For geophysical inversion problems,deterministic inversion methods can easily fall into local optimal solutions,while stochastic optimization methods can theoretically converge to global optimal solutions.These proble...For geophysical inversion problems,deterministic inversion methods can easily fall into local optimal solutions,while stochastic optimization methods can theoretically converge to global optimal solutions.These problems have always been a concern for researchers.Among many stochastic optimization methods,particle swarm optimization(PSO)has been applied to solve geophysical inversion problems due to its simple principle and the fact that only a few parameters require adjustment.To overcome the nonuniqueness of inversion,model constraints can be added to PSO optimization.However,using fixed regularization parameters in PSO iteration is equivalent to keeping the default model constraint at a certain level,yielding an inversion result that is considerably affected by the model constraint.This study proposes a hybrid method that combines the regularized least squares method(RLSM)with the PSO method.The RLSM is used to improve the global optimal particle and accelerate convergence,while the adaptive regularization strategy is used to update the regularization parameters to avoid the influence of model constraints on the inversion results.Further,the inversion results of the RLSM and hybrid algorithm are compared and analyzed by considering the audio magnetotelluric synthesis and field data as examples.Experiments show that the proposed hybrid method is superior to the RLSM.Furthermore,compared with the standard PSO algorithm,the hybrid algorithm needs a broader model space but a smaller particle swarm and fewer iteration steps,thus reducing the prior conditions and the computational cost used in the inversion.展开更多
A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. T...A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.展开更多
An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;usi...An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.展开更多
集值折扣{0-1}背包问题(Discounted{0-1}Knapsack Problem with Setup,D{0-1}KPS)指在同一类别中可选择多个项,每个类别对目标函数和约束条件都增加了额外的固定设置成本。提出一种求解D{0-1}KPS的改进动态规划算法,算法针对D{0-1}KPS...集值折扣{0-1}背包问题(Discounted{0-1}Knapsack Problem with Setup,D{0-1}KPS)指在同一类别中可选择多个项,每个类别对目标函数和约束条件都增加了额外的固定设置成本。提出一种求解D{0-1}KPS的改进动态规划算法,算法针对D{0-1}KPS问题本身结构特征,融合多目标优化问题中非支配解集思想,通过利用状态之间的支配与非支配关系,对每个阶段的状态集进行剪枝,形成非支配状态集,从而提出改进动态规划算法。通过实例验证了该算法的有效性和可行性。展开更多
群智能启发式算法求解折扣{0-1}背包问题(D{0-1}KP)时,为提升求解效率和求解质量,需采用某种修复与优化策略将非正常编码个体转换为符合解约束条件的编码个体。在引入项集价值密度概念基础上,以粒子群算法(PSO)为例,提出一组基于项集的...群智能启发式算法求解折扣{0-1}背包问题(D{0-1}KP)时,为提升求解效率和求解质量,需采用某种修复与优化策略将非正常编码个体转换为符合解约束条件的编码个体。在引入项集价值密度概念基础上,以粒子群算法(PSO)为例,提出一组基于项集的贪婪修复与优化方法(group greedy repair and optimization algorithm,GGROA),并进一步构造PSO-GGRDKP算法(PSO based GGROA for solving D{0-1}KP)以探究GGROA方法的可行性和性能。PSO-NGROADKP(PSO based NGROA for solving D{0-1}KP)和PSO-GRDKP(PSO based GROA for solving D{0-1}KP)是基于项贪心修复与优化方法的粒子群算法。在D{0-1}KP标准数据集的实验结果表明:与PSO-NGROADKP和PSO-GRDKP相比,PSO-GGRDKP算法的解误差率略高,但算法时间性能分别提升了13.8%、12.9%。展开更多
One-dimensional retrieval was performed on Typhoon Haiyan utilizing the advanced technology microwave sounder onboard the satellite Suomi NPP to retrieve the temperature and water vapor profiles of the typhoon.Compari...One-dimensional retrieval was performed on Typhoon Haiyan utilizing the advanced technology microwave sounder onboard the satellite Suomi NPP to retrieve the temperature and water vapor profiles of the typhoon.Comparisons of the retrieved profiles and ECMWF reanalysis were made to assess the results. The main conclusions are as follows.(1) The results have high spatial resolution and therefore can precisely represent the temperature and humidity distribution of the typhoon.(2) The retrieved temperature is low in the areas of low temperature and high in the areas of high temperature; similar patterns are observed for humidity. This means that systematic revision may be needed during routine application.(3) The results of the retrieved temperature and humidity profiles are generally accurate, which is quite important for typhoon monitoring.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)[grant number 41374133]
