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Application of A* Algorithm for Real-time Path Re-planning of an Unmanned Surface Vehicle Avoiding Underwater Obstacles 被引量:8
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作者 Thanapong Phanthong Toshihiro Maki +2 位作者 Tamaki Ura Takashi Sakamaki Pattara Aiyarak 《Journal of Marine Science and Application》 2014年第1期105-116,共12页
This paper describes path re-planning techniques and underwater obstacle avoidance for unmanned surface vehicle(USV) based on multi-beam forward looking sonar(FLS). Near-optimal paths in static and dynamic environment... This paper describes path re-planning techniques and underwater obstacle avoidance for unmanned surface vehicle(USV) based on multi-beam forward looking sonar(FLS). Near-optimal paths in static and dynamic environments with underwater obstacles are computed using a numerical solution procedure based on an A* algorithm. The USV is modeled with a circular shape in 2 degrees of freedom(surge and yaw). In this paper, two-dimensional(2-D) underwater obstacle avoidance and the robust real-time path re-planning technique for actual USV using multi-beam FLS are developed. Our real-time path re-planning algorithm has been tested to regenerate the optimal path for several updated frames in the field of view of the sonar with a proper update frequency of the FLS. The performance of the proposed method was verified through simulations, and sea experiments. For simulations, the USV model can avoid both a single stationary obstacle, multiple stationary obstacles and moving obstacles with the near-optimal trajectory that are performed both in the vehicle and the world reference frame. For sea experiments, the proposed method for an underwater obstacle avoidance system is implemented with a USV test platform. The actual USV is automatically controlled and succeeded in its real-time avoidance against the stationary undersea obstacle in the field of view of the FLS together with the Global Positioning System(GPS) of the USV. 展开更多
关键词 UNDERWATER OBSTACLE AVOIDANCE real-time pathre-planning A* algorithm SONAR image unmanned surface vehicle
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A Class of Fast Algorithms in Real-Time Simulation 被引量:4
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作者 Zhu Zhenmin & Liu Degui(Beijing Institute of Computer Application and Simulation Technology, 100854, P. R. China)Li Shoufu(Mathematics Department of Xiangtan University, 411105, P. R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1999年第4期10-20,共11页
A class of hybrid algorithms of real-time simulation based on evaluation of non-integerstep right-hand side function are presented in this paper. And some results of the convergence and stability of the algorithms are... A class of hybrid algorithms of real-time simulation based on evaluation of non-integerstep right-hand side function are presented in this paper. And some results of the convergence and stability of the algorithms are given. Using the class of algorithms, evaluation for the right-hand side function is needed once in every integration-step. Moreover, comparing with the other methods with the same amount of work, their numerical stability regions are larger and the method errors are smaller, and the numerical experiments show that the algorithms are very effective. 展开更多
关键词 real-time simulation algorithm Numerical stability CONVERGENCE Dynamic system
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An improving energy efficiency cooperation algorithm based on Nash bargaining solution in selfish user cooperative networks
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作者 张闯 赵洪林 贾敏 《Journal of Southeast University(English Edition)》 EI CAS 2015年第2期181-187,共7页
