In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global c...In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported.展开更多
Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,...Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.展开更多
The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system.The increasingly large and complex natural ...The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system.The increasingly large and complex natural gas pipeline network requires more strictly on the calculation efficiency of transient simulation.To this end,this paper proposes a new method for the transient simulation of natural gas pipeline networks based on fracture-dimension-reduction algorithm.Firstly,a pipeline network model is abstracted into a station model,inter-station pipeline network model and connection node model.Secondlly,the pressure at the connection node connecting the station and the inter-station pipeline network is used as the basic variable to solve the general solution of the flow rate at the connection node,reconstruct the simulation model of the inter-station pipeline network,and reduce the equation set dimension of the inter-station pipeline network model.Thirdly,the transient simulation model of the natural gas pipeline network system is constructed based on the reconstructed simulation model of the inter-station pipeline network.Fnally,the calculation accuracy and efficiency of the proposed algorithm are compared and analyzed for the two working conditions of slow change of compressor speed and rapid shutdown of the compressor.And the following research results are obtained.First,the fracture-dimension-reduction algorithm has a high calculation accuracy,and the relative error of compressor outlet pressure and user pressure is less than 0.1%.Second,the calculation efficiency of the new fracture-dimension-reduction algorithm is high,and compared with the nonlinear equations solv ing method,the speed-up ratios under the two conditions are high up to 17.3 and 12.2 respectively.Third,the speed-up ratio of the fracture-dimension-reduction algorithm is linearly related to the equation set dimension of the transient simulation model of the pipeline network system.The larger the equation set dimension,the higher the speed-up ratio,which means the more complex the pipeline network model,the more remarkable the calculation speed-up effect.In conclusion,this new method improves the calculation speed while keeping the calculation accuracy,which is of great theoretical value and reference significance for improving the calculation efficiency of the transient simulation of complex natural gas pipeline network systems.展开更多
This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informat...This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.展开更多
A new method of model reduction combining the genetic algorithm（GA） with the Routh approximation method is presented. It is suggested that a high-order system can be approximated by a low-order model with a time del...A new method of model reduction combining the genetic algorithm（GA） with the Routh approximation method is presented. It is suggested that a high-order system can be approximated by a low-order model with a time delay. The denominator parameters of the reduced-order model are determined by the Routh approximation method, then the numerator parameters and time delay are identified by the GAL. The reduced-order models obtained by the proposed method will always be stable if the original system is stable and produce a good approximation to the original system in both the frequency domain and time domain. Two numerical examples show that the method is cornputationally simple and efficient.展开更多
In dealing with high-dimensional data, such as the global climate model, facial data analysis, human gene distribution and so on, the problem of dimensionality reduction is often encountered, that is, to find the low ...In dealing with high-dimensional data, such as the global climate model, facial data analysis, human gene distribution and so on, the problem of dimensionality reduction is often encountered, that is, to find the low dimensional structure hidden in high-dimensional data. Nonlinear dimensionality reduction facilitates the discovery of the intrinsic structure and relevance of the data and can make the high-dimensional data visible in the low dimension. The isometric mapping algorithm (Isomap) is an important algorithm for nonlinear dimensionality reduction, which originates from the traditional dimensionality reduction algorithm MDS. The MDS algorithm is based on maintaining the distance between the samples in the original space and the distance between the samples in the lower dimensional space;the distance used here is Euclidean distance, and the Isomap algorithm discards the Euclidean distance, and calculates the shortest path between samples by Floyd algorithm to approximate the geodesic distance along the manifold surface. Compared with the previous nonlinear dimensionality reduction algorithm, the Isomap algorithm can effectively compute a global optimal solution, and it can ensure that the data manifold converges to the real structure asymptotically.展开更多
