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
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
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
Data-driven surrogate models that assist with efficient evolutionary algorithms to find the optimal development scheme have been widely used to solve reservoir production optimization problems.However,existing researc...Data-driven surrogate models that assist with efficient evolutionary algorithms to find the optimal development scheme have been widely used to solve reservoir production optimization problems.However,existing research suggests that the effectiveness of a surrogate model can vary depending on the complexity of the design problem.A surrogate model that has demonstrated success in one scenario may not perform as well in others.In the absence of prior knowledge,finding a promising surrogate model that performs well for an unknown reservoir is challenging.Moreover,the optimization process often relies on a single evolutionary algorithm,which can yield varying results across different cases.To address these limitations,this paper introduces a novel approach called the multi-surrogate framework with an adaptive selection mechanism(MSFASM)to tackle production optimization problems.MSFASM consists of two stages.In the first stage,a reduced-dimensional broad learning system(BLS)is used to adaptively select the evolutionary algorithm with the best performance during the current optimization period.In the second stage,the multi-objective algorithm,non-dominated sorting genetic algorithm II(NSGA-II),is used as an optimizer to find a set of Pareto solutions with good performance on multiple surrogate models.A novel optimal point criterion is utilized in this stage to select the Pareto solutions,thereby obtaining the desired development schemes without increasing the computational load of the numerical simulator.The two stages are combined using sequential transfer learning.From the two most important perspectives of an evolutionary algorithm and a surrogate model,the proposed method improves adaptability to optimization problems of various reservoir types.To verify the effectiveness of the proposed method,four 100-dimensional benchmark functions and two reservoir models are tested,and the results are compared with those obtained by six other surrogate-model-based methods.The results demonstrate that our approach can obtain the maximum net present value(NPV)of the target production optimization problems.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.
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.
基金This work is supported by the National Natural Science Foundation of China under Grant 52274057,52074340 and 51874335the Major Scientific and Technological Projects of CNPC under Grant ZD2019-183-008+2 种基金the Major Scientific and Technological Projects of CNOOC under Grant CCL2022RCPS0397RSNthe Science and Technology Support Plan for Youth Innovation of University in Shandong Province under Grant 2019KJH002111 Project under Grant B08028.
文摘Data-driven surrogate models that assist with efficient evolutionary algorithms to find the optimal development scheme have been widely used to solve reservoir production optimization problems.However,existing research suggests that the effectiveness of a surrogate model can vary depending on the complexity of the design problem.A surrogate model that has demonstrated success in one scenario may not perform as well in others.In the absence of prior knowledge,finding a promising surrogate model that performs well for an unknown reservoir is challenging.Moreover,the optimization process often relies on a single evolutionary algorithm,which can yield varying results across different cases.To address these limitations,this paper introduces a novel approach called the multi-surrogate framework with an adaptive selection mechanism(MSFASM)to tackle production optimization problems.MSFASM consists of two stages.In the first stage,a reduced-dimensional broad learning system(BLS)is used to adaptively select the evolutionary algorithm with the best performance during the current optimization period.In the second stage,the multi-objective algorithm,non-dominated sorting genetic algorithm II(NSGA-II),is used as an optimizer to find a set of Pareto solutions with good performance on multiple surrogate models.A novel optimal point criterion is utilized in this stage to select the Pareto solutions,thereby obtaining the desired development schemes without increasing the computational load of the numerical simulator.The two stages are combined using sequential transfer learning.From the two most important perspectives of an evolutionary algorithm and a surrogate model,the proposed method improves adaptability to optimization problems of various reservoir types.To verify the effectiveness of the proposed method,four 100-dimensional benchmark functions and two reservoir models are tested,and the results are compared with those obtained by six other surrogate-model-based methods.The results demonstrate that our approach can obtain the maximum net present value(NPV)of the target production optimization problems.
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.
