In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained...In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.展开更多
City cluster is an effective platform for encouraging regionally coordinated development.Coordinated reduction of carbon emissions within city cluster via the spatial association network between cities can help coordi...City cluster is an effective platform for encouraging regionally coordinated development.Coordinated reduction of carbon emissions within city cluster via the spatial association network between cities can help coordinate the regional carbon emission management,realize sustainable development,and assist China in achieving the carbon peaking and carbon neutrality goals.This paper applies the improved gravity model and social network analysis(SNA)to the study of spatial correlation of carbon emissions in city clusters and analyzes the structural characteristics of the spatial correlation network of carbon emissions in the Yangtze River Delta(YRD)city cluster in China and its influencing factors.The results demonstrate that:1)the spatial association of carbon emissions in the YRD city cluster exhibits a typical and complex multi-threaded network structure.The network association number and density show an upward trend,indicating closer spatial association between cities,but their values remain generally low.Meanwhile,the network hierarchy and network efficiency show a downward trend but remain high.2)The spatial association network of carbon emissions in the YRD city cluster shows an obvious‘core-edge’distribution pattern.The network is centered around Shanghai,Suzhou and Wuxi,all of which play the role of‘bridges’,while cities such as Zhoushan,Ma'anshan,Tongling and other cities characterized by the remote location,single transportation mode or lower economic level are positioned at the edge of the network.3)Geographic proximity,varying levels of economic development,different industrial structures,degrees of urbanization,levels of technological innovation,energy intensities and environmental regulation are important influencing factors on the spatial association of within the YRD city cluster.Finally,policy implications are provided from four aspects:government macro-control and market mechanism guidance,structural characteristics of the‘core-edge’network,reconfiguration and optimization of the spatial layout of the YRD city cluster,and the application of advanced technologies.展开更多
The correspondence analysis will describe elemental association accompanying an indicator samples.This analysis indicates strong mineralization of Ag,As,Pb,Te,Mo,Au,Zn and to a lesser extent S,W,Cu at Glojeh polymetal...The correspondence analysis will describe elemental association accompanying an indicator samples.This analysis indicates strong mineralization of Ag,As,Pb,Te,Mo,Au,Zn and to a lesser extent S,W,Cu at Glojeh polymetallic mineralization,NW Iran.This work proposes a backward elimination approach(BEA)that quantitatively predicts the Au concentration from main effects(X),quadratic terms(X2)and the first order interaction(Xi×Xj)of Ag,Cu,Pb,and Zn by initialization,order reduction and validation of model.BEA is done based on the quadratic model(QM),and it was eliminated to reduced quadratic model(RQM)by removing insignificant predictors.During the QM optimization process,overall convergence trend of R2,R2(adj)and R2(pred)is obvious,corresponding to increase in the R2(pred)and decrease of R2.The RQM consisted of(threshold value,Cu,Ag×Cu,Pb×Zn,and Ag2-Pb2)and(Pb,Ag×Cu,Ag×Pb,Cu×Zn,Pb×Zn,and Ag2)as main predictors of optimized model according to288and679litho-samples in trenches and boreholes,respectively.Due to the strong genetic effects with Au mineralization,Pb,Ag2,and Ag×Pb are important predictors in boreholes RQM,while the threshold value is known as an important predictor in the trenches model.The RQMs R2(pred)equal74.90%and60.62%which are verified by R2equal to73.9%and60.9%in the trenches and boreholes validation group,respectively.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
This paper analyses the diversity and spatial pattern of the altitudinal belts in the Hengduan Mountains in China. A total of 7 types of base belts and 26 types of altitudinal belts are identified in the study region....This paper analyses the diversity and spatial pattern of the altitudinal belts in the Hengduan Mountains in China. A total of 7 types of base belts and 26 types of altitudinal belts are identified in the study region. The main altitudinal belt lines, such as forest line, the upper limit of dark coniferous forest and snow line, have similar latitudinal and longitudinal spatial patterns, namely, arched quadratic curve model with latitudes and concave quadratic curve model along longitudinal direction. These patterns can be together ealled as ＂Hyperbolic-paraboloid model＂, revealing the complexity and speciality of the environment and ecology in the study region. This result further validates the hypnosis of a common quadratic model for spatial pattern of mountain altitudinal belts proposed by the authors. The spatial pattern of altitudinal belts is closely related with moisture-related exposure effect in the Hengduan Mountains. Different combinations （spectra） of altitudinal belts and different base belt types appear in windward and leeward flanks and even in the same flanks of different ranges. This is closely related with the parallel mountain ranges of the Hengduan Mountains, which, at nearly right angle with the moving direction of prevailing moisture-laden air masses from west and east, hold up the warm and humid monsoon wind from moving into the core region and result in different moisture conditions in windward and leeward flanks. However, how to quantitatively describe the moisture-related exposure effect needs further study. In addition, the data quality and data accuracy at present also affect to some extent the result of quantitative modeling and should be improved with RS/GIS in the future.展开更多
Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimat...Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimate of the modeled function and thus also an estimate of the economic optimum, Nopt. Obtaining the accuracy of such estimates by confidence intervals for Nopt is subject to the model assumptions. The dependence of these assumptions is a further source of inaccuracy. The Nopt estimate also strongly depends on the N level design, i.e., the area on which the model is fitted. A small area around the supposed Nopt diminishes the dependence of the model assumptions, but prolongs the confidence interval. The investigations of the impact of the mentioned sources on the inaccuracy of the Nopt estimate rely on N rate trials on the experimental field Sieblerfeld (Bavaria). The models applied are the quadratic and the linear-plus-plateau yield regression model.展开更多
Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer exper...Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used. This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.展开更多
In feeder automation transformation there are difficulties in equipment and location selection.To help with this,an optimal layout model of feeder automation equipment oriented to the type of fault detection and local...In feeder automation transformation there are difficulties in equipment and location selection.To help with this,an optimal layout model of feeder automation equipment oriented to the type of fault detection and local action is pro-posed.It analyzes the coordination relationship of the three most common types of automation equipment,i.e.,fault indicator,over-current trip switch and non-voltage trip switch in the fault handling process,and the explicit expres-sions of power outage time caused by a fault on different layouts of the above three types of equipment are given.Given constraints of power supply reliability and the goal of minimizing the sum of equipment-related capital invest-ment and power interruption cost,a mixed-integer quadratic programming model for optimal layout is established,in which the functional failure probability of equipment is linearized using the 3δprinciple in statistics.Finally,the basic characteristics of the proposed model are illustrated by different scenarios on the IEEE RBTS-BUS6 system.It can not only take into account fault location and fault isolation to enhance user power consumption perception,but also can guide precise investment to improve the operational quality and efficiency of a power company.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
We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a(probably nonconvex)smooth function and a(probably nonsmooth)convex functi...We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a(probably nonconvex)smooth function and a(probably nonsmooth)convex function.The model function of our trust-region subproblem is always quadratic and the linear term of the model is generated using abstract descent directions.Therefore,the trust-region subproblems can be easily constructed as well as efficiently solved by cheap and standard methods.When the accuracy of the model function at the solution of the subproblem is not sufficient,we add a safeguard on the stepsizes for improving the accuracy.For a class of functions that can be“truncated”,an additional truncation step is defined and a stepsize modification strategy is designed.The overall scheme converges globally and we establish fast local convergence under suitable assumptions.In particular,using a connection with a smooth Riemannian trust-region method,we prove local quadratic convergence for partly smooth functions under a strict complementary condition.Preliminary numerical results on a family of Ei-optimization problems are reported and demonstrate the eficiency of our approach.展开更多
In order to solve the problems of road traffic congestion and the increasing parking time caused by the imbalance of parking lot supply and demand,this paper proposes an asymptotically optimal public parking lot locat...In order to solve the problems of road traffic congestion and the increasing parking time caused by the imbalance of parking lot supply and demand,this paper proposes an asymptotically optimal public parking lot location algorithm based on intuitive reasoning to optimize the parking lot location problem.Guided by the idea of intuitive reasoning,we use walking distance as indicator to measure the variability among location data and build a combinatorial optimization model aimed at guiding search decisions in the solution space of complex problems to find optimal solutions.First,Selective Attention Mechanism(SAM)is introduced to reduce the search space by adaptively focusing on the important information in the features.Then,Quantum Annealing(QA)algorithm with quantum tunneling effect is used to jump out of the local extremum in the search space with high probability and further approach the global optimal solution.Experiments on the parking lot location dataset in Luohu District,Shenzhen,show that the proposed method has improved the accuracy and running speed of the solution,and the asymptotic optimality of the algorithm and its effectiveness in solving the public parking lot location problem are verified.展开更多
基金This work was partially supported by the Doctoral Foundation of Hebei University(Grant No.Y2006084)the National Natural Science Foundation of China(Grant No.10231060)
文摘In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.