The computation burden in the model-based predictive control algorithm is heavy when solving QR optimization with a limited sampling step, especially for a complicated system with large dimension. A fast algorithm is ...The computation burden in the model-based predictive control algorithm is heavy when solving QR optimization with a limited sampling step, especially for a complicated system with large dimension. A fast algorithm is proposed in this paper to solve this problem, in which real-time values are modulated to bit streams to simplify the multiplication. In addition, manipulated variables in the prediction horizon are deduced to the current control horizon approximately by a recursive relation to decrease the dimension of QR optimization. The simulation results demonstrate the feasibility of this fast algorithm for MIMO systems.展开更多
As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becomin...As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments.展开更多
在雷达通信一体化领域,设计出既能实现雷达探测功能又能实现通信信息传输功能的同波形信号是至关重要的一个环节。针对在雷达信号脉冲内对通信信息调制后自相关性能低的问题,提出一种高频带利用率以及低自相关旁瓣的基于非线性调频(NLFM...在雷达通信一体化领域,设计出既能实现雷达探测功能又能实现通信信息传输功能的同波形信号是至关重要的一个环节。针对在雷达信号脉冲内对通信信息调制后自相关性能低的问题,提出一种高频带利用率以及低自相关旁瓣的基于非线性调频(NLFM)信号的雷达通信一体化信号形式。将NLFM信号作为16阶正交幅度调制(16QAM)信号的载波,建立NLFM-16QAM雷达通信一体化信号模型,分析该信号的模糊函数以及相关的雷达与通信性能。在此基础上,针对所提出的NLFM-16QAM信号因其通信基带信号的随机性使雷达功能受到影响,从而降低了运动目标探测性能这一问题,将一体化系统的接收端作出改进,提出小波包降噪联合自然梯度算法对NLFM-16QAM信号进行接收处理。仿真结果表明,所提信号的频带利用率明显高于低阶调制的雷达通信一体化信号的频带利用率,在自相关性能方面,所提信号比16QAM-LFM信号的积分旁瓣比降低了23.07 d B,峰值旁瓣比降低了26.08 d B,NLFM-16QAM信号在经过改进接收端的联合算法处理后,运动目标的检测结果获得显著改善。展开更多
In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterat...In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterative processes, are obtained.展开更多
文摘In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported.
基金This work was supported by the National Natural Science Foundation of China(62073341)in part by the Natural Science Fund for Distinguished Young Scholars of Hunan Province(2019JJ20026).
文摘Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.
文摘The transient simulation technology of natural gas pipeline networks plays an increasingly prominent role in the scheduling management of natural gas pipeline network system.The increasingly large and complex natural gas pipeline network requires more strictly on the calculation efficiency of transient simulation.To this end,this paper proposes a new method for the transient simulation of natural gas pipeline networks based on fracture-dimension-reduction algorithm.Firstly,a pipeline network model is abstracted into a station model,inter-station pipeline network model and connection node model.Secondlly,the pressure at the connection node connecting the station and the inter-station pipeline network is used as the basic variable to solve the general solution of the flow rate at the connection node,reconstruct the simulation model of the inter-station pipeline network,and reduce the equation set dimension of the inter-station pipeline network model.Thirdly,the transient simulation model of the natural gas pipeline network system is constructed based on the reconstructed simulation model of the inter-station pipeline network.Fnally,the calculation accuracy and efficiency of the proposed algorithm are compared and analyzed for the two working conditions of slow change of compressor speed and rapid shutdown of the compressor.And the following research results are obtained.First,the fracture-dimension-reduction algorithm has a high calculation accuracy,and the relative error of compressor outlet pressure and user pressure is less than 0.1%.Second,the calculation efficiency of the new fracture-dimension-reduction algorithm is high,and compared with the nonlinear equations solv ing method,the speed-up ratios under the two conditions are high up to 17.3 and 12.2 respectively.Third,the speed-up ratio of the fracture-dimension-reduction algorithm is linearly related to the equation set dimension of the transient simulation model of the pipeline network system.The larger the equation set dimension,the higher the speed-up ratio,which means the more complex the pipeline network model,the more remarkable the calculation speed-up effect.In conclusion,this new method improves the calculation speed while keeping the calculation accuracy,which is of great theoretical value and reference significance for improving the calculation efficiency of the transient simulation of complex natural gas pipeline network systems.
