiment on a real-world test set. Experimental results demonstrate that MAENS-GN can obtain high-quality solutions on both small-scale and larger-scale instances of CARPTDSC. © 2024, The Authors. All rights reserved.

关键词： Combinatorial optimization