文摘For geophysical inversion problems,deterministic inversion methods can easily fall into local optimal solutions,while stochastic optimization methods can theoretically converge to global optimal solutions.These problems have always been a concern for researchers.Among many stochastic optimization methods,particle swarm optimization(PSO)has been applied to solve geophysical inversion problems due to its simple principle and the fact that only a few parameters require adjustment.To overcome the nonuniqueness of inversion,model constraints can be added to PSO optimization.However,using fixed regularization parameters in PSO iteration is equivalent to keeping the default model constraint at a certain level,yielding an inversion result that is considerably affected by the model constraint.This study proposes a hybrid method that combines the regularized least squares method(RLSM)with the PSO method.The RLSM is used to improve the global optimal particle and accelerate convergence,while the adaptive regularization strategy is used to update the regularization parameters to avoid the influence of model constraints on the inversion results.Further,the inversion results of the RLSM and hybrid algorithm are compared and analyzed by considering the audio magnetotelluric synthesis and field data as examples.Experiments show that the proposed hybrid method is superior to the RLSM.Furthermore,compared with the standard PSO algorithm,the hybrid algorithm needs a broader model space but a smaller particle swarm and fewer iteration steps,thus reducing the prior conditions and the computational cost used in the inversion.
文摘A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.
文摘An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.
文摘集值折扣{0-1}背包问题(Discounted{0-1}Knapsack Problem with Setup,D{0-1}KPS)指在同一类别中可选择多个项,每个类别对目标函数和约束条件都增加了额外的固定设置成本。提出一种求解D{0-1}KPS的改进动态规划算法,算法针对D{0-1}KPS问题本身结构特征,融合多目标优化问题中非支配解集思想,通过利用状态之间的支配与非支配关系,对每个阶段的状态集进行剪枝,形成非支配状态集,从而提出改进动态规划算法。通过实例验证了该算法的有效性和可行性。
文摘群智能启发式算法求解折扣{0-1}背包问题(D{0-1}KP)时,为提升求解效率和求解质量,需采用某种修复与优化策略将非正常编码个体转换为符合解约束条件的编码个体。在引入项集价值密度概念基础上,以粒子群算法(PSO)为例,提出一组基于项集的贪婪修复与优化方法(group greedy repair and optimization algorithm,GGROA),并进一步构造PSO-GGRDKP算法(PSO based GGROA for solving D{0-1}KP)以探究GGROA方法的可行性和性能。PSO-NGROADKP(PSO based NGROA for solving D{0-1}KP)和PSO-GRDKP(PSO based GROA for solving D{0-1}KP)是基于项贪心修复与优化方法的粒子群算法。在D{0-1}KP标准数据集的实验结果表明:与PSO-NGROADKP和PSO-GRDKP相比,PSO-GGRDKP算法的解误差率略高,但算法时间性能分别提升了13.8%、12.9%。
基金National Natural Science Foundation of China(91215302,51278308)Open Project for State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry,Institute of Atmospheric Physics(LAPC)
文摘One-dimensional retrieval was performed on Typhoon Haiyan utilizing the advanced technology microwave sounder onboard the satellite Suomi NPP to retrieve the temperature and water vapor profiles of the typhoon.Comparisons of the retrieved profiles and ECMWF reanalysis were made to assess the results. The main conclusions are as follows.(1) The results have high spatial resolution and therefore can precisely represent the temperature and humidity distribution of the typhoon.(2) The retrieved temperature is low in the areas of low temperature and high in the areas of high temperature; similar patterns are observed for humidity. This means that systematic revision may be needed during routine application.(3) The results of the retrieved temperature and humidity profiles are generally accurate, which is quite important for typhoon monitoring.