基金supported in part by the National Natural Science Foundation of China(72171172,62088101)in part by the Shanghai Science and Technology Major Special Project of Shanghai Development and Reform Commission(2021SHZDZX0100)+2 种基金in part by the Shanghai Commission of Science and Technology(19511132100,19511132101)in part by the China Scholarship Councilin part by the Deanship of Scientific Research(DSR)at King Abdulaziz University(KAU),Jeddah,Saudi Arabia(FP-146-43)。
文摘This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.
文摘A new method of model reduction combining the genetic algorithm（GA） with the Routh approximation method is presented. It is suggested that a high-order system can be approximated by a low-order model with a time delay. The denominator parameters of the reduced-order model are determined by the Routh approximation method, then the numerator parameters and time delay are identified by the GAL. The reduced-order models obtained by the proposed method will always be stable if the original system is stable and produce a good approximation to the original system in both the frequency domain and time domain. Two numerical examples show that the method is cornputationally simple and efficient.
文摘In dealing with high-dimensional data, such as the global climate model, facial data analysis, human gene distribution and so on, the problem of dimensionality reduction is often encountered, that is, to find the low dimensional structure hidden in high-dimensional data. Nonlinear dimensionality reduction facilitates the discovery of the intrinsic structure and relevance of the data and can make the high-dimensional data visible in the low dimension. The isometric mapping algorithm (Isomap) is an important algorithm for nonlinear dimensionality reduction, which originates from the traditional dimensionality reduction algorithm MDS. The MDS algorithm is based on maintaining the distance between the samples in the original space and the distance between the samples in the lower dimensional space;the distance used here is Euclidean distance, and the Isomap algorithm discards the Euclidean distance, and calculates the shortest path between samples by Floyd algorithm to approximate the geodesic distance along the manifold surface. Compared with the previous nonlinear dimensionality reduction algorithm, the Isomap algorithm can effectively compute a global optimal solution, and it can ensure that the data manifold converges to the real structure asymptotically.
基金Supported by the National Natural Science Foundation of China(61333010,61203157)the Fundamental Research Funds for the Central Universities+2 种基金the National High-Tech Research and Development Program of China(2013AA040701)Shanghai Natural Science Foundation Project(15ZR1408900)Shanghai Key Technologies R&D Program Project(13111103800)
文摘The computation burden in the model-based predictive control algorithm is heavy when solving QR optimization with a limited sampling step, especially for a complicated system with large dimension. A fast algorithm is proposed in this paper to solve this problem, in which real-time values are modulated to bit streams to simplify the multiplication. In addition, manipulated variables in the prediction horizon are deduced to the current control horizon approximately by a recursive relation to decrease the dimension of QR optimization. The simulation results demonstrate the feasibility of this fast algorithm for MIMO systems.
文摘As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments.
文摘在雷达通信一体化领域,设计出既能实现雷达探测功能又能实现通信信息传输功能的同波形信号是至关重要的一个环节。针对在雷达信号脉冲内对通信信息调制后自相关性能低的问题,提出一种高频带利用率以及低自相关旁瓣的基于非线性调频(NLFM)信号的雷达通信一体化信号形式。将NLFM信号作为16阶正交幅度调制(16QAM)信号的载波,建立NLFM-16QAM雷达通信一体化信号模型,分析该信号的模糊函数以及相关的雷达与通信性能。在此基础上,针对所提出的NLFM-16QAM信号因其通信基带信号的随机性使雷达功能受到影响,从而降低了运动目标探测性能这一问题,将一体化系统的接收端作出改进,提出小波包降噪联合自然梯度算法对NLFM-16QAM信号进行接收处理。仿真结果表明,所提信号的频带利用率明显高于低阶调制的雷达通信一体化信号的频带利用率,在自相关性能方面,所提信号比16QAM-LFM信号的积分旁瓣比降低了23.07 d B,峰值旁瓣比降低了26.08 d B,NLFM-16QAM信号在经过改进接收端的联合算法处理后,运动目标的检测结果获得显著改善。
文摘In this paper a new approach to construction of iterative methods of bilateral approximations of eigenvalue is proposed and investigated. The conditions on initial approximation, which ensure the convergence of iterative processes, are obtained.