A bandwidth-exchange cooperation algorithm based on the Nash bargaining solution (NBS) is proposed to encourage the selfish users to participate with more cooperation so as to improve the users' energy efficiency. ... A bandwidth-exchange cooperation algorithm based on the Nash bargaining solution (NBS) is proposed to encourage the selfish users to participate with more cooperation so as to improve the users' energy efficiency. As a result, two key problems, i.e. , when to cooperate and how to cooperate, are solved. For the first problem, a proposed cooperation condition that can decide when to cooperate and guarantee users' energy efficiency achieved through cooperation is not lower than that achieved without cooperation. For the second problem, the cooperation bandwidth allocations (CBAs) based on the NBS solve the problem how to cooperate when cooperation takes place. Simulation results show that, as the modulation order of quadrature amplitude modulation (QAM) increases, the cooperation between both users only occurs with a large signal-to-noise ratio (SNR). Meanwhile, the energy efficiency decreases as the modulation order increases. Despite all this, the proposed algorithm can obviously improve the energy efficiency measured in bits-per-Joule compared with non-cooperation. 展开更多
关键词 cooperation algorithm Nash bargaining solution(NBS) resource-exchange quadrature amplitude modulation(QAM)
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Application of the asynchronous advantage actor–critic machine learning algorithm to real-time accelerator tuning 被引量:3
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作者 Yun Zou Qing-Zi Xing +4 位作者 Bai-Chuan Wang Shu-Xin Zheng Cheng Cheng Zhong-Ming Wang Xue-Wu Wang 《Nuclear Science and Techniques》 SCIE CAS CSCD 2019年第10期133-141,共9页
This paper describes a real-time beam tuning method with an improved asynchronous advantage actor–critic(A3C)algorithm for accelerator systems.The operating parameters of devices are usually inconsistent with the pre... This paper describes a real-time beam tuning method with an improved asynchronous advantage actor–critic(A3C)algorithm for accelerator systems.The operating parameters of devices are usually inconsistent with the predictions of physical designs because of errors in mechanical matching and installation.Therefore,parameter optimization methods such as pointwise scanning,evolutionary algorithms(EAs),and robust conjugate direction search are widely used in beam tuning to compensate for this inconsistency.However,it is difficult for them to deal with a large number of discrete local optima.The A3C algorithm,which has been applied in the automated control field,provides an approach for improving multi-dimensional optimization.The A3C algorithm is introduced and improved for the real-time beam tuning code for accelerators.Experiments in which optimization is achieved by using pointwise scanning,the genetic algorithm(one kind of EAs),and the A3C-algorithm are conducted and compared to optimize the currents of four steering magnets and two solenoids in the low-energy beam transport section(LEBT)of the Xi’an Proton Application Facility.Optimal currents are determined when the highest transmission of a radio frequency quadrupole(RFQ)accelerator downstream of the LEBT is achieved.The optimal work points of the tuned accelerator were obtained with currents of 0 A,0 A,0 A,and 0.1 A,for the four steering magnets,and 107 A and 96 A for the two solenoids.Furthermore,the highest transmission of the RFQ was 91.2%.Meanwhile,the lower time required for the optimization with the A3C algorithm was successfully verified.Optimization with the A3C algorithm consumed 42%and 78%less time than pointwise scanning with random initialization and pre-trained initialization of weights,respectively. 展开更多
关键词 real-time BEAM tuning Parameter optimization ASYNCHRONOUS ADVANTAGE actor–critic algorithm Low-energy BEAM transport
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A Real-time Lithological Identification Method based on SMOTE-Tomek and ICSA Optimization
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作者 DENG Song PAN Haoyu +5 位作者 LI Chaowei YAN Xiaopeng WANG Jiangshuai SHI Lin PEI Chunyu CAI Meng 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2024年第2期518-530,共13页