基金Under the auspices of the National Natural Science Foundation of China (No.72273151)。
文摘City cluster is an effective platform for encouraging regionally coordinated development.Coordinated reduction of carbon emissions within city cluster via the spatial association network between cities can help coordinate the regional carbon emission management,realize sustainable development,and assist China in achieving the carbon peaking and carbon neutrality goals.This paper applies the improved gravity model and social network analysis(SNA)to the study of spatial correlation of carbon emissions in city clusters and analyzes the structural characteristics of the spatial correlation network of carbon emissions in the Yangtze River Delta(YRD)city cluster in China and its influencing factors.The results demonstrate that:1)the spatial association of carbon emissions in the YRD city cluster exhibits a typical and complex multi-threaded network structure.The network association number and density show an upward trend,indicating closer spatial association between cities,but their values remain generally low.Meanwhile,the network hierarchy and network efficiency show a downward trend but remain high.2)The spatial association network of carbon emissions in the YRD city cluster shows an obvious‘core-edge’distribution pattern.The network is centered around Shanghai,Suzhou and Wuxi,all of which play the role of‘bridges’,while cities such as Zhoushan,Ma'anshan,Tongling and other cities characterized by the remote location,single transportation mode or lower economic level are positioned at the edge of the network.3)Geographic proximity,varying levels of economic development,different industrial structures,degrees of urbanization,levels of technological innovation,energy intensities and environmental regulation are important influencing factors on the spatial association of within the YRD city cluster.Finally,policy implications are provided from four aspects:government macro-control and market mechanism guidance,structural characteristics of the‘core-edge’network,reconfiguration and optimization of the spatial layout of the YRD city cluster,and the application of advanced technologies.
基金support of the IMIDRO(Iranian Mines and Mining Industries Development & Renovation Organization) for our research
文摘The correspondence analysis will describe elemental association accompanying an indicator samples.This analysis indicates strong mineralization of Ag,As,Pb,Te,Mo,Au,Zn and to a lesser extent S,W,Cu at Glojeh polymetallic mineralization,NW Iran.This work proposes a backward elimination approach(BEA)that quantitatively predicts the Au concentration from main effects(X),quadratic terms(X2)and the first order interaction(Xi×Xj)of Ag,Cu,Pb,and Zn by initialization,order reduction and validation of model.BEA is done based on the quadratic model(QM),and it was eliminated to reduced quadratic model(RQM)by removing insignificant predictors.During the QM optimization process,overall convergence trend of R2,R2(adj)and R2(pred)is obvious,corresponding to increase in the R2(pred)and decrease of R2.The RQM consisted of(threshold value,Cu,Ag×Cu,Pb×Zn,and Ag2-Pb2)and(Pb,Ag×Cu,Ag×Pb,Cu×Zn,Pb×Zn,and Ag2)as main predictors of optimized model according to288and679litho-samples in trenches and boreholes,respectively.Due to the strong genetic effects with Au mineralization,Pb,Ag2,and Ag×Pb are important predictors in boreholes RQM,while the threshold value is known as an important predictor in the trenches model.The RQMs R2(pred)equal74.90%and60.62%which are verified by R2equal to73.9%and60.9%in the trenches and boreholes validation group,respectively.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
基金supported by the National Natural Science foundation of China (40971064)the Innovatioin Program of Chinese Academy of Sciences (No. kzcx2-yw-308)IGSNRR Youth Innovation Project,and the LREIS Self-determined Project
文摘This paper analyses the diversity and spatial pattern of the altitudinal belts in the Hengduan Mountains in China. A total of 7 types of base belts and 26 types of altitudinal belts are identified in the study region. The main altitudinal belt lines, such as forest line, the upper limit of dark coniferous forest and snow line, have similar latitudinal and longitudinal spatial patterns, namely, arched quadratic curve model with latitudes and concave quadratic curve model along longitudinal direction. These patterns can be together ealled as ＂Hyperbolic-paraboloid model＂, revealing the complexity and speciality of the environment and ecology in the study region. This result further validates the hypnosis of a common quadratic model for spatial pattern of mountain altitudinal belts proposed by the authors. The spatial pattern of altitudinal belts is closely related with moisture-related exposure effect in the Hengduan Mountains. Different combinations （spectra） of altitudinal belts and different base belt types appear in windward and leeward flanks and even in the same flanks of different ranges. This is closely related with the parallel mountain ranges of the Hengduan Mountains, which, at nearly right angle with the moving direction of prevailing moisture-laden air masses from west and east, hold up the warm and humid monsoon wind from moving into the core region and result in different moisture conditions in windward and leeward flanks. However, how to quantitatively describe the moisture-related exposure effect needs further study. In addition, the data quality and data accuracy at present also affect to some extent the result of quantitative modeling and should be improved with RS/GIS in the future.
