Identifying the unknown geometric and material information of a multi-shield object by analyzing the radiation signature measurements is always an important problem in national and global security. In order to identif...Identifying the unknown geometric and material information of a multi-shield object by analyzing the radiation signature measurements is always an important problem in national and global security. In order to identify the unknown shielding layer thicknesses of a source/shield system with gamma-ray spectra, we have developed a derivative-free inverse radiation transport model based on a differential evolution algorithm with global and local neighbourhoods(IRT-DEGL). In the present paper, the IRT-DEGL model is further extended for estimating the unknown thicknesses with random initial guesses and material mass densities of multi-shielding layers as well as their combinations. Using the detected gamma-ray spectra,the illustration of inverse studies is implemented and the main influence factors for inverse results are also analyzed.展开更多
This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of conver...This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of convergence. We also establish the connection of derivative-free and derivative presence three-point iterations. The use of the sufficient convergence conditions allows us to design wide class of optimal derivative-free iterations. The proposed family of iterations includes not only existing methods but also new methods with a higher order of convergence.展开更多
The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some conditions.The authors propose the derivative-free optimization algorithm S...The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some conditions.The authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration step.They analyze the optimization dynamics and convergence of the algorithm SUSD-TR.Details of the trial step and structure step are given.Numerical results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD direction.Their algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.展开更多
Reinforcement learning is about learning agent models that make the best sequential decisions in unknown environments.In an unknown environment,the agent needs to explore the environment while exploiting the collected...Reinforcement learning is about learning agent models that make the best sequential decisions in unknown environments.In an unknown environment,the agent needs to explore the environment while exploiting the collected information,which usually forms a sophisticated problem to solve.Derivative-free optimization,meanwhile,is capable of solving sophisticated problems.It commonly uses a sampling-andupdating framework to iteratively improve the solution,where exploration and exploitation are also needed to be well balanced.Therefore,derivative-free optimization deals with a similar core issue as reinforcement learning,and has been introduced in reinforcement learning approaches,under the names of learning classifier systems and neuroevolution/evolutionary reinforcement learning.Although such methods have been developed for decades,recently,derivative-free reinforcement learning exhibits attracting increasing attention.However,recent survey on this topic is still lacking.In this article,we summarize methods of derivative-free reinforcement learning to date,and organize the methods in aspects including parameter updating,model selection,exploration,and parallel/distributed methods.Moreover,we discuss some current limitations and possible future directions,hoping that this article could bring more attentions to this topic and serve as a catalyst for developing novel and efficient approaches.展开更多
A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential,designing a field development plan,and making investment decisions.However,quantitative analysis ca...A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential,designing a field development plan,and making investment decisions.However,quantitative analysis can be challenging because production performance is dominated by the complex interaction among a series of geological and engineering factors.In fact,each factor can be viewed as a player who makes cooperative contributions to the production payoff within the constraints of physical laws and models.Inspired by the idea,we propose a hybrid data-driven analysis framework in this study,where the contributions of dominant factors are quantitatively evaluated,the productions are precisely forecasted,and the development optimization suggestions are comprehensively generated.More specifically,game theory and machine learning models are coupled to determine the dominating geological and engineering factors.The Shapley value with definite physical meaning is employed to quantitatively measure the effects of individual factors.A multi-model-fused stacked model is trained for production forecast,which provides the basis for derivative-free optimization algorithms to optimize the development plan.The complete workflow is validated with actual production data collected from the Fuling shale gas field,Sichuan Basin,China.The validation results show that the proposed procedure can draw rigorous conclusions with quantified evidence and thereby provide specific and reliable suggestions for development plan optimization.Comparing with traditional and experience-based approaches,the hybrid data-driven procedure is advanced in terms of both efficiency and accuracy.展开更多
Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, econ...Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we introduced an integer m in the algorithm which controls the number of steps of iteration update. We mean along the descent direction to allow the algorithm to?go ahead m steps at most to explore whether we can get better solution further. The experiment proved the strategy’s efficiency.展开更多
Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactio...Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactions, traditionally modeled by the deterministic reaction rate equations. In the cellular environment, many biological processes are inherently stochastic. The stochastic fluctuations due to the presence of some low molecular populations may have a great impact on the biochemical system behavior. Then, stochastic models are required for an accurate description of the system dynamics. An important stochastic model of biochemical kinetics is the Chemical Langevin Equation. In this work, we provide a numerical method for approximating the solution of the Chemical Langevin Equation, namely the derivative-free Milstein scheme. The method is compared with the widely used strategy for this class of problems, the Milstein method. As opposed to the Milstein scheme, the proposed strategy has the advantage that it does not require the calculation of exact derivatives, while having the same strong order of accuracy as the Milstein scheme. Therefore it may be used for an automatic simulation of the numerical solution of the Chemical Langevin Equation. The tests on several models of practical interest show that our method performs very well.展开更多
