This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to ...This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.展开更多
An improved genetic algorithm and its application to resolve cutting stock problem arc presented. It is common to apply simple genetic algorithm (SGA) to cutting stock problem, but the huge amount of computing of SG...An improved genetic algorithm and its application to resolve cutting stock problem arc presented. It is common to apply simple genetic algorithm (SGA) to cutting stock problem, but the huge amount of computing of SGA is a serious problem in practical application. Accelerating genetic algorithm (AGA) based on integer coding and AGA's detailed steps are developed to reduce the amount of computation, and a new kind of rectangular parts blank layout algorithm is designed for rectangular cutting stock problem. SGA is adopted to produce individuals within given evolution process, and the variation interval of these individuals is taken as initial domain of the next optimization process, thus shrinks searching range intensively and accelerates the evaluation process of SGA. To enhance the diversity of population and to avoid the algorithm stagnates at local optimization result, fixed number of individuals are produced randomly and replace the same number of parents in every evaluation process. According to the computational experiment, it is observed that this improved GA converges much sooner than SGA, and is able to get the balance of good result and high efficiency in the process of optimization for rectangular cutting stock problem.展开更多
In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on p...In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.展开更多
The dynamic finite element model (FEM) of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing (AVT) using a...The dynamic finite element model (FEM) of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing (AVT) using a real-coded accelerating genetic algorithm (RAGA). The objective functions are defined based on natural frequency and modal assurance criterion (MAC) metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge .展开更多
Combining real accelerating genetic algorithm(RAGA) with the optimization design of multi-hole and varied diameter pipe, the authors solved the problem of optimizing multi-dimensional parameters at the same time. In w...Combining real accelerating genetic algorithm(RAGA) with the optimization design of multi-hole and varied diameter pipe, the authors solved the problem of optimizing multi-dimensional parameters at the same time. In which the advanced convergence and easily to run into partial optimization were avoid. Applied the RAGA to solving the problem in the optimization design of fixed piping sprinkler irrigation system. The optimized parameters, such as diameters and the length of pipe were calculated and the result was reasonable, which provides as a reference to readers who work at related research.展开更多
In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCA...In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous results.Then,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization capability.Finally,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.展开更多
In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over un...In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.展开更多
Gradient descent(GD)algorithm is the widely used optimisation method in training machine learning and deep learning models.In this paper,based on GD,Polyak’s momentum(PM),and Nesterov accelerated gradient(NAG),we giv...Gradient descent(GD)algorithm is the widely used optimisation method in training machine learning and deep learning models.In this paper,based on GD,Polyak’s momentum(PM),and Nesterov accelerated gradient(NAG),we give the convergence of the algorithms from an ini-tial value to the optimal value of an objective function in simple quadratic form.Based on the convergence property of the quadratic function,two sister sequences of NAG’s iteration and par-allel tangent methods in neural networks,the three-step accelerated gradient(TAG)algorithm is proposed,which has three sequences other than two sister sequences.To illustrate the perfor-mance of this algorithm,we compare the proposed algorithm with the three other algorithms in quadratic function,high-dimensional quadratic functions,and nonquadratic function.Then we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep learning.For conveniently facilitate the proposed algorithms,we rewite the R package‘neuralnet’and extend it to‘supneuralnet’.All kinds of deep learning algorithms in this paper are included in‘supneuralnet’package.Finally,we show our algorithms are superior to other algorithms in four case studies.展开更多
The Hankel transform is widely used to solve various engineering and physics problems,such as the representation of electromagnetic field components in the medium,the representation of dynamic stress intensity factors...The Hankel transform is widely used to solve various engineering and physics problems,such as the representation of electromagnetic field components in the medium,the representation of dynamic stress intensity factors,vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of integration.However,traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function,so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integral of high oscillation.In this paper,the improved Gaver-Stehfest(G-S)inverse Laplace transform method for arbitrary real-order Bessel function integration is presented by using the asymptotic characteristics of the Bessel function and the accumulation of integration,and the optimized G-S coefficients are given.The effectiveness of the algorithm is verified by numerical examples.Compared with the linear transformation accelerated convergence algorithm,it shows that the G-S inverse Laplace transform method is suitable for arbitrary real order Hankel transform,and the time consumption is relatively stable and short,which provides a reliable calculation method for the study of electromagnetic mechanics,wave propagation,and fracture dynamics.展开更多