In petroleum engineering,real-time lithology identification is very important for reservoir evaluation,drilling decisions and petroleum geological exploration.A lithology identification method while drilling based on ... In petroleum engineering,real-time lithology identification is very important for reservoir evaluation,drilling decisions and petroleum geological exploration.A lithology identification method while drilling based on machine learning and mud logging data is studied in this paper.This method can effectively utilize downhole parameters collected in real-time during drilling,to identify lithology in real-time and provide a reference for optimization of drilling parameters.Given the imbalance of lithology samples,the synthetic minority over-sampling technique(SMOTE)and Tomek link were used to balance the sample number of five lithologies.Meanwhile,this paper introduces Tent map,random opposition-based learning and dynamic perceived probability to the original crow search algorithm(CSA),and establishes an improved crow search algorithm(ICSA).In this paper,ICSA is used to optimize the hyperparameter combination of random forest(RF),extremely random trees(ET),extreme gradient boosting(XGB),and light gradient boosting machine(LGBM)models.In addition,this study combines the recognition advantages of the four models.The accuracy of lithology identification by the weighted average probability model reaches 0.877.The study of this paper realizes high-precision real-time lithology identification method,which can provide lithology reference for the drilling process. 展开更多
关键词 mud logging data real-time lithological identification improved crow search algorithm petroleum geological exploration SMOTE-Tomek
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Real-Time Spreading Thickness Monitoring of High-core Rockfill Dam Based on K-nearest Neighbor Algorithm 被引量:4
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作者 Denghua Zhong Rongxiang Du +2 位作者 Bo Cui Binping Wu Tao Guan 《Transactions of Tianjin University》 EI CAS 2018年第3期282-289,共8页
During the storehouse surface rolling construction of a core rockfilldam, the spreading thickness of dam face is an important factor that affects the construction quality of the dam storehouse' rolling surface and... During the storehouse surface rolling construction of a core rockfilldam, the spreading thickness of dam face is an important factor that affects the construction quality of the dam storehouse' rolling surface and the overallquality of the entire dam. Currently, the method used to monitor and controlspreading thickness during the dam construction process is artificialsampling check after spreading, which makes it difficult to monitor the entire dam storehouse surface. In this paper, we present an in-depth study based on real-time monitoring and controltheory of storehouse surface rolling construction and obtain the rolling compaction thickness by analyzing the construction track of the rolling machine. Comparatively, the traditionalmethod can only analyze the rolling thickness of the dam storehouse surface after it has been compacted and cannot determine the thickness of the dam storehouse surface in realtime. To solve these problems, our system monitors the construction progress of the leveling machine and employs a real-time spreading thickness monitoring modelbased on the K-nearest neighbor algorithm. Taking the LHK core rockfilldam in Southwest China as an example, we performed real-time monitoring for the spreading thickness and conducted real-time interactive queries regarding the spreading thickness. This approach provides a new method for controlling the spreading thickness of the core rockfilldam storehouse surface. 展开更多
关键词 Core rockfill dam Dam storehouse surface construction Spreading thickness K-nearest neighbor algorithm real-time monitor
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A Class of Parallel Algorithms of Real-TimeNumerical Simulation for Stiff Dynamic System 被引量:2
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作者 Cao Xuenian Liu Degui Li Shoufu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2000年第4期51-58,共8页
In this paper a class of real-time parallel modified Rosenbrock methods of numerical simulation is constructed for stiff dynamic systems on a multiprocessor system, and convergence and numerical stability of these met... In this paper a class of real-time parallel modified Rosenbrock methods of numerical simulation is constructed for stiff dynamic systems on a multiprocessor system, and convergence and numerical stability of these methods are discussed. A-stable real-time parallel formula of two-stage third-order and A(α)-stable real-time parallel formula with o ≈ 89.96° of three-stage fourth-order are particularly given. The numerical simulation experiments in parallel environment show that the class of algorithms is efficient and applicable, with greater speedup. 展开更多
关键词 Dynamic system real-time simulation Parallel algorithms?
