This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one c...This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.展开更多
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the ent...In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.展开更多
Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constra...Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constraint and minimum mass was established based on the finite element method through these parameters.Then,the sequential quadratic programming algorithm was employed to search the optimal solutions.Several groups of value for initial design variables were chosen,for the purpose of not only finding much more local optimal results but also analyzing which discipline that the variables according to could be benefit for the convergence and robustness.Response surface method and Monte Carlo simulations were used to analyze whether the objective function and constraint function are sensitive to the variation of variables or not.Then the robust results could be found among a group of different local optimal solutions.展开更多
By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the o...By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.展开更多
Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then consi...Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed.展开更多
In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the p...In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position.Grey Wolf Optimization-based Linear Quadratic Regulator(GWO-LQR)and GWO-based Fuzzy LQR(FLQR)control algorithms are used in the control process.To improve the performance of the LQR and FLQR methods,the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm.Both a graphic and a numerical analysis of the outcomes are provided.In the comparative analysis,it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm.Furthermore,this approach outperformed comparable research in the literature with a settling time of 2.4 s.These findings demonstrate that the suggested GWO-based FLQR controlmethod outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.展开更多
The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off betwee...The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.展开更多
Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equa...Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.展开更多
Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, anothe...Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.展开更多
With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the m...With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.展开更多
In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD）...In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.展开更多
Complex quadratically constrained quadratic programs(QCQPs)with underlying acyclic graph structures have special interests in some important practical applications.In this paper,we propose a new second-order cone rela...Complex quadratically constrained quadratic programs(QCQPs)with underlying acyclic graph structures have special interests in some important practical applications.In this paper,we propose a new second-order cone relaxation for complex QCQPs,and prove some sufficient conditions under which the proposed relaxation is tight.Then,based on the proposed second-order cone relaxation,a branch-and-bound algorithm is developed.The main feature of the proposed branch-and-bound algorithm is that some complex variables are selected with their bounds on modules or phase angles partitioned in the branching procedure.Numerical results indicate that the proposed branch-and-bound algorithm runs faster than Baron on randomly generated test instances,and is also effective in solving some publicly available test instances of optimal power flow problems.展开更多
为提高月径流时间序列预测精度,改进最小二乘孪生支持向量回归机(Least Squares Twin Support Vector Regression,LSTSVR)性能,首次基于高斯核函数、多项式核函数、线性核函数构建混合核函数,提出4种季节趋势分解(Seasonal and Trend de...为提高月径流时间序列预测精度,改进最小二乘孪生支持向量回归机(Least Squares Twin Support Vector Regression,LSTSVR)性能,首次基于高斯核函数、多项式核函数、线性核函数构建混合核函数,提出4种季节趋势分解(Seasonal and Trend decomposition using Loess,STL)-小波包变换(Wavelet Packet Transform,WPT)-裂狐优化(Rüppell's Fox Optimizer,RFO)算法-混合核最小二乘孪生支持向量回归机(Hybrid Kernel Least Squares Twin Support Vector Regression,HLSTSVR)模型,并构建STL-WPT-RFO-LSTSVR、STL-WPT-RFO-混合核最小二乘支持向量回归机(Hybrid Kerllel Least Squares Twin Suppart Vector Regression,HLSSVR)、STL-WPT-RFO-最小二乘支持向量回归机(Least Squares Support Vector Regression,LSSVR)等17种对比分析模型,通过云南省高桥、凤屯水文站月径流时间序列预测实例对21种模型进行验证。首先利用STL-WPT二次分解技术对月径流序列进行分解处理,合理划分训练集和验证集;然后基于高斯核函数、多项式核函数、线性核函数,采用“三三”线性组合和“两两”线性组合的方式构建4种混合核函数对月径流分解分量进行空间映射;最后利用RFO寻优HLSTSVR/LSTSVR/HLSSVR/LSSVR最佳超参数,利用最佳超参数建立21种模型对实例月径流序列各分解分量进行训练、预测和重构。结果表明:①4种STL-WPT-RFO-HLSTSVR模型能适应不同尺度的月径流数据分布,具有较好的模型性能和较小的预测误差,其中STL-WPT-RFO-HLSTSVR(高斯+多项式+线性)模型对高桥、凤屯站月径流预测的平均绝对百分比误差MAPE分别为2.85%、2.19%,决定系数R2均为0.9994,预测精度最高、效果最好;②混合核函数兼顾了不同核函数优势,能在模型复杂度与泛化能力之间取得平衡,显著提升模型性能和预测精度;③STL-WPT二次分解技术能有效解决复杂时间序列的非平稳性、非线性和多尺度特征,较STL更具分解优势;④组合模型融合了STL-WPT、RFO和HLSTSVR优点,具有较好的普适性和参考价值。展开更多