This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(M...This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(MILP)are popular approaches to solving TCUC.However,with many binary unit commitment variables,LR suffers from slow convergence and MILP presents heavy computation burden.The proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems.A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible(ASF)approaches,which is then leveraged to efficiently solve new TCUC instances online.On/off statuses of considerable units can be fixed in the online calculation according to the database,which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances.A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables,which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure changes.Numerical tests illustrate the efficiency of the proposed approach.展开更多
With rapid developments in platforms and sensors technology in terms of digital cameras and video recordings,crowd monitoring has taken a considerable attentions in many disciplines such as psychology,sociology,engine...With rapid developments in platforms and sensors technology in terms of digital cameras and video recordings,crowd monitoring has taken a considerable attentions in many disciplines such as psychology,sociology,engineering,and computer vision.This is due to the fact that,monitoring of the crowd is necessary to enhance safety and controllable movements to minimize the risk particularly in highly crowded incidents(e.g.sports).One of the platforms that have been extensively employed in crowd monitoring is unmanned aerial vehicles(UAVs),because UAVs have the capability to acquiring fast,low costs,high-resolution and real-time images over crowd areas.In addition,geo-referenced images can also be provided through integration of on-board positioning sensors(e.g.GPS/IMU)with vision sensors(digital cameras and laser scanner).In this paper,a new testing procedure based on feature from accelerated segment test(FAST)algorithms is introduced to detect the crowd features from UAV images taken from different camera orientations and positions.The proposed test started with converting a circle of 16 pixels surrounding the center pixel into a vector and sorting it in ascending/descending order.A single pixel which takes the ranking number 9(for FAST-9)or 12(for FAST-12)was then compared with the center pixel.Accuracy assessment in terms of completeness and correctness was used to assess the performance of the new testing procedure before and after filtering the crowd features.The results show that the proposed algorithms are able to extract crowd features from different UAV images.Overall,the values of Completeness range from 55 to 70%whereas the range of correctness values was 91 to 94%.展开更多
We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with ...We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.展开更多
基金Supported by Natural Science Foundation of Shanghai(14ZR1429200)National Science Foundation of China(11171221)+4 种基金Shanghai Leading Academic Discipline Project(XTKX2012)Innovation Program of Shanghai Municipal Education Commission(14YZ094)Doctoral Program Foundation of Institutions of Higher Educationof China(20123120110004)Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)Young Teacher Training Projection Program of Shanghai for Science and Technology
文摘This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.
基金This project is supported by National Natural Science Foundation of China (No.50575153)Provincial Key Technology Projects of Sichuan, China (No.03GG010-002)
文摘An improved genetic algorithm and its application to resolve cutting stock problem arc presented. It is common to apply simple genetic algorithm (SGA) to cutting stock problem, but the huge amount of computing of SGA is a serious problem in practical application. Accelerating genetic algorithm (AGA) based on integer coding and AGA's detailed steps are developed to reduce the amount of computation, and a new kind of rectangular parts blank layout algorithm is designed for rectangular cutting stock problem. SGA is adopted to produce individuals within given evolution process, and the variation interval of these individuals is taken as initial domain of the next optimization process, thus shrinks searching range intensively and accelerates the evaluation process of SGA. To enhance the diversity of population and to avoid the algorithm stagnates at local optimization result, fixed number of individuals are produced randomly and replace the same number of parents in every evaluation process. According to the computational experiment, it is observed that this improved GA converges much sooner than SGA, and is able to get the balance of good result and high efficiency in the process of optimization for rectangular cutting stock problem.
文摘In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion problems.In our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor set.Moreover,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational cost.Meanwhile,the convergence of the new algorithm is discussed under some reasonable conditions.Finally,the numerical experiments show the effectiveness of the proposed algorithm.
基金National Natural Science Foundation of China Under Grant No.50575101Transportation Science Research Item of Jiangsu Province Under Grant No.06Y20
文摘The dynamic finite element model (FEM) of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing (AVT) using a real-coded accelerating genetic algorithm (RAGA). The objective functions are defined based on natural frequency and modal assurance criterion (MAC) metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge .
文摘Combining real accelerating genetic algorithm(RAGA) with the optimization design of multi-hole and varied diameter pipe, the authors solved the problem of optimizing multi-dimensional parameters at the same time. In which the advanced convergence and easily to run into partial optimization were avoid. Applied the RAGA to solving the problem in the optimization design of fixed piping sprinkler irrigation system. The optimized parameters, such as diameters and the length of pipe were calculated and the result was reasonable, which provides as a reference to readers who work at related research.
基金supported by the Major Program of National Natural Science Foundation of China(Grant Nos.11991020 and 11991024)the Team Project of Innovation Leading Talent in Chongqing(Grant No.CQYC20210309536)+1 种基金NSFC-RGC(Hong Kong)Joint Research Program(Grant No.12261160365)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202300528)。
文摘In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous results.Then,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization capability.Finally,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.