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An Algorithm for Solutions of Nonlinear Difference-differential Equations 被引量:1
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作者 许丽萍 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期598-605,共8页
In this paper,an algorithm is developed for using the G' /G-expansion method to obtain exact solutions for discrete nonlinear systems.Applying this method,some kinds of travelling wave solutions for AL system and ... In this paper,an algorithm is developed for using the G' /G-expansion method to obtain exact solutions for discrete nonlinear systems.Applying this method,some kinds of travelling wave solutions for AL system and Toda lattice system are derived.These solutions are expressed by hyperbolic function,trigonometric function and rational function with parameters.When the parameters are taken as special values,some known solutions including kink-type solitary wave solution and singular travelling wave solution are recovered. It is shown that the developed algorithm is effective and direct.It also can be used for many other nonlinear differential-difference equations in mathematical physics. 展开更多
关键词 an algorithm AL system Toda lattice system exact solutions
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Enhancing Cybersecurity through Cloud Computing Solutions in the United States
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作者 Omolola F. Hassan Folorunsho O. Fatai +4 位作者 Oluwadare Aderibigbe Abdullah Oladoyin Akinde Tolulope Onasanya Mariam Adetoun Sanusi Oduwunmi Odukoya 《Intelligent Information Management》 2024年第4期176-193,共18页
This study investigates how cybersecurity can be enhanced through cloud computing solutions in the United States. The motive for this study is due to the rampant loss of data, breaches, and unauthorized access of inte... This study investigates how cybersecurity can be enhanced through cloud computing solutions in the United States. The motive for this study is due to the rampant loss of data, breaches, and unauthorized access of internet criminals in the United States. The study adopted a survey research design, collecting data from 890 cloud professionals with relevant knowledge of cybersecurity and cloud computing. A machine learning approach was adopted, specifically a random forest classifier, an ensemble, and a decision tree model. Out of the features in the data, ten important features were selected using random forest feature importance, which helps to achieve the objective of the study. The study’s purpose is to enable organizations to develop suitable techniques to prevent cybercrime using random forest predictions as they relate to cloud services in the United States. The effectiveness of the models used is evaluated by utilizing validation matrices that include recall values, accuracy, and precision, in addition to F1 scores and confusion matrices. Based on evaluation scores (accuracy, precision, recall, and F1 scores) of 81.9%, 82.6%, and 82.1%, the results demonstrated the effectiveness of the random forest model. It showed the importance of machine learning algorithms in preventing cybercrime and boosting security in the cloud environment. It recommends that other machine learning models be adopted to see how to improve cybersecurity through cloud computing. 展开更多
关键词 CYBERSECURITY Cloud Computing Cloud solutions Machine Learning algorithm
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Novel Real-Time Seam Tracking Algorithm Based on Vector Angle and Least Square Method 被引量:1
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作者 Guanhao Liang Qingsheng Luo +1 位作者 Zhuo Ge Xiaoqing Guan 《Journal of Beijing Institute of Technology》 EI CAS 2017年第2期150-157,共8页
Real-time seam tracking can improve welding quality and enhance welding efficiency during the welding process in automobile manufacturing.However,the teaching-playing welding process,an off-line seam tracking method,i... Real-time seam tracking can improve welding quality and enhance welding efficiency during the welding process in automobile manufacturing.However,the teaching-playing welding process,an off-line seam tracking method,is still dominant in automobile industry,which is less flexible when welding objects or situation change.A novel real-time algorithm consisting of seam detection and generation is proposed to track seam.Using captured 3D points,space vectors were created between two adjacent points along each laser line and then a vector angle based algorithm was developed to detect target points on the seam.Least square method was used to fit target points to a welding trajectory for seam tracking.Furthermore,the real-time seam tracking process was simulated in MATLAB/Simulink.The trend of joint angles vs.time was logged and a comparison between the off-line and the proposed seam tracking algorithm was conducted.Results show that the proposed real-time seam tracking algorithm can work in a real-time scenario and have high accuracy in welding point positioning. 展开更多
关键词 real-time seam tracking real-time seam detection laser scanner vector angle leastsquare method algorithm research
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A Mathematical Model of Real-Time Simulation and the Convergence Analysis on Real-Time Runge-Kutta Algorithms 被引量:1
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作者 Song Xiaoqiu, Li Bohu, Liu Degui, Yuan ZhaodingBeijing Institute of Computer Application and Simulation Technology, P. O. Box 142-213, Beijing 100854, China 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1991年第1期129-139,共11页
In this paper, a mathematical model of real-time simulation is given, and the problem of convergence on real-time Runge-Kutta algorithms is analysed. At last a theorem on the relation between the order of compensation... In this paper, a mathematical model of real-time simulation is given, and the problem of convergence on real-time Runge-Kutta algorithms is analysed. At last a theorem on the relation between the order of compensation and the convergent order of real-time algorithm is proved. 展开更多
关键词 real-time simulation Runge-Kutta algorithm Convergence analysis.