A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems a...A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.展开更多
The conventional linear quadratic regulator(LQR) control algorithm is one of the most popular active control algorithms.One important issue for LQR control algorithm is the reduction of structure's degrees of free...The conventional linear quadratic regulator(LQR) control algorithm is one of the most popular active control algorithms.One important issue for LQR control algorithm is the reduction of structure's degrees of freedom(DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element(FE) model for structure. In proposed model, the Craig-Bampton(C-B) method, which is one of the component mode syntheses(CMS), is used to establish superelement modeling to reduce structure's DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.展开更多
A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle ...A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.展开更多
基金Project supported by the National Science Foundation of China (60574071) the Foundation for University Key Teacher by the Ministry of Education.
文摘This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O（√nL） iteration complexity which is the best result for convex quadratic programming so far.
基金supported by the National Natural Science Foundation of China (60873099)
文摘A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金Supported by the National Natural Science Foundation of China(71471102)
文摘In this paper, we propose an arc-search interior-point algorithm for convex quadratic programming with a wide neighborhood of the central path, which searches the optimizers along the ellipses that approximate the entire central path. The favorable polynomial complexity bound of the algorithm is obtained, namely O（nlog（（ x^0）~TS^0/ε）） which is as good as the linear programming analogue. Finally, the numerical experiments show that the proposed algorithm is efficient.
文摘Several structural design parameters for the description of the geometric features of a hollow fan blade were determined.A structural design optimization model of a hollow fan blade which based on the strength constraint and minimum mass was established based on the finite element method through these parameters.Then,the sequential quadratic programming algorithm was employed to search the optimal solutions.Several groups of value for initial design variables were chosen,for the purpose of not only finding much more local optimal results but also analyzing which discipline that the variables according to could be benefit for the convergence and robustness.Response surface method and Monte Carlo simulations were used to analyze whether the objective function and constraint function are sensitive to the variation of variables or not.Then the robust results could be found among a group of different local optimal solutions.
基金Supported by the National Natural Science Foundation of China (70371032,60574071)
文摘By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.
文摘Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed.
文摘In this study,a dynamic model for an inverted pendulum system(IPS)attached to a car is created,and two different control methods are applied to control the system.The designed control algorithms aim to stabilize the pendulum arms in the upright position and the car to reach the equilibrium position.Grey Wolf Optimization-based Linear Quadratic Regulator(GWO-LQR)and GWO-based Fuzzy LQR(FLQR)control algorithms are used in the control process.To improve the performance of the LQR and FLQR methods,the optimum values of the coefficients corresponding to the foot points of the membership functions are determined by the GWO algorithm.Both a graphic and a numerical analysis of the outcomes are provided.In the comparative analysis,it is observed that the GWO-based FLQR method reduces the settling time by 22.58% and the maximum peak value by 18.2% when evaluated in terms of the angular response of the pendulum arm.Furthermore,this approach outperformed comparable research in the literature with a settling time of 2.4 s.These findings demonstrate that the suggested GWO-based FLQR controlmethod outperforms existing literature in terms of the time required for the pendulum arm to reach equilibrium.
文摘The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interiorpoint method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.
文摘Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.
文摘Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.
基金Supported by Science and Technology Foundation of China University of Mining & Technology
文摘With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.
文摘In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
基金supported by the National Natural Science Foundation of China(No.12171151)supported by the National Natural Science Foundation of China(No.T2293774)+1 种基金Fundamental Research Funds for the Central University(No.E2ET0808X2)a grant from MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS.
