线性规划优化分析的元模型方法及其比较

线性规划优化分析在经济管理等领域有着广泛的应用。当线性规划约束条件的右端向量在一定范围内变化时,目标函数的最优值是右端向量的一个复杂的分片线性函数,但通常难以给出分析表达式。应用多项式回归、径向基函数、Kriging法及多项式回归 Kriging法这四种元模型方法,能快速预测最优值函数。通过仿真实验,对这四种形式的元模型作较全面的比较分析。数值实验的结果表明,用次数较少的实验设计,后三种方法都具有较高的拟合精度;特别地,多项式回归 Kriging法不仅拟合精度高,而且还能用一个二阶多项式给出最优值函数的一个简明的近似描述。结果表明,元模型方法是研究线性规划优化分析问题的有效途径。     

基于地统计方法的滑坡因子敏感度分析

滑坡的发生及演化都与各种滑坡因子之间存在着一定的关联。通过滑坡因子数据探测及其与滑坡相关关系分析，结合地统计方法可确定滑坡因子的敏感度排序，从而确定因子对滑坡发生确定性的影响程度，为武警部队执勤过程中的科学调度提供重要依据。     

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO: A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging (A-Kriging) into an improved partial swarm optimization algorithm (IPSO) to give a so-called A-Kriging-IPSO for maxi-mizing the buckling load of laminated composite plates (LCPs) under uniaxial and biaxial compressions. In this method, a novel iterative adaptive Kriging model, which is structured using two training sample sets as active and adaptive points, is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process. The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples. The cell-based smoothed discrete shear gap method (CS-DSG3) is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets. The buckling load of the LCPs is maximized by utilizing the IPSO algorithm. To demonstrate the efficiency and accuracy of the proposed methodology, the LCPs with different layers (2, 3, 4, and 10 layers), boundary conditions, aspect ratios and load patterns (biaxial and uniaxial loads) are investigated. The results obtained by proposed method are in good agreement with the literature results, but with less computational burden. By applying adaptive radial Kriging model, the accurate optimal results-based predictions of the buckling load are obtained for the studied LCPs.     

On gamma estimation via matrix kriging

In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.