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Real-time Design Constraints in Implementing Active Vibration Control Algorithms 被引量:1
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作者 Mohammed Alamgir Hossain Mohammad Osman Tokhi 《International Journal of Automation and computing》 EI 2006年第3期252-262,共11页
Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorith... Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorithm so as to exploit special features of the hardware and avoid associated architecture shortcomings. This paper presents an investigation into the analysis and design mechanisms that will lead to reduction in the execution time in implementing real-time control algorithms. The proposed mechanisms are exemplified by means of one algorithm, which demonstrates their applicability to real-time applications. An active vibration control (AVC) algorithm for a flexible beam system simulated using the finite difference (FD) method is considered to demonstrate the effectiveness of the proposed methods. A comparative performance evaluation of the proposed design mechanisms is presented and discussed through a set of experiments. 展开更多
关键词 algorithm analysis and design active vibration control (AVC) flexible beam system real-time control memory management.
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Real-Time Front Vehicle Detection Algorithm Based on Local Feature Tracking Method 被引量:1
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作者 Jae-hyoung YU Young-joon HAN Hern-soo HAHN 《Journal of Measurement Science and Instrumentation》 CAS 2011年第3期244-246,共3页
This paper proposes an algorithm that extracts features of back side of the vehicle and detects the front vehicle in real-time by local feature tracking of vehicle in the continuous images.The features in back side of... This paper proposes an algorithm that extracts features of back side of the vehicle and detects the front vehicle in real-time by local feature tracking of vehicle in the continuous images.The features in back side of the vehicle are vertical and horizontal edges,shadow and symmetry.By comparing local features using the fixed window size,the features in the continuous images are tracked.A robust and fast Haarlike mask is used for detecting vertical and horizontal edges,and shadow is extracted by histogram equalization,and the sliding window method is used to compare both side templates of the detected candidates for extracting symmetry.The features for tracking are vertical edges,and histogram is used to compare location of the peak and magnitude of the edges.The method using local feature tracking in the continuous images is more robust for detecting vehicle than the method using single image,and the proposed algorithm is evaluated by continuous images obtained on the expressway and downtown.And it can be performed on real-time through applying it to the embedded system. 展开更多
关键词 vehicle detection object tracking real-time algorithm Haarlike edge detection
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Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X-A^(H)X^(-1)A=Q 被引量:1
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作者 Xiao-Xia Guo Hong-Xiao Wu 《Communications on Applied Mathematics and Computation》 2021年第1期123-135,共13页
In this paper,we study the nonlinear matrix equation X-A^(H)X^(-1)A=Q,where A,Q∈C^(n×n),Q is a Hermitian positive definite matrix and X∈C^(n×n)is an unknown matrix.We prove that the equation always has a u... In this paper,we study the nonlinear matrix equation X-A^(H)X^(-1)A=Q,where A,Q∈C^(n×n),Q is a Hermitian positive definite matrix and X∈C^(n×n)is an unknown matrix.We prove that the equation always has a unique Hermitian positive definite solution.We present two structure-preserving-doubling like algorithms to find the Hermitian positive definite solution of the equation,and the convergence theories are established.Finally,we show the effectiveness of the algorithms by numerical experiments. 展开更多
关键词 Positive definite solution Structure-preserving-doubling like algorithm CONVERGENCE Numerical experiment
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Optimized quantum random-walk search algorithm for multi-solution search 被引量:1
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作者 张宇超 鲍皖苏 +1 位作者 汪翔 付向群 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第11期133-139,共7页
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the se... This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value. 展开更多
关键词 quantum search algorithm quantum random walk multi-solution abstract search algorithm
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PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS
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作者 王国荣 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1993年第1期1-10,共10页
This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt... This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise. 展开更多
关键词 Parallel algorithm the minimum-norm LEAST-SQUARES solution inconsistent linear EQUATIONS generalized inverse.
