A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its referenc...A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its reference objectives were the best particle and the centroid of all particles except the best particle.The convergence theorems of linear time-varying discrete system proved that simplex-PSO is of consistent asymptotic convergence.In order to reduce the probability of trapping into a local optimal value,an extremum mutation was introduced into simplex-PSO and simplex-PSO-t(simplex-PSO with turbulence) was devised.Several experiments were carried out to verify the validity of simplex-PSO and simplex-PSO-t,and the experimental results confirmed the conclusions:(1) simplex-PSO-t can optimize high-dimension functions with 200-dimensionality;(2) compared PSO with chaos PSO(CPSO),the best optimum index increases by a factor of 1×102-1×104.展开更多
为了有效实现板件的抗振性动力学设计,研究约束阻尼板拓扑动力学优化方法。建立约束阻尼板有限元动力学分析模型,推导出模态损耗因子计算公式;建立了基于模态损耗因子最大化目标,以阻尼层单元相对密度为拓扑变量,以阻尼材料使用量及结...为了有效实现板件的抗振性动力学设计,研究约束阻尼板拓扑动力学优化方法。建立约束阻尼板有限元动力学分析模型,推导出模态损耗因子计算公式;建立了基于模态损耗因子最大化目标,以阻尼层单元相对密度为拓扑变量,以阻尼材料使用量及结构频率作为控制的阻尼板优化数学模型;利用序列凸规划理论而对传统优化准则法进行改进,采用改进准则法GCMOC(global extreme point converged by method of optimization criterion)解算优化模型以求取全域性优化解,推导出面向GCMOC的拓扑变量迭代式;考虑到多阶次RAMP(rational approxination of material properties)函数的形状具有较理想的可控下凹几何特征,提出在优化迭代中采用多阶次RAMP材料插值模型(MO-RAMP)对拓扑变量集合进行惩罚以实现其快速的0,1二值化,并尽量减少处于0.3~0.7的中间拓扑变量值出现;编制了面向约束阻尼板的拓扑动力学优化程序,实现了基于MO-RAMP的约束阻尼板GCMOC法变密度式减振拓扑动力学优化过程。算例分析表明,MO-RAMP与GCMOC复合的算法用于阻尼板拓扑迭代时,可将阻尼单元密度值快速地推向逼近0或1的值。它能得到清晰的阻尼单元优化密度云并有利于优化构型的实现;能在大幅减少阻尼材料用量条件下充分发挥其黏弹耗能效应,能在保证阻尼板动力学特性基本稳定的前提下使结构获得更好的减振效果。展开更多
Control constrained parabolic optimal control problems are generally challenging,from either theoretical analysis or algorithmic design perspectives.Conceptually,the well-known alternating direction method of multipli...Control constrained parabolic optimal control problems are generally challenging,from either theoretical analysis or algorithmic design perspectives.Conceptually,the well-known alternating direction method of multipliers(ADMM)can be directly applied to such problems.An attractive advantage of this direct ADMM application is that the control constraints can be untied from the parabolic optimal control problem and thus can be treated individually in the iterations.At each iteration of the ADMM,the main computation is for solving an unconstrained parabolic optimal control subproblem.Because of its inevitably high dimensionality after space-time discretization,the parabolicoptimal control subproblem at each iteration can be solved only inexactly by implementing certain numerical scheme internally and thus a two-layer nested iterative algorithm is required.It then becomes important to find an easily implementable and efficient inexactness criterion to perform the internal iterations,and to prove the overall convergence rigorously for the resulting two-layer nested iterative algorithm.To implement the ADMM efficiently,we propose an inexactness criterion that is independent of the mesh size of the involved discretization,and that can be performed automatically with no need to set empirically perceived constant accuracy a priori.The inexactness criterion turns out to allow us to solve the resulting parabolic optimal control subproblems to medium or even low accuracy and thus save computation significantly,yet convergence of the overall two-layer nested iterative algorithm can be still guaranteed rigorously.Efficiency of this ADMM implementation is promisingly validated by some numerical results.Our methodology can also be extended to a range of optimal control problems modeled by other linear PDEs such as elliptic equations,hyperbolic equations,convection-diffusion equations,and fractional parabolic equations.展开更多
In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex pr...In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex procedure with lexicographic scheme is proposed to deal with the degenerative case in the sense that the gradients of active constraints at the iteration point are dependent. Unlike other methods, the new algorithm possesses the following important property that, at any iteration point generated by the algorithm, one can choose a set of the most suitable basis and from it one can drop all constraints which can be relaxed, not only one constraint once. This property will be helpful in decreasing the computation amount of the algorithm. The global convergence and superlinear convergence of this algorithm are proved,without any assumption of linear independence of the gradients of active constraints.展开更多
基金Project(50275150) supported by the National Natural Science Foundation of ChinaProject(20070533131) supported by Research Fund for the Doctoral Program of Higher Education of China
文摘A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its reference objectives were the best particle and the centroid of all particles except the best particle.The convergence theorems of linear time-varying discrete system proved that simplex-PSO is of consistent asymptotic convergence.In order to reduce the probability of trapping into a local optimal value,an extremum mutation was introduced into simplex-PSO and simplex-PSO-t(simplex-PSO with turbulence) was devised.Several experiments were carried out to verify the validity of simplex-PSO and simplex-PSO-t,and the experimental results confirmed the conclusions:(1) simplex-PSO-t can optimize high-dimension functions with 200-dimensionality;(2) compared PSO with chaos PSO(CPSO),the best optimum index increases by a factor of 1×102-1×104.