Channel knowledge map(CKM)has recently emerged as a viable new solution to facilitate the placement and trajectory optimization for unmanned aerial vehicle(UAV)communications,by exploiting the siteand location-specifi...Channel knowledge map(CKM)has recently emerged as a viable new solution to facilitate the placement and trajectory optimization for unmanned aerial vehicle(UAV)communications,by exploiting the siteand location-specific radio propagation information.This paper investigates a CKM-assisted multi-UAV wireless network,by focusing on the construction and utilization of CKMs for multi-UAV placement optimization.First,we consider the CKM construction problem when data measurements for only a limited number of points are available.Towards this end,we exploit a data-driven interpolation technique,namely the Kriging method,to construct CKMs to characterize the signal propagation environments.Next,we study the multi-UAV placement optimization problem by utilizing the constructed CKMs,in which the multiple UAVs aim to optimize their placement locations to maximize the weighted sum rate with their respectively associated ground base stations(GBSs).However,the weighted sum rate function based on the CKMs is generally non-differentiable,which renders the conventional optimization techniques relying on function derivatives inapplicable.To tackle this issue,we propose a novel iterative algorithm based on derivative-free optimization,in which a series of quadratic functions are iteratively constructed to approximate the objective function under a set of interpolation conditions,and accordingly,the UAVs’placement locations are updated by maximizing the approximate function subject to a trust region constraint.Finally,numerical results are presented to validate the performance of the proposed designs.It is shown that the Kriging method can construct accurate CKMs for UAVs.Furthermore,the proposed derivative-free placement optimization design based on the Kriging-constructed CKMs achieves a weighted sum rate that is close to the optimal exhaustive search design based on ground-truth CKMs,but with much lower implementation complexity.In addition,the proposed design is shown to significantly outperform other benchmark schemes.展开更多
Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for shor...Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11605163 and 21504085)the China Academy of Engineering Physics Foundation for Development of Science and Technology(No.201580103014 and No.2015B0301063)+1 种基金the Foundation for Special Talents in China Academy of Engineering Physics(No.TP201502-3)the Sichuan Science and Technology Development Foundation for Young Scientists(No.2017Q0050)
文摘Identifying the unknown geometric and material information of a multi-shield object by analyzing the radiation signature measurements is always an important problem in national and global security. In order to identify the unknown shielding layer thicknesses of a source/shield system with gamma-ray spectra, we have developed a derivative-free inverse radiation transport model based on a differential evolution algorithm with global and local neighbourhoods(IRT-DEGL). In the present paper, the IRT-DEGL model is further extended for estimating the unknown thicknesses with random initial guesses and material mass densities of multi-shielding layers as well as their combinations. Using the detected gamma-ray spectra,the illustration of inverse studies is implemented and the main influence factors for inverse results are also analyzed.
文摘This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of convergence. We also establish the connection of derivative-free and derivative presence three-point iterations. The use of the sufficient convergence conditions allows us to design wide class of optimal derivative-free iterations. The proposed family of iterations includes not only existing methods but also new methods with a higher order of convergence.
基金Supported by Guizhou Provincial Department of Education’s Higher Education Scientific Research Project(No.[2022]172)Guizhou Province Science and Technology Plan Project(No.ZK[2022]General022)Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(No.2023013)。
基金supported by the National Natural Science Foundation of China(No.12288201)。
文摘The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some conditions.The authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration step.They analyze the optimization dynamics and convergence of the algorithm SUSD-TR.Details of the trial step and structure step are given.Numerical results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD direction.Their algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
基金This work was supported by the Program A for Outstanding PhD Candidate of Nanjing University,National Science Foundation of China(61876077)Jiangsu Science Foundation(BK20170013)Collaborative Innovation Center of Novel Software Technology and Industrialization.
文摘Reinforcement learning is about learning agent models that make the best sequential decisions in unknown environments.In an unknown environment,the agent needs to explore the environment while exploiting the collected information,which usually forms a sophisticated problem to solve.Derivative-free optimization,meanwhile,is capable of solving sophisticated problems.It commonly uses a sampling-andupdating framework to iteratively improve the solution,where exploration and exploitation are also needed to be well balanced.Therefore,derivative-free optimization deals with a similar core issue as reinforcement learning,and has been introduced in reinforcement learning approaches,under the names of learning classifier systems and neuroevolution/evolutionary reinforcement learning.Although such methods have been developed for decades,recently,derivative-free reinforcement learning exhibits attracting increasing attention.However,recent survey on this topic is still lacking.In this article,we summarize methods of derivative-free reinforcement learning to date,and organize the methods in aspects including parameter updating,model selection,exploration,and parallel/distributed methods.Moreover,we discuss some current limitations and possible future directions,hoping that this article could bring more attentions to this topic and serve as a catalyst for developing novel and efficient approaches.