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TWO TYPES OF NEW ALGORITHMS FOR FINDING EXPLICIT ANALYTICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
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作者 张鸿庆 闫振亚 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第12期1423-1431,共9页
The idea of AC = BD was applied to solve the nonlinear differential equations. Suppose that Au = 0 is a given equation to he solved and Dv = 0 is an equation to be easily solved. If the transformation u = Cv is obtain... The idea of AC = BD was applied to solve the nonlinear differential equations. Suppose that Au = 0 is a given equation to he solved and Dv = 0 is an equation to be easily solved. If the transformation u = Cv is obtained so that v satisfies Dv = 0, then the solutions for Au = 0 can be found. In order to illustrate this approach, several examples about the transformation C are given. 展开更多
关键词 nonlinear differential equations transformation algorithm analytical solution
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Generating Epsilon-Efficient Solutions in Multiobjective Optimization by Genetic Algorithm
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作者 El-Desouky Rahmo Marcin Studniarski 《Applied Mathematics》 2017年第3期395-409,共15页
We develop a new evolutionary method of generating epsilon-efficient solutions of a continuous multiobjective programming problem. This is achieved by discretizing the problem and then using a genetic algorithm with s... We develop a new evolutionary method of generating epsilon-efficient solutions of a continuous multiobjective programming problem. This is achieved by discretizing the problem and then using a genetic algorithm with some derived probabilistic stopping criteria to obtain all minimal solutions for the discretized problem. We prove that these minimal solutions are the epsilon-optimal solutions to the original problem. We also present some computational examples illustrating the efficiency of our method. 展开更多
关键词 Vector Optimization APPROXIMATE solutions GENETIC algorithm STOPPING CRITERIA
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An Adaptive Genetic Algorithm for Multiprocessor Real-time Task Scheduling
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作者 李亚军 杨宇航 《Journal of Donghua University(English Edition)》 EI CAS 2009年第2期111-118,共8页
Real-time task scheduling is of primary significance in multiprocessor systems.Meeting deadlines and achieving high system utilization are the two main objectives of task scheduling in such systems.In this paper,we re... Real-time task scheduling is of primary significance in multiprocessor systems.Meeting deadlines and achieving high system utilization are the two main objectives of task scheduling in such systems.In this paper,we represent those two goals as the minimization of the average response time and the average task laxity.To achieve this,we propose a genetic-based algorithm with problem-specific and efficient genetic operators.Adaptive control parameters are also employed in our work to improve the genetic algorithms' efficiency.The simulation results show that our proposed algorithm outperforms its counterpart considerably by up to 36% and 35% in terms of the average response time and the average task laxity,respectively. 展开更多
关键词 SCHEDULING genetic algorithm real-time DEADLINE
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Sniffer Technique for Numerical Solution of Korteweg-de Vries Equation Using Genetic Algorithm
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作者 Dilip P. Ahalpara 《Journal of Applied Mathematics and Physics》 2015年第7期814-820,共7页
A novel heuristic technique has been developed for solving Ordinary Differential Equation (ODE) numerically under the framework of Genetic Algorithm (GA). The method incorporates a sniffer procedure that helps carry o... A novel heuristic technique has been developed for solving Ordinary Differential Equation (ODE) numerically under the framework of Genetic Algorithm (GA). The method incorporates a sniffer procedure that helps carry out a memetic search within the solution domain in the vicinity of the currently found best chromosome. The technique has been successfully applied to the Korteweg- de Vries (KdV) equation, a well-known nonlinear Partial Differential Equation (PDE). In the present study we consider its solution in the regime of solitary waves, or solitons that is first used to convert the PDE into an ODE. It is then shown that using the sniffer technique assisted GA procedure, numerical solution has successfully been generated quite efficiently for the one-dimensional ODE version of the KdV equation in space variable (x). The technique is quite promising for its applications to systems involving ODE equations where analytical solutions are not directly available. 展开更多
关键词 SNIFFER TECHNIQUE Genetic algorithm Numerical solution of ODE EVOLUTIONARY Computation
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