文摘为了有效实现板件的抗振性动力学设计,研究约束阻尼板拓扑动力学优化方法。建立约束阻尼板有限元动力学分析模型,推导出模态损耗因子计算公式;建立了基于模态损耗因子最大化目标,以阻尼层单元相对密度为拓扑变量,以阻尼材料使用量及结构频率作为控制的阻尼板优化数学模型;利用序列凸规划理论而对传统优化准则法进行改进,采用改进准则法GCMOC(global extreme point converged by method of optimization criterion)解算优化模型以求取全域性优化解,推导出面向GCMOC的拓扑变量迭代式;考虑到多阶次RAMP(rational approxination of material properties)函数的形状具有较理想的可控下凹几何特征,提出在优化迭代中采用多阶次RAMP材料插值模型(MO-RAMP)对拓扑变量集合进行惩罚以实现其快速的0,1二值化,并尽量减少处于0.3~0.7的中间拓扑变量值出现;编制了面向约束阻尼板的拓扑动力学优化程序,实现了基于MO-RAMP的约束阻尼板GCMOC法变密度式减振拓扑动力学优化过程。算例分析表明,MO-RAMP与GCMOC复合的算法用于阻尼板拓扑迭代时,可将阻尼单元密度值快速地推向逼近0或1的值。它能得到清晰的阻尼单元优化密度云并有利于优化构型的实现;能在大幅减少阻尼材料用量条件下充分发挥其黏弹耗能效应,能在保证阻尼板动力学特性基本稳定的前提下使结构获得更好的减振效果。
基金supported by the seed fund for basic research at The University of Hong Kong(project No.201807159005)a General Research Fund from Hong Kong Research Grants Council。
文摘Control constrained parabolic optimal control problems are generally challenging,from either theoretical analysis or algorithmic design perspectives.Conceptually,the well-known alternating direction method of multipliers(ADMM)can be directly applied to such problems.An attractive advantage of this direct ADMM application is that the control constraints can be untied from the parabolic optimal control problem and thus can be treated individually in the iterations.At each iteration of the ADMM,the main computation is for solving an unconstrained parabolic optimal control subproblem.Because of its inevitably high dimensionality after space-time discretization,the parabolicoptimal control subproblem at each iteration can be solved only inexactly by implementing certain numerical scheme internally and thus a two-layer nested iterative algorithm is required.It then becomes important to find an easily implementable and efficient inexactness criterion to perform the internal iterations,and to prove the overall convergence rigorously for the resulting two-layer nested iterative algorithm.To implement the ADMM efficiently,we propose an inexactness criterion that is independent of the mesh size of the involved discretization,and that can be performed automatically with no need to set empirically perceived constant accuracy a priori.The inexactness criterion turns out to allow us to solve the resulting parabolic optimal control subproblems to medium or even low accuracy and thus save computation significantly,yet convergence of the overall two-layer nested iterative algorithm can be still guaranteed rigorously.Efficiency of this ADMM implementation is promisingly validated by some numerical results.Our methodology can also be extended to a range of optimal control problems modeled by other linear PDEs such as elliptic equations,hyperbolic equations,convection-diffusion equations,and fractional parabolic equations.
文摘In this paper, the problem of minimizing a convex function subject to general linear constraints is considered. An algorithm which is an extension of the method described in [4] is presented. And a new dual simplex procedure with lexicographic scheme is proposed to deal with the degenerative case in the sense that the gradients of active constraints at the iteration point are dependent. Unlike other methods, the new algorithm possesses the following important property that, at any iteration point generated by the algorithm, one can choose a set of the most suitable basis and from it one can drop all constraints which can be relaxed, not only one constraint once. This property will be helpful in decreasing the computation amount of the algorithm. The global convergence and superlinear convergence of this algorithm are proved,without any assumption of linear independence of the gradients of active constraints.