基金supported by the National Natural Science Foundation of China (Grant Nos. 91748112,61991403,61991404,and 61991400)。
文摘In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents' local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation(ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.
基金This work was supported by National Natural Science Foun-dation of China(11271136,81530086)Program of Shanghai Subject Chief Scientist(14XD1401600)the 111 Project of China(No.B14019).
文摘Gradient descent(GD)algorithm is the widely used optimisation method in training machine learning and deep learning models.In this paper,based on GD,Polyak’s momentum(PM),and Nesterov accelerated gradient(NAG),we give the convergence of the algorithms from an ini-tial value to the optimal value of an objective function in simple quadratic form.Based on the convergence property of the quadratic function,two sister sequences of NAG’s iteration and par-allel tangent methods in neural networks,the three-step accelerated gradient(TAG)algorithm is proposed,which has three sequences other than two sister sequences.To illustrate the perfor-mance of this algorithm,we compare the proposed algorithm with the three other algorithms in quadratic function,high-dimensional quadratic functions,and nonquadratic function.Then we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep learning.For conveniently facilitate the proposed algorithms,we rewite the R package‘neuralnet’and extend it to‘supneuralnet’.All kinds of deep learning algorithms in this paper are included in‘supneuralnet’package.Finally,we show our algorithms are superior to other algorithms in four case studies.
基金Supported by the National Natural Science Foundation of China(42064004,12062022,11762017,11762016)
文摘The Hankel transform is widely used to solve various engineering and physics problems,such as the representation of electromagnetic field components in the medium,the representation of dynamic stress intensity factors,vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of integration.However,traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function,so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integral of high oscillation.In this paper,the improved Gaver-Stehfest(G-S)inverse Laplace transform method for arbitrary real-order Bessel function integration is presented by using the asymptotic characteristics of the Bessel function and the accumulation of integration,and the optimized G-S coefficients are given.The effectiveness of the algorithm is verified by numerical examples.Compared with the linear transformation accelerated convergence algorithm,it shows that the G-S inverse Laplace transform method is suitable for arbitrary real order Hankel transform,and the time consumption is relatively stable and short,which provides a reliable calculation method for the study of electromagnetic mechanics,wave propagation,and fracture dynamics.
基金supported in part by the National Natural Science Foundation of China(No.61773309)。
文摘This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment(TCUC).Lagrangian relaxation(LR)and mixed-integer linear programming(MILP)are popular approaches to solving TCUC.However,with many binary unit commitment variables,LR suffers from slow convergence and MILP presents heavy computation burden.The proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems.A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible(ASF)approaches,which is then leveraged to efficiently solve new TCUC instances online.On/off statuses of considerable units can be fixed in the online calculation according to the database,which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances.A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables,which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure changes.Numerical tests illustrate the efficiency of the proposed approach.
文摘With rapid developments in platforms and sensors technology in terms of digital cameras and video recordings,crowd monitoring has taken a considerable attentions in many disciplines such as psychology,sociology,engineering,and computer vision.This is due to the fact that,monitoring of the crowd is necessary to enhance safety and controllable movements to minimize the risk particularly in highly crowded incidents(e.g.sports).One of the platforms that have been extensively employed in crowd monitoring is unmanned aerial vehicles(UAVs),because UAVs have the capability to acquiring fast,low costs,high-resolution and real-time images over crowd areas.In addition,geo-referenced images can also be provided through integration of on-board positioning sensors(e.g.GPS/IMU)with vision sensors(digital cameras and laser scanner).In this paper,a new testing procedure based on feature from accelerated segment test(FAST)algorithms is introduced to detect the crowd features from UAV images taken from different camera orientations and positions.The proposed test started with converting a circle of 16 pixels surrounding the center pixel into a vector and sorting it in ascending/descending order.A single pixel which takes the ranking number 9(for FAST-9)or 12(for FAST-12)was then compared with the center pixel.Accuracy assessment in terms of completeness and correctness was used to assess the performance of the new testing procedure before and after filtering the crowd features.The results show that the proposed algorithms are able to extract crowd features from different UAV images.Overall,the values of Completeness range from 55 to 70%whereas the range of correctness values was 91 to 94%.
基金supported financially by the National Science and Engineering Research Council of Canada(NSERC).
文摘We present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations.The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations.To benchmark accuracy and performance,we compare simulation results with those generated from a previously validated population dynamics algorithm.The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions.Considering the increasing complexity of cell population models,the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient,coarse-grained exploration of parameter space.