文摘Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimate of the modeled function and thus also an estimate of the economic optimum, Nopt. Obtaining the accuracy of such estimates by confidence intervals for Nopt is subject to the model assumptions. The dependence of these assumptions is a further source of inaccuracy. The Nopt estimate also strongly depends on the N level design, i.e., the area on which the model is fitted. A small area around the supposed Nopt diminishes the dependence of the model assumptions, but prolongs the confidence interval. The investigations of the impact of the mentioned sources on the inaccuracy of the Nopt estimate rely on N rate trials on the experimental field Sieblerfeld (Bavaria). The models applied are the quadratic and the linear-plus-plateau yield regression model.
基金Research supported by the National Natural Science Foundation of China (10301015)the Science and Technology Innovation Fund of Nankai University, the Visiting Scholar Program at Chern Institute of Mathematicsa Hong Kong Research Grants Council Grant (RGC/HKBU 200804)
文摘Supersaturated design is essentially a fractional factorial design in which the number of potential effects is greater than the number of runs. In this article, the supersaturated design is applied to a computer experiment through an example of steady current circuit model problem. A uniform mixed-level supersaturated design and the centered quadratic regression model are used. This example shows that supersaturated design and quadratic regression modeling method are very effective for screening effects and building the predictor. They are not only useful in computer experiments but also in industrial and other scientific experiments.
基金supported by the National Natural Science Foundation of China(Grant No.51777067).
文摘In feeder automation transformation there are difficulties in equipment and location selection.To help with this,an optimal layout model of feeder automation equipment oriented to the type of fault detection and local action is pro-posed.It analyzes the coordination relationship of the three most common types of automation equipment,i.e.,fault indicator,over-current trip switch and non-voltage trip switch in the fault handling process,and the explicit expres-sions of power outage time caused by a fault on different layouts of the above three types of equipment are given.Given constraints of power supply reliability and the goal of minimizing the sum of equipment-related capital invest-ment and power interruption cost,a mixed-integer quadratic programming model for optimal layout is established,in which the functional failure probability of equipment is linearized using the 3δprinciple in statistics.Finally,the basic characteristics of the proposed model are illustrated by different scenarios on the IEEE RBTS-BUS6 system.It can not only take into account fault location and fault isolation to enhance user power consumption perception,but also can guide precise investment to improve the operational quality and efficiency of a power company.
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partly supported by the Fundamental Research Fund-Shenzhen Research Institute for Big Data(SRIBD)Startup Fund JCYJ-AM20190601partly supported by the NSFC grant 11831002the Beijing Academy of Artificial Intelligence.
文摘We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a(probably nonconvex)smooth function and a(probably nonsmooth)convex function.The model function of our trust-region subproblem is always quadratic and the linear term of the model is generated using abstract descent directions.Therefore,the trust-region subproblems can be easily constructed as well as efficiently solved by cheap and standard methods.When the accuracy of the model function at the solution of the subproblem is not sufficient,we add a safeguard on the stepsizes for improving the accuracy.For a class of functions that can be“truncated”,an additional truncation step is defined and a stepsize modification strategy is designed.The overall scheme converges globally and we establish fast local convergence under suitable assumptions.In particular,using a connection with a smooth Riemannian trust-region method,we prove local quadratic convergence for partly smooth functions under a strict complementary condition.Preliminary numerical results on a family of Ei-optimization problems are reported and demonstrate the eficiency of our approach.
基金supported by the Special Zone Project of National Defense Innovation and the Science and Technology Program of Education Department of Jiangxi Province(No.GJJ171503).
文摘In order to solve the problems of road traffic congestion and the increasing parking time caused by the imbalance of parking lot supply and demand,this paper proposes an asymptotically optimal public parking lot location algorithm based on intuitive reasoning to optimize the parking lot location problem.Guided by the idea of intuitive reasoning,we use walking distance as indicator to measure the variability among location data and build a combinatorial optimization model aimed at guiding search decisions in the solution space of complex problems to find optimal solutions.First,Selective Attention Mechanism(SAM)is introduced to reduce the search space by adaptively focusing on the important information in the features.Then,Quantum Annealing(QA)algorithm with quantum tunneling effect is used to jump out of the local extremum in the search space with high probability and further approach the global optimal solution.Experiments on the parking lot location dataset in Luohu District,Shenzhen,show that the proposed method has improved the accuracy and running speed of the solution,and the asymptotic optimality of the algorithm and its effectiveness in solving the public parking lot location problem are verified.