文摘Complex quadratically constrained quadratic programs(QCQPs)with underlying acyclic graph structures have special interests in some important practical applications.In this paper,we propose a new second-order cone relaxation for complex QCQPs,and prove some sufficient conditions under which the proposed relaxation is tight.Then,based on the proposed second-order cone relaxation,a branch-and-bound algorithm is developed.The main feature of the proposed branch-and-bound algorithm is that some complex variables are selected with their bounds on modules or phase angles partitioned in the branching procedure.Numerical results indicate that the proposed branch-and-bound algorithm runs faster than Baron on randomly generated test instances,and is also effective in solving some publicly available test instances of optimal power flow problems.
文摘为提高月径流时间序列预测精度,改进最小二乘孪生支持向量回归机(Least Squares Twin Support Vector Regression,LSTSVR)性能,首次基于高斯核函数、多项式核函数、线性核函数构建混合核函数,提出4种季节趋势分解(Seasonal and Trend decomposition using Loess,STL)-小波包变换(Wavelet Packet Transform,WPT)-裂狐优化(Rüppell's Fox Optimizer,RFO)算法-混合核最小二乘孪生支持向量回归机(Hybrid Kernel Least Squares Twin Support Vector Regression,HLSTSVR)模型,并构建STL-WPT-RFO-LSTSVR、STL-WPT-RFO-混合核最小二乘支持向量回归机(Hybrid Kerllel Least Squares Twin Suppart Vector Regression,HLSSVR)、STL-WPT-RFO-最小二乘支持向量回归机(Least Squares Support Vector Regression,LSSVR)等17种对比分析模型,通过云南省高桥、凤屯水文站月径流时间序列预测实例对21种模型进行验证。首先利用STL-WPT二次分解技术对月径流序列进行分解处理,合理划分训练集和验证集;然后基于高斯核函数、多项式核函数、线性核函数,采用“三三”线性组合和“两两”线性组合的方式构建4种混合核函数对月径流分解分量进行空间映射;最后利用RFO寻优HLSTSVR/LSTSVR/HLSSVR/LSSVR最佳超参数,利用最佳超参数建立21种模型对实例月径流序列各分解分量进行训练、预测和重构。结果表明:①4种STL-WPT-RFO-HLSTSVR模型能适应不同尺度的月径流数据分布,具有较好的模型性能和较小的预测误差,其中STL-WPT-RFO-HLSTSVR(高斯+多项式+线性)模型对高桥、凤屯站月径流预测的平均绝对百分比误差MAPE分别为2.85%、2.19%,决定系数R2均为0.9994,预测精度最高、效果最好;②混合核函数兼顾了不同核函数优势,能在模型复杂度与泛化能力之间取得平衡,显著提升模型性能和预测精度;③STL-WPT二次分解技术能有效解决复杂时间序列的非平稳性、非线性和多尺度特征,较STL更具分解优势;④组合模型融合了STL-WPT、RFO和HLSTSVR优点,具有较好的普适性和参考价值。
文摘A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.
基金Project(LZ2015022)supported by Educational Commission of Liaoning Province of ChinaProjects(51138001,51178081)supported by the National Natural Science Foundation of China+1 种基金Project(2013CB035905)supported by the Basic Research Program of ChinaProjects(DUT15LK34,DUT14QY10)supported by Fundamental Research Funds for the Central Universities,China
文摘The conventional linear quadratic regulator(LQR) control algorithm is one of the most popular active control algorithms.One important issue for LQR control algorithm is the reduction of structure's degrees of freedom(DOF). In this work, an LQR control algorithm with superelement model is intended to solve this issue leading to the fact that LQR control algorithm can be used in large finite element(FE) model for structure. In proposed model, the Craig-Bampton(C-B) method, which is one of the component mode syntheses(CMS), is used to establish superelement modeling to reduce structure's DOF and applied to LQR control algorithm to calculate Kalman gain matrix and obtain control forces. And then, the control forces are applied to original structure to simulate the responses of structure by vibration control. And some examples are given. The results show the computational efficiency of proposed model using synthesized models is higher than that of the classical method of LQR control when the DOF of structure is large. And the accuracy of proposed model is well. Meanwhile, the results show that the proposed control has more effects of vibration absorption on the ground structures than underground structures.
文摘A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.