基金This work was supported by the National Natural Science Foundation of China(Grant No.42050104)the Science Foundation of SINOPEC Group(Grant No.P20030).
文摘A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential,designing a field development plan,and making investment decisions.However,quantitative analysis can be challenging because production performance is dominated by the complex interaction among a series of geological and engineering factors.In fact,each factor can be viewed as a player who makes cooperative contributions to the production payoff within the constraints of physical laws and models.Inspired by the idea,we propose a hybrid data-driven analysis framework in this study,where the contributions of dominant factors are quantitatively evaluated,the productions are precisely forecasted,and the development optimization suggestions are comprehensively generated.More specifically,game theory and machine learning models are coupled to determine the dominating geological and engineering factors.The Shapley value with definite physical meaning is employed to quantitatively measure the effects of individual factors.A multi-model-fused stacked model is trained for production forecast,which provides the basis for derivative-free optimization algorithms to optimize the development plan.The complete workflow is validated with actual production data collected from the Fuling shale gas field,Sichuan Basin,China.The validation results show that the proposed procedure can draw rigorous conclusions with quantified evidence and thereby provide specific and reliable suggestions for development plan optimization.Comparing with traditional and experience-based approaches,the hybrid data-driven procedure is advanced in terms of both efficiency and accuracy.
文摘Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we introduced an integer m in the algorithm which controls the number of steps of iteration update. We mean along the descent direction to allow the algorithm to?go ahead m steps at most to explore whether we can get better solution further. The experiment proved the strategy’s efficiency.
文摘Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactions, traditionally modeled by the deterministic reaction rate equations. In the cellular environment, many biological processes are inherently stochastic. The stochastic fluctuations due to the presence of some low molecular populations may have a great impact on the biochemical system behavior. Then, stochastic models are required for an accurate description of the system dynamics. An important stochastic model of biochemical kinetics is the Chemical Langevin Equation. In this work, we provide a numerical method for approximating the solution of the Chemical Langevin Equation, namely the derivative-free Milstein scheme. The method is compared with the widely used strategy for this class of problems, the Milstein method. As opposed to the Milstein scheme, the proposed strategy has the advantage that it does not require the calculation of exact derivatives, while having the same strong order of accuracy as the Milstein scheme. Therefore it may be used for an automatic simulation of the numerical solution of the Chemical Langevin Equation. The tests on several models of practical interest show that our method performs very well.
基金The work was supported in part by the National Natural Science Foundation of China under Grant U2001208the Basic Research Project No.HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone,the National Natural Science Foundation of China under Grant 92267202,Shenzhen Fundamental Research Program under Grant JCYJ20210324133405015+5 种基金Guangdong Provincial Key Laboratory of Future Networks of Intelligence under Grant 2022B1212010001,the National Key R&D Program of China under Grant 2018YFB1800800the Shenzhen Key Laboratory of Big Data and Artificial Intelligence under Grant ZDSYS201707251409055the Key Area R&D Program of Guangdong Province under Grant 2018B030338001the National Science Foundation of China under Grant of 62171398Guangdong Research Projects under Grants 2019QN01X895,2017ZT07X152,and 2019CX01X104,Shenzhen Outstanding Talents Training Fund 202002he Natural Science Foundation of China under Grant 62071114.
文摘Channel knowledge map(CKM)has recently emerged as a viable new solution to facilitate the placement and trajectory optimization for unmanned aerial vehicle(UAV)communications,by exploiting the siteand location-specific radio propagation information.This paper investigates a CKM-assisted multi-UAV wireless network,by focusing on the construction and utilization of CKMs for multi-UAV placement optimization.First,we consider the CKM construction problem when data measurements for only a limited number of points are available.Towards this end,we exploit a data-driven interpolation technique,namely the Kriging method,to construct CKMs to characterize the signal propagation environments.Next,we study the multi-UAV placement optimization problem by utilizing the constructed CKMs,in which the multiple UAVs aim to optimize their placement locations to maximize the weighted sum rate with their respectively associated ground base stations(GBSs).However,the weighted sum rate function based on the CKMs is generally non-differentiable,which renders the conventional optimization techniques relying on function derivatives inapplicable.To tackle this issue,we propose a novel iterative algorithm based on derivative-free optimization,in which a series of quadratic functions are iteratively constructed to approximate the objective function under a set of interpolation conditions,and accordingly,the UAVs’placement locations are updated by maximizing the approximate function subject to a trust region constraint.Finally,numerical results are presented to validate the performance of the proposed designs.It is shown that the Kriging method can construct accurate CKMs for UAVs.Furthermore,the proposed derivative-free placement optimization design based on the Kriging-constructed CKMs achieves a weighted sum rate that is close to the optimal exhaustive search design based on ground-truth CKMs,but with much lower implementation complexity.In addition,the proposed design is shown to significantly outperform other benchmark schemes.
基金the National Natural Science Foundation of China
文摘Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.
